Re: [EM] Upper-Bucklin naming (was: Median systems, branding....)

[Andy Jennings]

On Fri, Jun 14, 2013 at 5:52 PM, Jameson Quinn wrote:

> So I think we should have a poll with various options (using the system
> itself to rate the options, of course). I'll start out with some proposals
> and my votes:
>
> -IRAV: B
> -Descending Approval Threshold (DAT) Voting: A
> -Descending Approval Threshold Adjudgment (DATA voting): B
> -Majority Approval Threshold (MAT; note that the M could also be
> backronymmed to "Median"): A
> -Bucklin: F (not that we shouldn't say that this system is a Bucklin
> system, just that that shouldn't be our only name for it)
> -Bucklin-ER or ER-Bucklin: D (has already been used for other systems, not
> a descriptive name)
> -Graded Approval Threshold (GAT): C (Not bad, but not great)
> -Majority Assignment of Grades (MAG): C (ditto)
> -Graded Majority Approval (GMA): B (this one seems simple and descriptive)
>


Okay, I've bounced my head against the names a few times.  Are we talking
about the name for us to use or a name for public branding?  I don't think
the former matters too much, so I'm thinking about the latter.

-IRAV: C
-Descending Approval Threshold (DAT) Voting: C
-Descending Approval Threshold Adjudgment (DATA voting): F
-Majority Approval Threshold (MAT; note that the M could also be
backronymmed to "Median"): B
-Bucklin: F
-Bucklin-ER or ER-Bucklin: F
-Graded Approval Threshold (GAT): D
-Majority Assignment of Grades (MAG): F
-Graded Majority Approval (GMA): D

Frankly, I'm not getting used to any of them.  I've imagined myself
introducing the system to people, even smart people, and I don't think we
get three words.  I think we only get two ("voting" at the end doesn't
count).  I only gave a B to MAT because I think "threshold" at the end
would fall off.  Here are some more suggestions:

-Majority Approval Voting: A
-Delayed Approval Voting: C
-Approval Level Voting: B
-Delayed Support Voting: C
-Majority Support Voting: A
-Support Level Voting: B (only if all the grade labels use the word
"support")
-Gradual Support Voting: D
-Gradual Approval Voting: D

Perhaps we could call it "Majority Approval Threshold" for a while and
then, if we still really like it, we can drop the "threshold".

In addition to my friend's concerns with the word "majority" that I
mentioned earlier, I have another one:  I think percentiles other than the
50th will be appropriate.  Obviously, it's the only thing that's
appropriate for political elections, but it's pretty blatant about ignoring
half the electorate.  In friendlier situations (choosing a restaurant or
something), I would want the outcome that gets to 75% approval first.  Or
90%.  Yet I still gave the best grades to labels with the word "majority"
in them, so I think I'm admitting that there's nothing we can do about
this.  If we call it "majority approval", then in situations where you're
going for 75 percent you would call it "75th-percentile approval" or
something like that.

~ Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] Upper-Bucklin naming (was: Median systems, branding....)

[Andy Jennings]

I also report that I was talking with a progressive activist (and former
legislator) here in Arizona last year who didn't like branding of the word
"majority".  He was afraid it would be a turn-off to those who feel like
the wrong majority is already too dominant.

~ Andy


On Sat, Jun 15, 2013 at 3:38 PM, Andy Jennings
wrote:

> It does sound like this system will have better resistance to the Chicken
> Dilemma.  I can support it, assuming noone finds any fatal flaws.
>
> I've thought about the top-down vs. bottom-up question and the naming for
> a while and can't form a strong opinion.  Let me think about it some more.
>
> I heard that a big reason FairVote has been moving to the "ranked choice"
> branding is that it fits better with their long-term strategy, STV.
>
> ~ Andy
>
>
>
> On Fri, Jun 14, 2013 at 5:52 PM, Jameson Quinn wrote:
>
>> So. Abd and I now agree that a Bucklin system which uses just the
>> above-median votes to break ties is probably the best first step towards
>> median voting. I'd like to get the details worked out, so we can stop using
>> different terms ("Bucklin", "MJ", "GMJ") and settle on a single
>> clearly-defined proposal. I'd love to hear what others feel about these
>> issues (though this isn't really the place for debating whether some other
>> class of voting system, such as Score or Condorcet or whatever, is better
>> or worse than Bucklin/Median systems in general).
>>
>> 1. How to best express the system? Two equivalent definitions:
>>
>>- *Top-down*: "Count the votes at the highest grade for each
>>candidate. If any one candidate has a majority, they win. If not, add in
>>lower grades, one at a time, until some candidate or candidates get a
>>majority. If two candidates would reach a majority at the same grade 
>> level,
>>then whichever has the most votes above that level wins. If there are no
>>votes above that level, the highest votes at or above that level wins."
>>- *Bottom-up*: "Count the votes at the lowest grade against each
>>candidate. If any candidates have a majority against, eliminate them from
>>consideration. Continue adding in the next-lowest grade, until there is
>>just one or zero candidates left. If there's one left, they win. 
>> Otherwise,
>>if the last few candidates are eliminated together, choose whichever of
>>that group was eliminated by the smallest majority against."
>>
>>
>> 2. How many rating/grade/rank levels should be used, and how should they
>> be labeled? I'd suggest the following 5, along the lines of something Abd
>> proposed:
>>
>> A: Unequivocal support
>> B: Probable support (unless there's a candidate with majority "A" support)
>> C: Neutral (support or oppose, depending on other candidates' results)
>> D: Probable opposition (unless all other candidates have majority "F"
>> opposition)
>> F: Unequivocal opposition
>>
>> (I've relabeled the categories to help clarify their strategic meaning;
>> for instance, I changed "strong" to "unequivocal")
>>
>> I would also be open to having blank votes count as "E" rather than "F",
>> but I think that's probably an unnecessary complication to begin with.
>>
>> 3. What should we call this system? Abd seemed happy with "Instant Runoff
>> Approval Voting". I'd be fine with that too, but before we settle on that,
>> we should look at the downsides:
>>
>>- FairVote has been moving away from "Instant Runoff / IRV" and
>>towards "ranked choice/ RCV" in recent years. I don't know all of their
>>reasons, but I suspect it is partially to do with the legalism of ballot
>>initiative language. That is, IRV is technically neither instant nor a
>>runoff, though it is certainly close on both counts.
>>- It could lead to confusion between IRAV and IRV. That has its
>>upsides — piggybacking on FairVote's existing publicity — but also its
>>downsides — as we know, IRV is actually a pretty flawed system.
>>
>> So I think we should have a poll with various options (using the system
>> itself to rate the options, of course). I'll start out with some proposals
>> and my votes:
>>
>> -IRAV: B
>> -Descending Approval Threshold (DAT) Voting: A
>> -Descending Approval Threshold Adjudgment (DATA voting): B
>> -Majority Approval Threshold (MAT; note that the M could also 

Re: [EM] Upper-Bucklin naming (was: Median systems, branding....)

[Andy Jennings]

It does sound like this system will have better resistance to the Chicken
Dilemma.  I can support it, assuming noone finds any fatal flaws.

I've thought about the top-down vs. bottom-up question and the naming for a
while and can't form a strong opinion.  Let me think about it some more.

I heard that a big reason FairVote has been moving to the "ranked choice"
branding is that it fits better with their long-term strategy, STV.

~ Andy



On Fri, Jun 14, 2013 at 5:52 PM, Jameson Quinn wrote:

> So. Abd and I now agree that a Bucklin system which uses just the
> above-median votes to break ties is probably the best first step towards
> median voting. I'd like to get the details worked out, so we can stop using
> different terms ("Bucklin", "MJ", "GMJ") and settle on a single
> clearly-defined proposal. I'd love to hear what others feel about these
> issues (though this isn't really the place for debating whether some other
> class of voting system, such as Score or Condorcet or whatever, is better
> or worse than Bucklin/Median systems in general).
>
> 1. How to best express the system? Two equivalent definitions:
>
>- *Top-down*: "Count the votes at the highest grade for each
>candidate. If any one candidate has a majority, they win. If not, add in
>lower grades, one at a time, until some candidate or candidates get a
>majority. If two candidates would reach a majority at the same grade level,
>then whichever has the most votes above that level wins. If there are no
>votes above that level, the highest votes at or above that level wins."
>- *Bottom-up*: "Count the votes at the lowest grade against each
>candidate. If any candidates have a majority against, eliminate them from
>consideration. Continue adding in the next-lowest grade, until there is
>just one or zero candidates left. If there's one left, they win. Otherwise,
>if the last few candidates are eliminated together, choose whichever of
>that group was eliminated by the smallest majority against."
>
>
> 2. How many rating/grade/rank levels should be used, and how should they
> be labeled? I'd suggest the following 5, along the lines of something Abd
> proposed:
>
> A: Unequivocal support
> B: Probable support (unless there's a candidate with majority "A" support)
> C: Neutral (support or oppose, depending on other candidates' results)
> D: Probable opposition (unless all other candidates have majority "F"
> opposition)
> F: Unequivocal opposition
>
> (I've relabeled the categories to help clarify their strategic meaning;
> for instance, I changed "strong" to "unequivocal")
>
> I would also be open to having blank votes count as "E" rather than "F",
> but I think that's probably an unnecessary complication to begin with.
>
> 3. What should we call this system? Abd seemed happy with "Instant Runoff
> Approval Voting". I'd be fine with that too, but before we settle on that,
> we should look at the downsides:
>
>- FairVote has been moving away from "Instant Runoff / IRV" and
>towards "ranked choice/ RCV" in recent years. I don't know all of their
>reasons, but I suspect it is partially to do with the legalism of ballot
>initiative language. That is, IRV is technically neither instant nor a
>runoff, though it is certainly close on both counts.
>- It could lead to confusion between IRAV and IRV. That has its
>upsides — piggybacking on FairVote's existing publicity — but also its
>downsides — as we know, IRV is actually a pretty flawed system.
>
> So I think we should have a poll with various options (using the system
> itself to rate the options, of course). I'll start out with some proposals
> and my votes:
>
> -IRAV: B
> -Descending Approval Threshold (DAT) Voting: A
> -Descending Approval Threshold Adjudgment (DATA voting): B
> -Majority Approval Threshold (MAT; note that the M could also be
> backronymmed to "Median"): A
> -Bucklin: F (not that we shouldn't say that this system is a Bucklin
> system, just that that shouldn't be our only name for it)
> -Bucklin-ER or ER-Bucklin: D (has already been used for other systems, not
> a descriptive name)
> -Graded Approval Threshold (GAT): C (Not bad, but not great)
> -Majority Assignment of Grades (MAG): C (ditto)
> -Graded Majority Approval (GMA): B (this one seems simple and descriptive)
>
> Note that all of the above names could, in principle, apply to almost any
> Bucklin system; but whichever one we pick, we'll arbitrarily define it as
> being this system in particular.
>
> Abd and anyone else who has an opinion: please vote among the above
> options.
>
> Jameson
>
>
> 2013/6/13 Abd ul-Rahman Lomax 
>
>> At 03:53 PM 6/13/2013, you wrote:
>>
>>> I just had a minor realization. As I said to Abd, his Bucklin-ER (as I
>>> understand it) has slightly less resistance to the chicken dilemma than
>>> GMJ, because the Bucklin-ER tiebreaker effectively ends up focusing
>>> slightly below the median in the grade distribution, while 

Re: [EM] Consensus Threshold Approval

[Andy Jennings]

>
> As Jameson notes, CTA is the same as the chiastic median, but applied to
> the thresholds instead of the scores.  However, the thresholds are 100
> minus the scores, so it definitely changes the meaning of things.


I should correct myself.  CTA is not exactly the same as the chiastic
median of the thresholds.  CTA calculates the largest number, x, between 0
and 100 such that x percent of people gave a threshold of x or below.
 Chiastic median applied to the thresholds would calculate the largest
number, x, between 0 and 100 such that x percent of people gave a threshold
of x or above.

But the three concerns I mentioned are still valid.

~ Andy


On Mon, Apr 8, 2013 at 10:12 AM, Andy Jennings
wrote:

> Forest,
>
> This is an interesting method.  It gives another good objective meaning
> for numerical scores on a 0-100 scale.
>
> The consensus threshold would be very useful in situations where
> compromise is paramount.  For instance, I can pledge to support a new
> taxation scheme only if 90% of the citizens support it.  (This is even more
> important in situations where participation is voluntary, such as
> donations.)  If 90% of the people say the same thing, it is probably a
> pretty good compromise.
>
> On the other hand, I see some situations where it could be problematic.
>  If 90% of people give a candidate a score of 11 and the other 10% of
> people give a score of 0, that candidate will have a consensus threshold
> approval of 90%.  I can imagine those voters being surprised that such a
> large coalition was built from people who liked the candidate so little.
>
> As Jameson notes, CTA is the same as the chiastic median, but applied to
> the thresholds instead of the scores.  However, the thresholds are 100
> minus the scores, so it definitely changes the meaning of things.  The CTA
> value probably has more natural real world meaning than the chiastic
> median, but it brings the following concerns:
>
> 1. In terms of the visual representation, I consider the area to be the
> best measure of support if everyone is honest.  Approval, median, and
> chiastic approval, as you describe below, all measure something related to
> the area under the curve.  Examining the other diagonal, like CTA, doesn't
> seem to measure anything related to the area.  So it might not be a good
> indicator of the total level of support.
>
> 2. CTA does not meet the unanimity criterion for aggregation functions,
> which says that if all voters give the same score, then the societal score
> should match.  Approval doesn't either, but median, score, and chiastic
> approval do.
>
> 3. CTA also can be extremely sensitive to one voter's input.  One voter,
> by lowering his score (raising his threshold) by one point, can scuttle the
> whole coalition and cause the societal score to go from 100 to 0.
>
> ~ Andy
>
>
>
> On Thu, Apr 4, 2013 at 4:44 PM, Forest Simmons  wrote:
>
>> For purposes of clarification, I would like to show how Approval,
>> Bucklin, Range, Chiastic Approval, and Consensus Threshold Approval
>> manifest themselves relative to each other visually.
>>
>>
>>
>> I assume versions of these methods that make use of range style ballots
>> on a scale of zero to 100.  These methods also have in common that once
>> the ballots are counted each candidate ends up with a score of some kind,
>> and the candidate with the largest score is elected.
>>
>>
>>
>> So let’s concentrate on how each of these methods would assign a score to
>> the same fixed candidate.
>>
>>
>>
>> All of these methods can be explained in terms of the graph of the
>> function F given by
>>
>>
>>
>> p=F(r) is the percentage of the ballots that rate our candidate strictly
>> greater than r.
>>
>>
>>
>> Each point (r, p) of this graph will lie somewhere in the 100 by 100
>> square with corners at (0,0), (0,100), (100, 0) and (100, 100).
>>
>>
>>
>> Furthermore, the graph will descend from left to right in steps whose
>> widths are whole numbers.
>>
>>
>>
>> The left endpoint of each step will be included but the right end point
>> will not be included.
>>
>>
>>
>> Color this graph blue.  Now join the steps with vertical segments.  The
>> interior points of the vertical segments are colored red, while the top end
>> point of each red segment will be colored red, and the bottom point will be
>> colored blue.
>>
>>
>>
>> Now the union of the red and blue separates the lower left corner from
>> the upper right corner of the square.  Therefore the diagonal from (0,
>> 0) to (100

[EM] Consensus Threshold Approval

[Andy Jennings]

the diagonal from the upper left corner (0, 100) to the lower
> right corner (100, 0).  If this diagonal does not intersect the blue,
> then the candidate’s Consensus Threshold Approval score is zero.  Otherwise
> it is the second coordinate of the highest (and therefore leftmost) blue
> point of intersection.
>
>
>
> In summary, we have bisected the 100 by 100 square vertically,
> horizontally, and diagonally.  The diagonal with positive slope leads us
> to the chiastic approval winner.  The other diagonal leads us to the
> consensus threshold approval winner.  The horizontal bisector leads us to
> the Bucklin winner.  The vertical bisector leads us to the Approval
> winner.  The area cut off by the colored graph determines the Range
> winner.
>
>
> On Wed, Apr 3, 2013 at 6:18 PM, Jameson Quinn wrote:
>
>>
>>
>>
>> 2013/4/3 Forest Simmons 
>>
>>>
>>>
>>> On Wed, Apr 3, 2013 at 12:07 AM, Kristofer Munsterhjelm <
>>> km_el...@lavabit.com> wrote:
>>>
>>>> On 04/03/2013 12:01 AM, Forest Simmons wrote:
>>>>
>>>>> Jobst has suggested that ballots be used to elicit voter's "consensus
>>>>> thresholds" for the various candidates.
>>>>>
>>>>> If your consensus threshold for candidate X is 80 percent, that means
>>>>> that you would be willing to support candidate X if more than 80
>>>>> percent
>>>>> of the other voters were also willing to support candidate X, but would
>>>>> forbid your vote from counting towards the election of X if the total
>>>>> support for X would end up short of 80 percent.
>>>>>
>>>>> The higher the threshold that you give to X the more reluctant you are
>>>>> to join in a consensus, but as long as your threshold t for X is less
>>>>> than than 100 percent, a sufficiently large consensus (i.e. larger than
>>>>> t percent) would garner your support, as long as it it is the largest
>>>>> consensus that qualifies for your support.
>>>>>
>>>>> A threshold of zero signifies that you are willing to support X no
>>>>> matter how small the consensus, as long as no larger consensus
>>>>> qualifies
>>>>> for your support.
>>>>>
>>>>> I suggest that we use score ballots on a scale of 0 to 100 with the
>>>>> convention that the score and the threshold for a candidate are related
>>>>> by  s+t=100.
>>>>>
>>>>> So given the score ballots, here's how the method is counted:
>>>>>
>>>>> For each candidate X let p(X) be the largest number p between 0 and 100
>>>>> such that p(X) ballots award a score strictly greater than 100-p to
>>>>> candidate X.
>>>>>
>>>>> The candidate X with the largest value of p(X) wins the election.
>>>>>
>>>>
>>>> I think a similar method has been suggested before. I don't remember
>>>> what it was called, but it had a very distinct name.
>>>>
>>>> It went: for each candidate x, let f(x) be the highest number so that
>>>> at least f(x)% rate the candidate above f(x).
>>>>
>>>> I *think* it went like that, at least. Sorry that I don't remember the
>>>> details!
>>>
>>>
>>> Good memory, that was Andy Jennings' Chiastic method.  Graphically these
>>> two methods are based on different diagonals of the same rectangle.
>>>
>>
>> Different, how? It seems to me they're just the same, but with the
>> numbers reversed.
>>
>>>
>>>>
>>>>  If there are two or more candidates that share this maximum value of p,
>>>>> then choose from the tied set the candidate ranked the highest in the
>>>>> following order:
>>>>>
>>>>> Candidate X precedes candidate Y if X is scored above zero on more
>>>>> ballots than Y.  If this doesn't break the tie, then X precedes Y if X
>>>>> is scored above one on more ballots than Y.  If that still doesn't
>>>>> break
>>>>> the tie, then X precedes Y if X is scored above two on more ballots
>>>>> than
>>>>> Y, etc.
>>>>>
>>>>> In the unlikely event that the tie isn't broken before you get to 100,
>>>>> choose the winner from the remaining tied candidates by random ballot.
&

Re: [EM] Historic opportunity in Arizona for Approval Voting

[Andy Jennings]

Abd,

When applied to cities with partisan primaries, the bill is not even clear:

1) Does it mean that only two candidates advance (the two with the most
votes from any party even though the party primaries had different numbers
of voters)?

2) Does it mean the top two from each party advance to the general?

You could probably argue that it's up to the city to decide between those
systems.  Is either one a good system?  I don't know.

I would favor your amendment: use AV in all party primaries, top one from
each party goes to the general, if we also mandate AV in the general
election.

BUT, we are only talking about one city here (who won't necessarily even
want approval) and we have much to lose by inserting this amendment.  If we
say anything about partisan elections, then we awaken all of the partisan
sensibilities in all of the legislators (and the governor).  I don't think
we want to risk it.

~ Andy


On Mon, Mar 18, 2013 at 9:52 AM, Abd ul-Rahman Lomax 
wrote:

> At 11:52 PM 3/17/2013, Andy Jennings wrote:
>
>> Abd,
>>
>> Thanks for your support.
>>
>>
>> Municipalities in Arizona have great flexibility in choosing their own
>> voting systems.
>>
>>
>> I wouldn't say that municipalities have great flexibility in choosing
>> their own voting systems.  That's why we need this bill.
>>
>
> Okay. Home rule municipalities may have some flexibility. And how much, I
> don't know. What I know is "some." Tucson demonstrated that.
>
>
>  In particular, Arizona statute says if there is one winner then the
>> ballot verbiage must say "Vote for no more than 1".  The way I see it, they
>> were just trying to standardize ballot language for the state and (since
>> all they knew was plurality) they inadvertently restricted us to either
>> single-shot plurality or plurality with a plurality primary.  Since the
>> constitution mandates a primary, that leaves us with either segregated
>> primaries or jungle primaries.
>>
>
> Combine this with partisan/no-partisan ballots, i.e, party designation,
> then the two sane choices are segregated primaries (by party), or unified
> nonpartisan primaries. In any case, then, using Approval in the primaries
> is a major step foward.
>
> Approval in party primaries, though, could use Approval. Could a city, as
> well, hold, in addition to party primaries, hold an open primary for all
> candidates who choose not to affiliate with the party primaries?
>
> The problem I'm seeing is that HB2518 appears to mandate two candidates to
> go to the general election. That doesn't work with party primaries. A
> partisan primary should choose one candidate. The Bill calls the second
> election a "Runoff," as one alternate name. But it explicitly excludes any
> consideration of "majority."
>
> Now, from an election methods perspective, with an Approval election, this
> is actually spectacular. The design of the system, with the primary being
> held early, i.e., not held with the general election, and with, then, the
> final election being held as a general election, with generally higher
> turnout, addresses some objections to Approval Voting, i.e,. multiple
> approval majorities and therefore failure of some definitions of the
> majority criterion.
>
>
>  (The courts have ruled that cities, if they want, can implement a rule
>> that avoids the runoff if someone gets a majority in the jungle primary.)
>>
>
> What I'd recommend is that cities begin with the process in the Bill, and
> study results. It is possible to extrapolate margins in the runoff from
> those in the primary, and this is especially true with nonpartisan
> elections. However, the cost of adding and canvassing an additional runoff
> election in the general election is relatively small. It's really just
> another question on the ballot.
>
> The big issue is turnout. However, turnout can cut both ways. It rewards
> motivation, which is probably a good thing.
>
> Classically, advanced voting systems cause candidate numbers to increase.
> That appears to have happened in San Francisco. It's particularly true with
> nonpartisan elections, if people can run at low cost.
>
> As to the problem of what the election law says -- I haven't read the
> entire code, just large chunks of it -- there is a *very* advanced system
> that vote-for-one works fine with, Asset. But we are focusing on Approval,
> one small step, Count All the Votes.
>
> And the next refinement would be to allow ranking on the ballot, which
> allows, then, a series of advanced canvassing techniques.
>
> By the way, if a city has an accumulated record, with the App

Re: [EM] Historic opportunity in Arizona for Approval Voting

[Andy Jennings]

Abd,

Thanks for your support.


> Municipalities in Arizona have great flexibility in choosing their own
> voting systems.


I wouldn't say that municipalities have great flexibility in choosing their
own voting systems.  That's why we need this bill.

In particular, Arizona statute says if there is one winner then the ballot
verbiage must say "Vote for no more than 1".  The way I see it, they were
just trying to standardize ballot language for the state and (since all
they knew was plurality) they inadvertently restricted us to either
single-shot plurality or plurality with a plurality primary.  Since the
constitution mandates a primary, that leaves us with either segregated
primaries or jungle primaries.

(The courts have ruled that cities, if they want, can implement a rule that
avoids the runoff if someone gets a majority in the jungle primary.)

That's the only statute I know of in AZ law that prohibits approval voting.
 Though there may be others.  HB2518 expressly allows approval voting, thus
overriding any other inadvertent prohibitions.

5. The passage of this bill in the Arizona House is the best news I've seen
> *ever* as to U.S. voting systems.
>

Thanks.  Maybe I'm just downplaying the accomplishment here, but the way I
understand it there are already hundreds (thousands) of home rule cities
around the US that could enact approval voting with an ordinance.  We're
just trying to catch AZ up to where these "home rule" cities already are.

But it is movement, hopefully it would be momentum to go to cities and say,
"The legislature just allowed this.  You can try it."

~ Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] Comments on MJ discussion

[Andy Jennings]

> IIAC merely says that removal of a losing candidate shouldn't change
> the result.
>
> IIAC says nothing about whether there should be another election if a
> losing candidate calls for one without hir in it..
>
> IIAC is merely about consistent count-mechanics, given an unchanging
> set of ballots.
>

Well, you're arguing for a definition of IIAC that even plurality passes.

I find it lacking, and do not accept it for my definition of "independence
of irrelevant alternatives".

~ Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] Election-Methods Digest, Vol 103, Issue 1

[Andy Jennings]

Jonathan,

In addition to Ualabio's argument that cutting down the number of
candidates is good so as not to overwhelm voters, I believe that almost
every voting system ever invented can benefit from winnowing down
candidates that are _too similar_ before the election.  Political parties
seem like the natural steward of this responsibility.

For reforming partisan elections, I promote approval voting in the primary
and approval voting in the general.  Also acceptable would be approval
voting in the general and letting the parties choose their nominees however
they like.

To me, this means that those who vote in one party's primary should be,
generally, of a shared ideology.  They should be the guardians of that
party's label in the general election.  Voters should choose to participate
in the party primary for the ideology they are closest to.  If they feel
divorced from both (or all) parties, then they can refuse to participate in
the primary.  Then they should focus on getting a good independent
candidate to run.  The good news is that with approval voting, independents
will do much better in general elections.

I don't really see a good way for voters to support one person in the
Republican primary and another person in the Democratic primary at the same
time.

~ Andy


On Sat, Jan 5, 2013 at 9:12 AM, Jonathan Denn  wrote:

> Greetings!
>
> As I've mentioned previously, I am on the board of a nonprofit that will
> be announcing a Clean Government Alliance shortly. It will have two
> prominent far left/ far right reformers, probably another pair of center
> left/right will be joining them. The purpose is to draft a Constitutional
> Amendment for omnibus electoral reform. For these people everything is on
> the table. We had to pass on another household name because that person
> wouldn't put Term Limits on the table.
>
> I have been flying your flag: Ban Single Mark Ballots, and I have to say,
> that these sophisticated folk need it explained to them. Anyway, and I have
> asked this question before, "What is the solution for primaries?"
>
> This is the biggest "open item" in the work that has to be done. 40% of
> the electorate are independents, probably centrists. We cannot vote in
> primaries in almost all states. It's a gaping yaw in a democratic republic.
>
> I've used this example before. I did live in CT until a few weeks ago, now
> MA, in the last Senate election there was a great Republican Brian K Hill,
> a reformer. And the former Democratic Sec of State Susan Byceiwicz was also
> an interesting candidate. I would have liked to vote for both in the
> primary, and would have loved to seen them in the general election against
> each other. Instead we had a plutocrat running against a billionaire. In
> the end the oligarchs won.
>
> I expect the amendment will begin being drafted in DC in a few weeks, so
> please, load me up with the arguments.
>
> Cheers,
> Jon Denn
> @jmdenn
>
>
>
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>

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Re: [EM] Comment on MJ discussion

[Andy Jennings]

> Removing a losing candidate from the ballots and from the election,
> and then re-counting the ballots, shouldn't change the winner.
>
> Approval and Score pass.
>

Michael, I find it very inconsistent for you to argue so adamantly for
voters to use maximal strategy and then to use a criterion that doesn't
allow them to adjust their ballot when one candidate is dropped.

If voters even do so much as re-normalize their ballot when a losing
candidate is dropped, that can ruin independence of irrelevant alternatives.

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Re: [EM] Election-Methods Digest, Vol 103, Issue 1

[Andy Jennings]

> Your response appears to be missing from the list.  I'll quote the
> paragraph I'm commenting on:
>

Oh.  You had emailed me off-list (yesterday) so I responded off-list.


The process you describe seems to be a rather complicated way of finding
> the top or bottom half of the votes.  The fact that 'B' is higher than 'D'
> and pushes a 'C' vote into the bottom half of the votes is nothing more
> than a Yes/No decision.  It helps you decide whether a candidate got more
> than one-half the votes, but is devoid of additional value.  A simple
> Yes/No ballot yields precisely that result with no mathematical constructs.
>
> If a voter grades a candidate as 'B' rather than 'A', the voter has
> detected some flaw in the candidate and is expressing it in the grade. To
> treat that voter's vote as simply above or below the median is to debase
> it.  Why should the voter take the trouble to assign a grade if it's only
> use is to place the vote in the higher or lower half of the votes cast?
>
> I'm sorry we disagree on this point, but if the grading system is to have
> significance in the electoral process, the higher ranks must be more
> valuable than the lower  ranks.


In this thread, I am only trying to clarify how MJ and CMJ work.  I have
not revealed my value judgments.

What I personally think about these systems is quite nuanced.  There are
things I like about them, things I find very mathematically interesting,
and things I don't like.

~ Andy

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Re: [EM] Election-Methods Digest, Vol 103, Issue 1

[Andy Jennings]

Here's the way I would explain the CMJ tiebreaker in your example:

"This candidate's median is a C, and to get up to the median vote uses
43.1% of those C votes."

What this means:

This candidate would be beaten by a candidate with a median of A or B or a
candidate with a median of C where the median used up more than 43.1% of
the C votes.  This candidate would beat any candidate with a median of D
and any candidate with a median of C where the median used up less than
43.1% of the C votes.

How it is calculated:

There are 578,536 voters, with half of that being 289,268.  The bottom half
of the votes, then, are the 19,663 F votes, plus the 81,286 E votes, plus
the 121,121 D votes, plus 67,198 of the 155,781 C votes.

 67198/155781 is 0.431.

~ Andy



On Wed, Jan 2, 2013 at 7:55 AM, Fred Gohlke  wrote:

> Good Morning, Jameson
>
> re:  "Each voter grades each candidate from A to F. Voters may
>   give as many or as few of each grade as they want. Then
>   each candidate's grades are put in order and the similar
>   grades are evenly spread out. For instance, grades of B
>   (3.0) are evenly spread over a continuum between B+ (3.5)
>   and B- (2.5)."
>
> It is not clear how or why grades should be adjusted.  If a voter gives a
> candidate a grade of B, what is the justification for changing it to B+ or
> B-?  More to the point, what is the benefit?  If a candidate gets:
>
> Grade   Voters
>   A 26,781
>   B173,904
>   C155,781
>   D121,121
>   E 81,286
>   F 19,663
>
> can not the candidate's grade be calculated without adjusting the value of
> any of the voters' wishes?
>
> Fred
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>

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Re: [EM] Majority-Judgement using adjectives versus alphabetical scales versus numerical ranges.

[Andy Jennings]

I'm in the U.S.  Even here, where the standard educational scale is
alphabetical, I much prefer actual adjectives for the grades:

Excellent, Very Good, Good, Fair, Poor, Reject

MJ works best when the voters, as much as possible, have a shared
understanding of the actual meaning of the grades.  With grading curves and
grade inflation, I feel that the A-F scale is not good enough as a "common
language" across our culture anymore.

~ Andy


On Thu, Dec 6, 2012 at 2:54 PM, ⸘Ŭalabio‽  wrote:

> ¡Hello!
>
> ¿How fare you?
>
> Yesterday, I noted that Majority-Judgements does not work if we
> have too many adjectives because we have only so many adjectives and voters
> might confuse adjectives too close in meaning..  ¿Would an alphabetical
> scale be acceptable?:
>
> In the United States of America, we grade students using letters:
>
> A+
> A
> A-
> B+
> B
> B-
> C+
> C
> C-
> D+
> D
> D-
> F+
> F
> F-
>
> I have 2 questions grading candidates on this scale.  1 question
> is for people not in the United States of America.  The other question is
> for everyone:
>
> People outside the United States of America:
>
> ¿Do you Understand this Scale?
>
> For everyone:
>
> ¿Is this scale acceptable to you?
>
> Followup question:
>
> If this scale is not acceptable to you, ¿why is it not acceptable
> to you?
>
> With 15 grades, this scale is not very different from the
> numerical ranges of 0 to 9 or negative -9 to positive +9.  This raises the
> question:
>
> ¿Why not just use the ranges 0 to 9 or negative -9 to positive +9
> instead?
>
> ¡Peace!
>
> --
>
> “⸘Ŭalabio‽” 
>
> Skype:
> Walabio
>
> An IntactWiki:
> http://circleaks.org/
>
> “You are entitled to your own opinion, but you are not entitled to
> your own facts.”
> ——
> Senator Daniel Patrick Moynihan
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>

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Re: [EM] Choosing leaders in a legislature

[Andy Jennings]

Jameson,

Your solution to the original problem (use an anonymous voting system) is
not a bad one, but it is still interesting to consider the problem where
the voting system is not anonymous and going against your caucus is indeed
punishable behavior.  Suppose the caucus loyalty is so strong that the
entire majority party votes as a bloc.  What voting systems will still
elect some kind of compromise candidate?

With all of our top-tier methods (Range, Approval, MJ, Condorcet), there is
a defined way for a majority bloc to vote that will ensure their outcome no
matter how the minority votes.  IRV too.

Interestingly enough, Borda Count can give us a compromise winner in this
situation, if the majority votes first and the minority can see the totals
and vote reactively.  The majority can't put enough distance between their
chosen winner and the other candidates to knock them all out of the
running.  In effect, they must leave N candidates within striking distance
and then, if the minority unites, they can elect any one of those
candidates.  I haven't had the time to calculate N.  It depends on the size
of the majority and the minority as well as how many candidates there are.
 My thinking was that if that's how the game theory works out (majority
nominates N candidates and the minority chooses between them) then why not
just make that process explicit?  Tell the majority to nominate N
candidates and then let the minority choose between them.  Then we can
choose the number N directly, we're not limited to the one that falls out
of the Borda construction.

This method can still choose the median leader without instituting
anonymity or challenging caucus loyalty.  I'm just not sure, yet, how it
extends to more than two parties.

~ Andy


On Mon, Nov 12, 2012 at 1:32 PM, Andy Jennings
wrote:

> Good thoughts, Jameson.
>
> I think you are right that if voting was anonymous and a good voting
> system were used, it would turn out pretty well.  Also, it is necessary
> that *running* for leadership not be a punishable offense.  The easiest way
> to fix this, I think, is to say that every legislator is in the running for
> leadership and you can't opt out.  Would those two structural changes be
> enough, then?
>
> More thinking about the original proposal:
>
> What if both parties, in their caucus and using whatever voting system
> they wanted, nominated 16 legislators for leader.  Then there will be at
> least one legislator approved by both parties.  (If there is more than one,
> then hold approval voting runoffs in the whole legislature, or something.)
>  This is pretty close to my earlier proposals, and I don't think the
> incentive to nominate turkeys would be all that great.
>
> If there were three parties, you could have each party nominate 21 people
> so there is at least one legislator approved by all three parties.   This
> is equivalent to allowing each party to eliminate 10 people.  You do these
> eliminations sequentially, largest party to smallest party, or the reverse.
>  Or you could let each party eliminate one at a time, in ten rounds, until
> there was only one left.  But any of these options seems to give a big
> advantage for a party with just under a minority to split into two parties.
>
>
> On Mon, Nov 12, 2012 at 5:33 AM, Jameson Quinn wrote:
>
>> Why not just use approval voting (or MJ) within the legislature? The
>> problem with the "nominate 16 and we'll pick one" idea (and the like) is
>> that it gives a strong incentive to nominate candidates that, for whatever
>> reason, everyone knows are unsuitable.
>>
>> To me, the basic way that the approval voting could go wrong is if voting
>> outside your caucus were a punishable betrayal. So, I think you'd need to
>> have a secret ballot. That's unfortunate for ordinary voters, who generally
>> should have the right to know what their representatives are doing in their
>> name. But other than that, I think that the incentives are pretty good, and
>> it would settle on a capable near-median candidate.
>>
>> Jameson
>>
>> 2012/11/11 Andy Jennings 
>>
>>>  What would be the ideal way to choose leaders in a legislature?
>>>
>>> In the Arizona house and senate, for example, once our legislators are
>>> elected, the majority party caucuses to choose the leadership.  Assuming
>>> the Hotelling model, let's say they end up choosing the median legislator
>>> on their half of the political spectrum.  It follows that the legislature
>>> will be led by someone from about the 25th percentile on the political
>>> spectrum.  Then, if the other party gains control, the leadership will
>>> swing to the 75th percentile on the political sp

Re: [EM] Approval voting and incumbents

[Andy Jennings]

Jon,

If we could get most people to agree that incumbents have an unfair
advantage, and to want to do something about it at the structural level,
then this proposal can accomodate that.  Still leave the incumbent off the
ballot, but instead of saying he/she sits at a virtual 50%, make it 40% or
something.  If any challenger gets above 40%, then elect the one with the
highest approval, otherwise re-elect the incumbent.  You can adjust that
40% number up or down until the right amount of incumbents are winning.

Or you could make that number could change over time.  After your first
term as governor, it's 50%.  After your second term, it's 40%.  After your
third term, it's 30%.  I think I would prefer this to hard term limits,
because the governor is still has to answer to the voters during all their
terms.  As it is now, they walk into their last term essentially as a lame
duck with no accountability.

Of course, it's not a simple system and I'm not proposing it could be
implemented any time soon.  But it's fun to think about.

~ Andy


On Tue, Nov 13, 2012 at 4:29 AM, aGREATER.US  wrote:

> Incumbents have a huge unfair advantage in that corporations (including
> unions) pour money into their reelection campaigns. It's the devil you know
> syndrome and also smart money as incumbents are statistically more likely
> to win and owe the favor. In this context I wonder if the best voting
> method for publically funded elections is different from the status quo.
> Like Schoedinger's Cat, we live in both universes until we know whether
> there will be meaningful reform or not. I'm guessing there will be but only
> if all reform groups form an overarching alliance of word and deed if not
> an actual formal group.
>
> The only thing I don't like about voting for all candidates to see who
> runs against the incumbents is it doesn't give them a chance to fail in the
> primary first, and they can save all the legalized graft for the general
> election.
>
> Jon
>
>
> Sent from my iPhone
>
> On Nov 13, 2012, at 12:04 AM, Andy Jennings 
> wrote:
>
> > A lot has been said about strategy in approval voting.  Here are some
> strategies that have been suggested:
> >
> > - U/A: If the candidates are basically in two groups for you,
> unacceptable and acceptable, then approve the ones who are acceptable.
> >
> > - Honest: Decide what "approval" means to you.  Consider each candidate
> separately and decide whether or not you approve him/her.
> >
> > - Rank all the candidates first, then decide where your approval cutoff
> is.  (perhaps based on polls)
> >
> > - Figure out who the two front runners are, approve the one you prefer
> as well as any candidates you like better than that.
> >
> > These are all good, simple strategies, but perhaps it will be even
> simpler than this.  I mean, in most political races there will be an
> incumbent, which is a natural cutoff.  So just approve everyone you like
> better than the incumbent.  As for the incumbent, approve him/her if you
> think he/she is doing a good job.
> >
> > In fact, this suggests a variant of approval voting that might be
> useful: you could leave the incumbent off the ballot and say that if no
> challengers achieve 50%, then the incumbent wins re-election.  That way,
> you're only replacing the incumbent when you're "trading up", or finding
> someone who most people like better than the incumbent.  With many good
> candidates on the ballot, it seems like it would be much less likely for
> incumbents to get re-elected.
> >
> > Thoughts?
> >
> > ~ Andy
> >
> > 
> > Election-Methods mailing list - see http://electorama.com/em for list
> info
>

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[EM] Approval voting and incumbents

[Andy Jennings]

A lot has been said about strategy in approval voting.  Here are some
strategies that have been suggested:

- U/A: If the candidates are basically in two groups for you, unacceptable
and acceptable, then approve the ones who are acceptable.

- Honest: Decide what "approval" means to you.  Consider each candidate
separately and decide whether or not you approve him/her.

- Rank all the candidates first, then decide where your approval cutoff is.
 (perhaps based on polls)

- Figure out who the two front runners are, approve the one you prefer as
well as any candidates you like better than that.

These are all good, simple strategies, but perhaps it will be even simpler
than this.  I mean, in most political races there will be an incumbent,
which is a natural cutoff.  So just approve everyone you like better than
the incumbent.  As for the incumbent, approve him/her if you think he/she
is doing a good job.

In fact, this suggests a variant of approval voting that might be useful:
you could leave the incumbent off the ballot and say that if no challengers
achieve 50%, then the incumbent wins re-election.  That way, you're only
replacing the incumbent when you're "trading up", or finding someone who
most people like better than the incumbent.  With many good candidates on
the ballot, it seems like it would be much less likely for incumbents to
get re-elected.

Thoughts?

~ Andy

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[EM] Choosing leaders in a legislature

[Andy Jennings]

What would be the ideal way to choose leaders in a legislature?

In the Arizona house and senate, for example, once our legislators are
elected, the majority party caucuses to choose the leadership.  Assuming
the Hotelling model, let's say they end up choosing the median legislator
on their half of the political spectrum.  It follows that the legislature
will be led by someone from about the 25th percentile on the political
spectrum.  Then, if the other party gains control, the leadership will
swing to the 75th percentile on the political spectrum.  Wouldn't it be
much better we could force the leadership to be near the median of elected
legislators?

In the Arizona senate, for example, which has thirty members, the majority
party may have as few as seventeen members and the caucus could be
controlled by nine, or thirty percent of the senate.  I'm not sure, but I
have to imagine that this is common.

Here are some ways to force the leadership near the median (assume a
legislative body of 31 members and just two parties, for now):

1. "The majority party shall nominate 16 senators for president and the
minority party shall choose among them."

2. "The minority party shall nominate 16 senators for president and the
majority party shall choose among them."

I think either of those would tend to choose a president near the median.
 Is one better than the other?  Is it possible to extend to multiple
parties?  Without forcing them to form a majority coalition first?

Say there are three parties.  Should each party, in turn, eliminate ten
people?  Does the largest party or the smallest go first?

Or should the first party eliminate 15 and then the other parties choose
among the remaining 16 via approval voting or something?

Other ideas?

~ Andy

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Re: [EM] Board Meeting Deadline

[Andy Jennings]

>
> My analysis has led me to believe the hole in this strategy is there is no
> position taken on primaries. Going back to the premise that the duopoly
> must be broken, it appears to me the whole "ball game" is how to structure
> primaries. Conservatives will want it left up the the States, liberals
> probably want Congress to pass something. Nevertheless, letting everyone
> vote, and having a diverse selection of viewpoints to choose from seems
> critical.
>

There are two schools of thought on this.

Some people feel like once we have a better voting system, one that can
support a dozen (or more) good candidates, political parties (and
primaries) will be unnecessary, which would eliminate some elections and
save money.  The counter-argument to this is that most systems (even the
ones that have no problem, in theory, with candidates that are similar to
each other) can, in practice, benefit from a primary round that winnows
down similar candidates.  Parties are the natural categorization framework
for this winnowing process.  Additionally, it is probably good to narrow
down the field to 6-8 candidates for the general election just so we don't
overwhelm the voters with too many choices.

The other school of thought is that we should start with encouraging
political parties to use these better methods internally.  In some states,
this may be possible without statute changes.  To my understanding,
Americans Elect was essentially using approval voting for their nomination
round.  Voters could register support for as many candidates as they
wanted.  There were, in effect, thousands of candidates on the "nomination"
ballot and I don't know of a system other than approval voting that would
work well in that situation.  I don't know what system they were going to
use to decide among their candidates once nominated, but I, for one, was
hopeful that they would eventually be willing to consider one of these
improved systems.  The thinking is that a political party which embraces
one of these better systems will be able to put up better candidates and
will have a competitive advantage over other parties.

~ Andy

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Re: [EM] Amateur peer-reviewed "journal" for voting methods, criteria, and compliances?

[Andy Jennings]

I'm willing to review articles.



On Wed, Oct 3, 2012 at 8:08 AM, Jameson Quinn wrote:

> This idea seems to have decent support in the community. I think we should
> be proceeding.
>
> However, we are still a long way from being able to pop the champagne. This
> article  provides
> a basic roadmap for starting a journal. This roadmap is clearly not suited
> to our particular case in all details, but it's still worth a read. In
> particular, it has a schedule of startup tasks:
>
> Week 1
>
>- Decision to proceed with journal, including budget and resource
>approvals.
>- Determine who will fill the roles of editor (& backup), managing
>editor/assistant to the editor (& backup), editorial board.
>- Agree on statement of purpose for the journal, and theme for first
>issue if desired.
>
> Week 2 - 3
>
>- Establish agreement with SFU for hosting service.
>- Conduct training for editor and managing editor and their backups.
>
>
>
> Week 3
>
>- Review “Design Options” and agree on approach to be adopted for the
>journal for each of these options.
>- Identify possible contributors to 1st issue of the journal
>and contact them to encourage contributions.
>
> Week 4
>
>- Identify contractors to perform copy editor, proofer and layout
>functions.
>- Complete initial set-up of the journal web-site with no articles.
>
> Week 5
>
>- Conduct training for editorial board (regarding their roles
>as reviewers), and, if necessary, the contractors who will be used for copy
>editing, proofing and layout functions.
>
> Week 6 - 7
>
>- Pilot process with dummy articles.
>
>
> Week 8
>
>- Send out broadly to the education community an announcement of the
>journal, theme of 1st issue if appropriate, request for contributions, link
>to journal.
>
> Week 9
>
>- Editorial board to make decision regarding possible collaboration
>opportunities identified in this report.
>
> So, for our equivalent of "week 1" we need:
> Managing editor: The person who makes sure the whole thing happens,
> including almost all the bullet points above. I'd happily put my self
> forward, but honestly if anyone else wants to take up this burden I won't
> stand in your way. Roughly one day a week of commitment.
> Editor: Responsible for the process of peer review itself - getting the
> peer reviewers assigned, making sure they do their work, scheduling
> articles for which issue they are targeted for, etc. Ideally, adademic
> experience would help here. Roughly 3 days a month of commitment.
> Backup: I'd like to have at least 1 backup for each of the above. Can be
> the same person.
> Webmaster and backup: Discussion of this is ongoing.
> "editorial board": Serve as reviewers, help with publicity. Probably
> around 1-2 days a month of commitment. We have 2 or 3 people who have sorta
> signed on for this level of involvement, but let's try to get that up to at
> least 7 formal offers.
> Title, statement of purpose: Might be time to start to talk about these.
>
> I think a reasonable goal is to be done with the above by the 22nd of this
> month,  2 and a half weeks from now. If we can't pull that together, I
> don't see how we can imagine that we'll manage to have a journal. That
> means, if you were thinking of volunteering for any of the above, *now is
> the time to speak*.
>
> Jameson
>
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>
>

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Re: [EM] Divided Majorities - Number Votes Matrix - Left Vote Shifts

[Andy Jennings]

> Related matter - majority votes for filling number blanks.
>
> Example-
> Percent of GDP for taxes --
> 0 to 100 percent in 1 percent units.
> Each legislator/voter picks a percentage
> Report the votes per percentage.
> Accumulate from 100 downward to get a bare majority of the total votes.
>
> i.e. NO endless amendments about filling number blanks.



It is not necessary to limit them to one percent units.

Once each legislator/voter picks a percentage, if there are an odd number
just find the median.  If there are an even number, you decide beforehand
which of the following you will do:
- pick the lower of the two middlemost values
- pick the higher of the two middlemost values
- average the two middlemost values

I prefer either the lower or the higher middlemost, because such order
statistics are "strategy-proof".  That is, assuming each voter's utility is
a single-peaked function of the output grade (and they aim to maximize
their utility), each voter's dominant strategy is to submit the percentage
that maximizes their utility.  In other words, this method incentivizes
honesty.

(If some voters aim to do something other than maximize their utility, like
"ruin the process" or "be the one who submitted the median value", then
things are not so simple...)

I have been thinking this for a while, and I would love to see it
implemented for precisely the situation you describe: the legislature, or
even the voters directly, choosing the overall tax rate.

~ Andy

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[EM] Majority Judgment

[Andy Jennings]

Hi Mike,

Can you elaborate on "worse chicken dilemma than approval or score"?  Or
point me to a specific message on the list where you prove that?

(Please don't tell me just to search the archive.  I'm interested in your
reasoning, but don't have the time right now to search the archive looking
for it.)

Thanks,

~ Andy



On Thu, Sep 6, 2012 at 6:43 AM, Michael Ossipoff wrote:

> Not exactly a winning combination of properties.
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>

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[EM] Methods which refuse to identify a winner sometimes

[Andy Jennings]

On Wed, Jun 13, 2012 at 1:39 AM, Nicholas Buckner wrote:

> Actually, on a weird second thought, wouldn't a method that refused to
> identify a winner in a three-way tie (Condorcet paradox) be compatible
> with both? It would be I guess case 5 (A, B, C, D, no winner). It
> wouldn't be a very practical method, as we need our voting methods to
> decide ties, but isn't deciding the tie what breaks the Participation
> criterion? My voting method only made the mistake of picking a winner
> in the first place (a mistake I'd happily do again).
>

Occasionally we talk about methods that refuse to identify winners in some
situations.  After all, "unrestricted domain" _is_ one of the conditions of
Arrow's impossibility theorem.  But usually that criterion is considered so
obvious that we don't talk about it.  I don't even mention "unrestricted
domain" when I explain Arrow's theorem to someone for the first time.

If you only consider the domain where there are no cycles, then "Condorcet"
is a single method and it meets Arrow's other criteria perfectly.

~ Andy

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Re: [EM] SODA terminology: opinions wanted.

[Andy Jennings]

On Fri, May 25, 2012 at 7:06 AM, Jameson Quinn wrote:

> I keep coming back to the basic question of terminology in SODA. If the
> voters delegate their votes, what is the verb for the thing the candidates
> do with those delegated votes? I want to be able to say: "Candidate A is
> first in the Xing order, so she Xs  for candidates B and C."
>  is probably "delegated approvals"; what is ?


How about: "Candidate A is first in the sharing order, so she shares her
delegated votes with candidates B and C." ?

I know we had a discussion in August where we decided to change "share" to
"add approvals to your vote" on the wiki, and I agreed that I liked it
better.  Maybe I'm reconsidering...

I like the word "share" because A passing on votes doesn't diminish her
own.  (Similar to filesharing.)

~ Andy

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Re: [EM] Democracy Chronicles, introductions

[Andy Jennings]

On Mon, Apr 23, 2012 at 11:28 PM, Richard Fobes <
electionmeth...@votefair.org> wrote:

> On 4/23/2012 12:05 PM, Kristofer Munsterhjelm wrote:
>
>> On 04/22/2012 05:07 PM, Richard Fobes wrote:
>>
>>  The core of the system is VoteFair popularity ranking, which is
>>> mathematically equivalent to the Condorcet-Kemeny method, which is
>>> one of the methods supported by the "Declaration of Election-Method
>>> Reform Advocates."
>>>
>>
>> You said there are ballot sets for which the Kemeny method and VoteFair
>> provides different winners. How, then, can VoteFair be /mathematically/
>> equivalent? You say the differences don't matter in practice, but for
>> the method to be mathematically equivalent, wouldn't the mapping have to
>> be completely identical?
>>
>
> First of all, in the context of a publication that is read by
> non-mathematicians (which is what the Democracy Chronicles is) the word
> "equivalent" does not refer to a rigorous "sameness."
>

When you qualify it as "mathematically equivalent", it definitely does
refer to a rigorous "sameness".

Perhaps you should say "essentially equivalent".

~ Andy

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Re: [EM] Democracy Chronicles, answers to interview questions

[Andy Jennings]

>
> Question 1.  Your name and the city and country you work in.
>

Name: Andrew Jennings.  Mesa, Arizona, USA


> Question 2.  What is your Company or Organization?
>

I'm on the board of the non-profit Center for Election Science, but these
opinions are my own.


> Question 3.  Any contact info you wish to give to be published with
> article for readers (for example your email or website.)


> Question 4. If you have signed the Declaration, is there any additional
> information, beyond what's in your signature, that you feel is important to
> mention?
>
> Question 5. If you have not signed the Declaration, why?
>
> Question 6. Briefly explain what characteristics you think are most
> important for a voting method to have?
>

Should allow many good candidates to run without splitting the vote.

The voting process should match up pretty well with the thought process
voters use to evaluate the candidates.

Never require voters to betray favorites.  If I think John Doe is the
absolute best candidate in the world to for US president, then usually John
Doe isn't in the race.  But if he were, even as a third-party candidate or
an independent and he had no chance of winning, I should be able to rank
him first or give him the highest grade without compromising my voice among
the other contenders.

Should allow, even encourage, honest voting, if possible.  Voting is so
much easier if you don't have to worry about being strategic, and society
is much happier if people don't feel like their opponents cheated to win.

Candidates should come out of the election with a societal grade, so they
really know whether they have a mandate, and so everyone feels like their
vote counts by having some effect on the final scores, however small.



> Question 7. What do you think is the most important election reform needed
> where you live (either locally or nationally)?  Why is this reform
> important?
>

Both locally and nationally, we need a system that allows many good
candidates to run.  One that doesn't encourage politics of fear.


> Question 8. What is your opinion on other aspects of election reform such
> as reforming money's role in politics or redistricting (particularly in the
> US but very interested as well concerning election reforms internationally)?
>

I wish there were some way to reform money's role in politics, but I'm
afraid it's impossible.   Politicians have power and money naturally flows
downhill toward power.  Whatever roadblocks we establish for businesses
trying to influence politicians, the money will find a way around them.  I
think the only answer is to try to decrease the power of big government and
bring all important decisions back to the local level.  Unfortunately,
government power and responsibility is much easier to ratchet up than to
ratchet down.

As for redistricting, for a jurisdiction with two legislative bodies, like
the United States or Arizona, I think one body should be elected with an
proportional voting system that ignores geography.  The other body can use
districting, but it should be done by computer (with an algorithm like
shortest splitline) or with a public contest and a predefined rule (anyone
can submit maps and the one with the lowest total perimeter wins).  We
should minimize or eliminate all human judgement in the redistricting
process.  A non-partisan committee is not good enough.

Election-Methods mailing list - see http://electorama.com/em for list info

[EM] Societal ranking from incomplete pairwise information. (Pinewood derby.)

[Andy Jennings]

Kristofer, (and others too)

If I recall, you were recently experimenting with how to best determine a
winner (or was it a full ranking) from incomplete pairwise information.
 What are the methods that you (or others) consider best for that?  It
seems like Kemeny would be a good fit (if it weren't computationally
prohibitive): for each pairwise contest you have data on, you just add one
point to each possible societal ranking which agrees with that pairwise
contest.  If your pairwise information has a notion of defeat strength,
then you can sum the defeat strengths to get a Borda-like method.
 Otherwise you can count the pairwise defeats and have a Copeland-like
method.  But for those last two each candidate should have about the same
number of contests, right?

Does the Schulze method extend naturally to incomplete data?

In your experimentation, were you the one who decided which pairwise
contests to run or was it decided by some other actor and you just had to
live with whatever data was generated?

A couple weeks ago, I found myself keeping score for a pinewood derby,
where 8-11 year old boys race wooden cars down a track.  When we thought
there were only 20 entrants, we were going to try to run the entire
pairwise matrix (190 races).  When 28 boys showed up, that became
impossible.  I quickly drew up a racing schedule.  Each boy got a number
and ended up racing against the next five and the previous five cars (mod
28).  (Then we did a quick tournament afterwards.)

It occurred to me that it would be better to use the outcomes of the early
races to decide who races against each other in the later races.  (Let A>B
signify that A has raced and won against B.)  If A>B, A>C, B>D, and C>D,
then there is really no point racing A against D.  You really want to use
the early race outcomes to determine which cars are comparable and race
those cars against each other.  This increases the information content of
each outcome.  It also contributes to the enjoyment by racing cars of the
same caliber and getting every boy a win if possible.  I've been thinking
about good methods for attacking this.

One other important constraint is that all cars should have about the same
amount of races, which rules out an "insertion-sort" type algorithm.

If the number of cars is 2^n, then I think the first n rounds are pretty
obvious.  For 32 cars, for example:  (Assuming no ties)

First round: Just pair them up randomly and race them.  There will be 16
winners and 16 losers.
Second round:  Race the 16 winners against each other (randomly) and the 16
losers against each other (randomly).
Third round:  Race the 8 undefeated cars against each other (randomly), the
8 winless cars against each other (randomly), and the 16 one-and-one cars
against each other (randomly).
etc.

(Instead of pure randomness, I would avoid racing cars that had faced each
other before if possible.)

After five rounds, you have one undefeated car, 5 cars with four wins, 10
cars with three wins, 10 cars with two wins, 5 cars with one win, and one
car with zero wins.

In each round, you're basically dividing the cars into tiers based on their
win-loss record and then racing cars in the same tier against each other
randomly.  And, for at least the first n rounds, there will always be an
even number of cars in each tier.  This is equivalent to a pure binary
tournament that has a losers' bracket as well as a two-loss bracket, a
three-loss bracket, etc. .

The question is what to do if you want to run more than n rounds, or if the
number of cars is not exactly a power of two.  I think the idea of dividing
them into tiers (or brackets) and racing them against other cars in the
same tier is still good, but using just their win-loss record is not
enough.  Lots of tiers will have an odd number of cars, so we need to know
which are the best and worst cars in each tier and have a few inter-tier
races.

So we can think of it as needing to come up with a secondary sort criterion
to use inside the win-loss tiers.

Or we can generalize and say that after each round we just come up with a
full societal ranking and then race the first against the second, the third
against the fourth, the fifth against the sixth, etc.  So I'm back to
needing to know the best way to come up with a societal ranking from
incomplete pairwise data.

Thoughts?

~ Andy

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Re: [EM] Approval-Runoff

[Andy Jennings]

>
> This was a very good idea, it sounds like. So how did it get shoved aside?
> It would be quite useful to know.
>

It didn't even get a hearing in the rules committee of the Arizona house of
representatives.  I think the chairman of the rules committee may have been
against it.  I heard that a prominent AZ Republican strategist opposes
approval voting because it would be "bad for conservatives".

I think it may be bad for the most extreme candidates, but in a place like
Arizona, I think it would be a slight positive for conservatives in
general.  (Since Arizona leans conservative, I think conservatives are the
most likely to be hurt by vote splitting and spoiler effects.)


> Does the law require a primary and runoff regardless of what happens in
> the primary? This seems a bit strange combined with the rest of what you
> wrote. If a majority found in the primary is adequate to declare a winner,
> no runoff, then there would be cost savings, if the required extra votes
> came from extra approvals.
>

The Arizona Constitution says, "The Legislature shall enact a direct
primary election law, which shall provide for the nomination of candidates
for all elective State, county, and city offices, including candidates for
United States Senator and for Representative in Congress..."

I believe this (in conjunction with existing statutes) is interpreted to
mean top-two runoff in nonpartisan situations, but if someone gets 50% in
the first round they can indeed omit the runoff.  I'm not sure how often
that runoff round has no other races and could actually save the entire
expense of an election.

~ Andy

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Re: [EM] Approval-Runoff

[Andy Jennings]

Story about Approval-Runoff:

I actually met with some state legislators last year and got one of them
interested in approval voting.  He was willing to introduce a bill allowing
cities to try approval voting.  (Arizona is at a disadvantage to other
states, in terms of voting reform, because state statute currently forces
cities to use top-two-runoff for their local elections.)

But the Arizona Constitution _requires_ a "primary" of some kind.  So,
rather than seek a constitutional amendment, we decided to go for approval
runoff.  We ran a bill this year that would allow cities to use
approval-runoff in their local elections.  (It was purely permissive.  That
is, even if it passed we still would've had the difficult job of convincing
a city to try it.)

Unfortunately, I'm pretty sure it's dead.  I won't go into the politics
here, but here are some other relevant notes:

- All city elections in Arizona (except for one city) are nominally
non-partisan.  In my city (Mesa), they really are non-partisan (probably
because nobody but a Republican could ever win) and I think approval-runoff
would work very well.  I've heard that in other cities, there are no
parties listed on the ballot but everyone knows who is the Democrat and who
is the Republican.

- As someone pointed out, having an extra runoff at the end is not such a
bad thing.  It shouldn't make the outcome worse, right?  I'm hoping it
could be sold as a safety valve, (i.e. "Try this new system, approval
voting, and we'll have a runoff election just to make doubly sure the
voters feel like they chose the right person.")

- It's a pity that it wouldn't save money.  I've heard that if I could
pitch something to city managers and clerks that would save money, then
they would be really excited.  But I don't see how to do that in Arizona.

- As someone pointed out, for a city currently using Top-Two Runoff, it is
just an incremental change.

- I think it mostly eliminates approval voting's biggest weakness, the
Chicken Dilemma.  Voters will be thinking much less strategically in the
first round.

- If two clones do make it into the final round, then yes, there will be
criticism that "this stupid voting system didn't give me any choice  in the
general election."

- I like Abd's suggestion for extending it to partisan elections (each
party only gets one slot in the approval round), but how are you going to
do that?  A party primary before the approval round?  Maybe you could say
that only the Republican who collects the most signatures gets on the
ballot (plurality in the petition phase).  You could let voters sign as
many petitions as they want, then you have approval voting in the petition
phase.

~ Andy

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Re: [EM] [CES #4445] Re: Looking at Condorcet

[Andy Jennings]

On Sat, Feb 4, 2012 at 10:01 PM, robert bristow-johnson <
r...@audioimagination.com> wrote:

> i really don't want this question distracted too much with "the guys and i
> are going out for pizza."  a little bit of distraction was okay, but the
> give-and-take relationship with my pizza-and-beer buds is just not the same
> as in a partisan contest that i bring my mace and shield.


It was, admittedly, an extreme example.  But a hyper-bitter cutthroat
political contest is the other extreme.  There are shades of gray in
between and there are many elections that fall nearer the pizza example
than the mace and shield one.

Any of the following might be a relatively friendly race:
- Party primaries
- Small town mayor in a non-partisan election
- School board
(By the way, does any town really elect their dog catcher anymore, or is
that just hyperbole?)

Also, I believe that we have such a bitter two-party system only because of
our plurality voting system (i.e. Duverger's Law).  Any good voting system
will entice more, and better, candidates to enter the races.  Hopefully,
then, the races can be less hostile and more civil.  But that argument
supports all of the "good" systems; it doesn't really distinguish between
them.

~ Andy

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Re: [EM] [CES #4445] Re: Looking at Condorcet

[Andy Jennings]

On Sat, Feb 4, 2012 at 10:14 AM, robert bristow-johnson <
r...@audioimagination.com> wrote:

> On 2/4/12 4:12 AM, Kristofer Munsterhjelm wrote:
>
>> On 02/04/2012 06:47 AM, robert bristow-johnson wrote:
>>
>>  On 2/3/12 11:06 PM, Jameson Quinn wrote:
>>>
>>>  No, he's saying that when the CW and the true, honest utility winner
 differ, the latter is better. I agree, but it's not an argument worth
 making, because most people who don't already agree will think it's a
 stupid one.

>>>
>>> as do i. it's like saying that the Pope ain't sufficiently Catholic or
>>> something like that. or that someone is better at being Woody Allen than
>>> Woody Allen.
>>>
>>> but for the moment, would you (Jameson, Clay, whoever) tell me, in as
>>> clear (without unnecessary nor undefined jargon) and technical language
>>> as possible, what/who the "true, honest utility winner" is? how is this
>>> candidate defined, in terms the preference of the voters?
>>>
>>
>> Utilitarianism is a form of ethics that proposes that the actions to be
>> taken are the ones that produces the greatest good for the greatest number.
>>
>
> thank you.  i *did* know what Utilitarianism is and suspected that the
> term "utility" referred to that.  and i understand the different norms for
> combining the individual utility measures to get an aggregate measure of
> utility to the group.  the "taxicab norm" and the minmax (more like the
> maxmin) norm was brought up.  no one seemed to mention the Euclidian norm.
>
> i would say that the most fair combination is the mean magnitude (taxicab)
> because it weights every voter's franchise equally.  but what is left
> unanswered is how the measure of utility for each voter is defined.  we can
> say that, for each voter that voted for the eventual winner as their 1st
> choice (or most highly scored), their measure of utility is "1".  but what
> measure of utility do you assign to voters that did not get their 1st
> choice?  that is not well defined.  given Abd's example:
>
>
>  2: Pepperoni (0.61), Cheese (0.5), Mushroom (0.4)
>> 1: Cheese (0.8), Mushroom (0.7), Pepperoni (0)
>>
>
> who says that for that 1 voter that the utility of Cheese is 0.8?  how is
> that function defined in the "proof" that Clay repeatedly refers to where
> "it's a mathematically proven fact that Score does a better job picking the
> Condorcet winner than does Condorcet"?  it's such a subjective thing and it
> can be defined in so many ways that i am dubious of any tight mathematical
> "proof" that is based on that.  it's not subject defining the boundaries.
>  if you get exactly what you want, the utility metric is 1.  if you get
> *nothing* of what you want, the utility is 0 (i.e. that pizza voter on the
> bottom may be a vegetarian and would not be eating pizza at all, if they
> got Pepperoni).  there's a whole range of quantity that goes in between
> that is not objectively defined.
>
> so, i have a few questions for everyone here:
>
>1.  do we all agree that every voter's franchise is precisely equal?
>2.  if each voter's franchise is equal, should we expect any voter
>that has an opinion regarding the candidates/choices to
>voluntarily dilute the weight or effectiveness of their vote,
>even if their preference is weak?
>

I suppose you think this has an obvious answer of "no".  But why not let a
voter dilute the weight of their vote, if it's their choice?

Some friends and I were deciding where to go for lunch the other day.
 Three of us said, "I'd prefer pizza to burgers but I could go for either."
 One said, "I got food poisoning last time I ate at that pizza joint and I
don't think I can do it today."  So we went for burgers and we were all
good with it.

Obviously, the higher the stakes, the less likely it is that people will
voluntarily dilute their vote, but there are many votes, decisions, and
elections, that are not bitter or partisan and would benefit from people
voluntarily diluting their vote.  I can imagine some people even in a
Presidential election choosing to do it, which is fine with me as long as
it's their choice.

~ Andy

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Re: [EM] [CES #4429] Looking at Condorcet

[Andy Jennings]

On Fri, Feb 3, 2012 at 2:05 PM, Jameson Quinn wrote:

>
> How would you vote with SODA?
>

I would usually end up delegating to my favorite.  I'd look at their
ranking and if it was pretty good I'd delegate.  Otherwise, I'd probably
come up with my own ranking (perhaps based on theirs) and then choose a
cutoff and vote approval-style.

So my strategy would be pretty similar to yours, I think.



> (go ahead and think of your answer before you read mine)
>
> I think I'd almost always just delegate to my favorite with SODA. If I
> don't like my favorite's delegation order, that would make me reconsider
> whether they're really my favorite. If I decide they still are, I would
> consider whether I thought the difference between my preferred order and
> their predeclared preferences would matter. If I decide it does, then look
> for the best candidate I think has a chance, and vote for them and everyone
> better. Chances of me ever getting to that last step would around one in
> 10, I reckon.
>
> Jameson
>
> 2012/2/3 Andy Jennings 
>
>>  On Thu, Feb 2, 2012 at 10:09 PM, Richard Fobes <
>> electionmeth...@votefair.org> wrote:
>>
>>> On 2/2/2012 11:07 AM, Kristofer Munsterhjelm wrote:
>>>
>>>> On 02/02/2012 05:28 AM, Jameson Quinn wrote:
>>>>
>>>>  I honestly think that honest rating is easier than honest ranking.
>>>>> ...
>>>>>
>>>>
>>>  As a contrast, to me, ranking is easier than rating. ...
>>>>
>>>
>>> I too find ranking easier than rating.
>>>
>>
>>
>> I go back and forth on this, myself.  Some thoughts:
>>
>> - If I had to rank more than ten candidates, I think it would be
>> difficult unless I put them into three or four tiers first.  Then, perhaps
>> I would choose to rank the candidates within the tiers or perhaps I would
>> leave them all tied if I didn't really care that much.  Thus, for me,
>> honest rating with just a few buckets is more basic than ranking.
>>
>> - If someone built a computer program that presented me pairs of
>> candidates at a time as Kristofer suggested, that would make it somewhat
>> easier.  I think I would still prefer to divide them into tiers first, but
>> if I divided them into tiers first, I might not need the pairwise
>> comparison hand-holding.  Also, suppose that I analyzed the candidates in
>> three different policy dimensions that I consider equally important and I
>> found that my policy preferences were:
>> Foreign Policy: A>B>C
>> Domestic Social Issues: B>C>A
>> Domestic Economic Issues: C>A>B
>> Now I prefer A to B, B to C, and C to A.  A cycle among my own personal
>> preferences when I compare them pairwise.  Then my output ranking would
>> depend on the order in which the pairwise questions were asked.  ??!?
>>
>> - If I were trying to cast an honest Approval Ballot, then I would think
>> about each candidate separately and decide whether I approve them or not.
>>
>> - If I were trying to cast a strategic Approval Ballot or a fully
>> strategic Score Voting Ballot, then I would first rank all the candidates,
>> then decide where to put my cutoff.  So I can definitely see the argument
>> of those who think that ranking is more fundamental than even approval
>> voting.
>>
>> - If I were trying to cast an honest Score Voting Ballot, I would have to
>> feel like there was an objective meaning for the various scores.  Then I
>> could consider each candidate separately and give them my honest scores.  I
>> probably wouldn't even normalize.  If I were going to normalize, then I
>> might as well go fully-strategic and vote approval-style.
>>
>> - If I were casting an MJ ballot, I think I would consider each candidate
>> separately and vote completely honestly, knowing that my vote was doing
>> everything it could to help any candidate where my score was higher than
>> society's median and, similarly, doing everything it could to hurt any
>> candidate where my score was lower than society's median.  I realize that
>> my vote would not be fully strategic if there were two frontrunners and I
>> liked both of them or disliked both of them, but in that situation, who
>> cares?
>>
>> - If a real election were being tabulated with Condorcet, I would vote
>> honestly.
>>
>> - If a real election were being tabulated with IRV, I would warn people
>> not to vote for minor candidates.
>>
>> Let me admit that a crucial point for me is that the only way to gain
>> Independence of Irrelevant Alternatives is to tell the voters to evaluate
>> each candidate independently and vote honestly, which may make me biased
>> towards rating methods.  FBC is very important to me and I'm still
>> skeptical of the FBC-compliant ranked-ballot methods recently proposed.
>>
>> ~ Andy
>>
>> 
>> Election-Methods mailing list - see http://electorama.com/em for list
>> info
>>
>>
>

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Re: [EM] [CES #4429] Looking at Condorcet

[Andy Jennings]

On Thu, Feb 2, 2012 at 10:09 PM, Richard Fobes  wrote:

> On 2/2/2012 11:07 AM, Kristofer Munsterhjelm wrote:
>
>> On 02/02/2012 05:28 AM, Jameson Quinn wrote:
>>
>>  I honestly think that honest rating is easier than honest ranking.
>>> ...
>>>
>>
>  As a contrast, to me, ranking is easier than rating. ...
>>
>
> I too find ranking easier than rating.
>


I go back and forth on this, myself.  Some thoughts:

- If I had to rank more than ten candidates, I think it would be difficult
unless I put them into three or four tiers first.  Then, perhaps I would
choose to rank the candidates within the tiers or perhaps I would leave
them all tied if I didn't really care that much.  Thus, for me, honest
rating with just a few buckets is more basic than ranking.

- If someone built a computer program that presented me pairs of candidates
at a time as Kristofer suggested, that would make it somewhat easier.  I
think I would still prefer to divide them into tiers first, but if I
divided them into tiers first, I might not need the pairwise comparison
hand-holding.  Also, suppose that I analyzed the candidates in three
different policy dimensions that I consider equally important and I found
that my policy preferences were:
Foreign Policy: A>B>C
Domestic Social Issues: B>C>A
Domestic Economic Issues: C>A>B
Now I prefer A to B, B to C, and C to A.  A cycle among my own personal
preferences when I compare them pairwise.  Then my output ranking would
depend on the order in which the pairwise questions were asked.  ??!?

- If I were trying to cast an honest Approval Ballot, then I would think
about each candidate separately and decide whether I approve them or not.

- If I were trying to cast a strategic Approval Ballot or a fully strategic
Score Voting Ballot, then I would first rank all the candidates, then
decide where to put my cutoff.  So I can definitely see the argument of
those who think that ranking is more fundamental than even approval voting.

- If I were trying to cast an honest Score Voting Ballot, I would have to
feel like there was an objective meaning for the various scores.  Then I
could consider each candidate separately and give them my honest scores.  I
probably wouldn't even normalize.  If I were going to normalize, then I
might as well go fully-strategic and vote approval-style.

- If I were casting an MJ ballot, I think I would consider each candidate
separately and vote completely honestly, knowing that my vote was doing
everything it could to help any candidate where my score was higher than
society's median and, similarly, doing everything it could to hurt any
candidate where my score was lower than society's median.  I realize that
my vote would not be fully strategic if there were two frontrunners and I
liked both of them or disliked both of them, but in that situation, who
cares?

- If a real election were being tabulated with Condorcet, I would vote
honestly.

- If a real election were being tabulated with IRV, I would warn people not
to vote for minor candidates.

Let me admit that a crucial point for me is that the only way to gain
Independence of Irrelevant Alternatives is to tell the voters to evaluate
each candidate independently and vote honestly, which may make me biased
towards rating methods.  FBC is very important to me and I'm still
skeptical of the FBC-compliant ranked-ballot methods recently proposed.

~ Andy

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Re: [EM] SODA might be the method we've been looking for.

[Andy Jennings]

Jameson,

Believe me, I'm on board with SODA.  I think I, too, like it better than
LRV, but I'm still trying to get a handle on LRV to make sure.

In my opinion (and my wording), SODA's advantages are:

1. The laziest possible voter, who just bullet votes for his favorite, is
still casting a (nearly?) optimal vote that is fair to him and to the rest
of society.

2. Voters can vote approval style, instead, if they want.

3. The only people who have to rank all the candidates are the candidates
themselves, who should be willing to do the work to come up with a full
honest ranking.  Their ratings are public, so we can call them out if they
try to use turkey-raising or other dishonest strategies.

4. There is a "delegation" phase after the election where the candidates
can negotiate an outcome, but their ability to negotiate back-room deals is
severely limited because they have to use their pre-declared rankings and
they have to play in an order determined by the votes.  In fact, there will
be a game-theory dominant equilibrium and the candidates will probably have
very little power to change the outcome.  Chicken scenarios are avoided
because they know the play order, the other candidates' rankings, and
exactly how much voting weight each one has.

5. If there is some super-weak Condorcet winner that is totally unfit to
govern, then the others can indeed block him in the delegation phase.

I don't see any huge theoretical downsides.  Do others still have
reservations about SODA?  I realize that some people may be opposed to
delegation, in principle.  And others think delegable systems just don't
have a chance of getting implemented.  So I think these debates about which
is the best voting system in the standard (non-delegable) model are still
useful.  I also think it's useful for Jameson to inject a plug about SODA
every now and then.

My main reservation about SODA at this point is that I see no practical
path to adoption.  It would be perfect for a large primary, like the
current Republican presidential field, but there's no way to start at that
level.  We have to start small.  But for small political elections,
professional societies, open source decisions, elementary school elections
etc. it seems too complicated.  I had a long discussion with a party
district chairman here.  He's interested in alternative voting systems to
fill his party positions but skeptical of complexity.  I don't even think
I've pitched him on SODA because he's still thinking about Approval Voting.

And with SODA, you can't just run a straw poll to show it off like you can
with so many other voting systems.  You need the participation of the
actual candidates to choose their rankings beforehand and to do their
delegation afterwards.

I know we haven't traditionally discussed implementation strategy on this
list (though that has changed some recently), but if you see a good
strategy for SODA adoption, please tell.

~ Andy



On Tue, Dec 13, 2011 at 6:55 PM, Jameson Quinn wrote:

> I believe that LRV (Least Resentment Voting) is indeed quite a clever
> solution to the chicken dilemma. But once more, I'd like to remind people
> that there is a way to solve the chicken dilemma without risking a victory
> by the plurality winner/condorcet loser. I'm speaking of course of SODA.
>
> First, SODA meets the FBC. In fact, in any 3-candidate scenario, and I
> believe in any 4-candidate one, it is strategically optimal to bullet vote
> for a candidate if you agree with their declared preferences. This ability,
> not just to vote your favorite equal-top, but unique-top, is not shared by
> any other method I know of. (Perhaps we could call this UFBC3, unique FBC
> for 3 candidates.)
>
> How does it do with chicken dilemma scenarios? For the following, I'll
> give honest ratings, then discuss the likely strategic implications under
> SODA.
>
> 40 C
> 25 A>B
> 35 B>A
>
> If this is the honest situation, then candidates A and B have every reason
> to find a way to include each other in their predeclared preference lists.
> These predeclared lists are made openly, and so one side cannot betray the
> other without giving the other side a chance to retaliate. The chance for
> retaliation will make betrayal a losing strategy.
>
> 40 C
> 25 A
> 35 B>A
>
> If the A camp is honestly indifferent between B and C, and candidate B
> finds this indifference credible, then B can still decide not to retaliate,
> that is, to ignore A's truncation and nonetheless declare a preference for
> A. This enables A to win without B spoiling the election.
>
> (Any single-round method which elects A here is subject to the chicken
> dilemma; electing B is, in my mind, crazy; and any method which elects C
> here has been spoiled by candidate B, and so encourages shenanigans of the
> republicans-funding-greens sort. Any method I know of except SODA fails in
> one of these ways.)
>
> 40 C
> 25 A>B
> 35 B
>
> This is like the above situation, but since A had no chance of winning
>

Re: [EM] This might be the method we've been looking for:

[Andy Jennings]

Yes, in standard game theory everyone would know the exact utility of the B
supporters in each outcome.

Here, those utilities are hidden, so there is some incentive for the B
supporters to lie and say they are indifferent between A and C.



On Mon, Dec 12, 2011 at 4:17 PM,  wrote:

> Thanks for checking the details.
>
> In traditional game theory the rational stratetgies are based on the
> assumption of perfect knowledge, so
> the A faction would know if the B faction was lying about its real
> preferences.  Even knowing that the
> other faction knew that they were lying they could still threaten to
> defect, and even carry out their threat.
> There is no absolute way out of that.
>
> - Original Message -
> From: Andy Jennings
> Date: Monday, December 12, 2011 12:40 pm
> Subject: Re: [EM] This might be the method we've been looking for:
> To: Jameson Quinn
> Cc: fsimm...@pcc.edu, election-methods@lists.electorama.com
>
> > You're right. I've drawn out the game theory matrix and the
> > honest outcome:
> > 49 C
> > 27 A>B
> > 24 B>A
> > is indeed the stable one, with A winning.
> >
> > So the only way for B to win is for his supporters to say they are
> > indifferent between A and C and threaten to bullet vote "B".
> > Then the A
> > supporters fall for it and vote "A=B" to prevent C from winning.
> > B wins.
> >
> > I wonder if this is sequence of events is likely at all.
> >
> > ~ Andy
> >
> >
> >
> > On Fri, Dec 9, 2011 at 2:31 PM, Jameson Quinn
> > wrote:
> > > No, the B group has nothing to gain by defecting; all they can
> > do is bring
> > > about a C win. Honestly, A group doesn't have a lot to gain
> > from defecting,
> > > either; either they win anyway, or they misread the election
> > and they're
> > > actually the B's.
> > >
> > > Jameson
> > >
> > > 2011/12/9 Andy Jennings
> > >
> > >> Here’s a method that seems to have the important properties
> > that we
> > >>> have been worrying about lately:
> > >>>
> > >>> (1) For each ballot beta, construct two matrices M1 and M2:
> > >>> In row X and column Y of matrix M1, enter a one if ballot
> > beta rates X
> > >>> above Y or if beta gives a top
> > >>> rating to X. Otherwise enter a zero.
> > >>> IN row X and column y of matrix M2, enter a 1 if y is rated
> > strictly>>> above x on beta. Otherwise enter a
> > >>> zero.
> > >>>
> > >>> (2) Sum the matrices M1 and M2 over all ballots beta.
> > >>>
> > >>> (3) Let M be the difference of these respective sums
> > >>> .
> > >>> (4) Elect the candidate who has the (algebraically)
> > greatest minimum
> > >>> row value in matrix M.
> > >>>
> > >>> Consider the scenario
> > >>> 49 C
> > >>> 27 A>B
> > >>> 24 B>A
> > >>> Since there are no equal top ratings, the method elects the same
> > >>> candidate A as minmax margins
> > >>> would.
> > >>>
> > >>> In the case
> > >>> 49 C
> > >>> 27 A>B
> > >>> 24 B
> > >>> There are no equal top ratings, so the method gives the same
> > result as
> > >>> minmax margins, namely C wins
> > >>> (by the tie breaking rule based on second lowest row value
> > between B and
> > >>> C).
> > >>>
> > >>> Now for
> > >>> 49 C
> > >>> 27 A=B
> > >>> 24 B
> > >>> In this case B wins, so the A supporters have a way of
> > stopping C from
> > >>> being elected when they know
> > >>> that the B voters really are indifferent between A and C.
> > >>>
> > >>> The equal top rule for matrix M1 essentially transforms
> > minmax into a
> > >>> method satisfying the FBC.
> > >>>
> > >>> Thoughts?
> > >>>
> > >>
> > >>
> > >> To me, it doesn't seem like this fully solves our Approval
> > Bad Example.
> > >> There still seems to be a chicken dilemma. Couldn't you
> > also say that the
> > >> B voters should equal-top-rank A to stop C from being elected:
> > >> 49 C
> > >> 27 A
> > >> 24 B=A
> > >> Then A wins, right?
> > >>
> > >> But now the A and B groups have a chicken dilemma. They should
> > >> equal-top-rank each other to prevent C from winning, but if
> > one group
> > >> defects and doesn't equal-top-rank the other, then they get
> > the outright
> > >> win.
> > >>
> > >> Am I wrong?
> > >>
> > >> ~ Andy
> > >>
> > >>
> > >>
> > >> 
> > >> Election-Methods mailing list - see http://electorama.com/em
> > for list
> > >> info
> > >>
> > >>
> > >
> >
>

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] This might be the method we've been looking for:

[Andy Jennings]

You're right.  I've drawn out the game theory matrix and the honest outcome:
49 C
27 A>B
24 B>A
is indeed the stable one, with A winning.

So the only way for B to win is for his supporters to say they are
indifferent between A and C and threaten to bullet vote "B".  Then the A
supporters fall for it and vote "A=B" to prevent C from winning.  B wins.

I wonder if this is sequence of events is likely at all.

~ Andy



On Fri, Dec 9, 2011 at 2:31 PM, Jameson Quinn wrote:

> No, the B group has nothing to gain by defecting; all they can do is bring
> about a C win. Honestly, A group doesn't have a lot to gain from defecting,
> either; either they win anyway, or they misread the election and they're
> actually the B's.
>
> Jameson
>
> 2011/12/9 Andy Jennings 
>
>>  Here’s a method that seems to have the important properties that we
>>> have been worrying about lately:
>>>
>>> (1) For each ballot beta, construct two matrices M1 and M2:
>>> In row X and column Y of matrix M1, enter a one if ballot beta rates X
>>> above Y or if beta  gives a top
>>> rating to X.  Otherwise enter a zero.
>>> IN row X and column y of matrix M2, enter a 1 if y is rated strictly
>>> above x on beta.  Otherwise enter a
>>> zero.
>>>
>>> (2) Sum the matrices M1 and M2 over all ballots beta.
>>>
>>> (3) Let M be the difference of these respective sums
>>> .
>>> (4) Elect the candidate who has the (algebraically) greatest minimum
>>> row value in matrix M.
>>>
>>> Consider the scenario
>>> 49 C
>>> 27 A>B
>>> 24 B>A
>>> Since there are no equal top ratings, the method elects the same
>>> candidate A as minmax margins
>>> would.
>>>
>>> In the case
>>> 49 C
>>> 27 A>B
>>> 24 B
>>> There are no equal top ratings, so the method gives the same result as
>>> minmax margins, namely C wins
>>> (by the tie breaking rule based on second lowest row value between B and
>>> C).
>>>
>>> Now for
>>> 49 C
>>> 27 A=B
>>> 24 B
>>> In this case B wins, so the A supporters have a way of stopping C from
>>> being elected  when they know
>>> that the B voters really are indifferent between A and C.
>>>
>>> The equal top rule for matrix M1 essentially transforms minmax into a
>>> method satisfying the FBC.
>>>
>>> Thoughts?
>>>
>>
>>
>> To me, it doesn't seem like this fully solves our Approval Bad Example.
>>  There still seems to be a chicken dilemma.  Couldn't you also say that the
>> B voters should equal-top-rank A to stop C from being elected:
>> 49 C
>> 27 A
>> 24 B=A
>> Then A wins, right?
>>
>> But now the A and B groups have a chicken dilemma.  They should
>> equal-top-rank each other to prevent C from winning, but if one group
>> defects and doesn't equal-top-rank the other, then they get the outright
>> win.
>>
>> Am I wrong?
>>
>> ~ Andy
>>
>>
>>
>> 
>> Election-Methods mailing list - see http://electorama.com/em for list
>> info
>>
>>
>

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] This might be the method we've been looking for:

[Andy Jennings]

>
> Here’s a method that seems to have the important properties that we have
> been worrying about lately:
>
> (1) For each ballot beta, construct two matrices M1 and M2:
> In row X and column Y of matrix M1, enter a one if ballot beta rates X
> above Y or if beta  gives a top
> rating to X.  Otherwise enter a zero.
> IN row X and column y of matrix M2, enter a 1 if y is rated strictly above
> x on beta.  Otherwise enter a
> zero.
>
> (2) Sum the matrices M1 and M2 over all ballots beta.
>
> (3) Let M be the difference of these respective sums
> .
> (4) Elect the candidate who has the (algebraically) greatest minimum
> row value in matrix M.
>
> Consider the scenario
> 49 C
> 27 A>B
> 24 B>A
> Since there are no equal top ratings, the method elects the same candidate
> A as minmax margins
> would.
>
> In the case
> 49 C
> 27 A>B
> 24 B
> There are no equal top ratings, so the method gives the same result as
> minmax margins, namely C wins
> (by the tie breaking rule based on second lowest row value between B and
> C).
>
> Now for
> 49 C
> 27 A=B
> 24 B
> In this case B wins, so the A supporters have a way of stopping C from
> being elected  when they know
> that the B voters really are indifferent between A and C.
>
> The equal top rule for matrix M1 essentially transforms minmax into a
> method satisfying the FBC.
>
> Thoughts?
>


To me, it doesn't seem like this fully solves our Approval Bad Example.
 There still seems to be a chicken dilemma.  Couldn't you also say that the
B voters should equal-top-rank A to stop C from being elected:
49 C
27 A
24 B=A
Then A wins, right?

But now the A and B groups have a chicken dilemma.  They should
equal-top-rank each other to prevent C from winning, but if one group
defects and doesn't equal-top-rank the other, then they get the outright
win.

Am I wrong?

~ Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] IRV variant

[Andy Jennings]

>
>
>>
>>
>> We typically abbreviate the names of criteria, using the initial letters of
>>
>>
>>
>> some of the words of their names.
>>
>> How about a new rule? We only get to abbreviate if there's an electowiki
> article / redirect at the abbreviation name (preferably linked from the
> abbreviation), or if we've fully spelled it out earlier in the same
> message.
>
> I unilaterally promise to follow this rule. This might be annoying to have
> to do sometimes but it would more than pay for itself if others followed
> suit.
>


I like it!  I'll follow it.

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] IRV3/AV3

[Andy Jennings]

>
> But there are ways in which I think IRV encourages spoiler scenarios.
>>  Consider a city that has a slight Democratic bias.  That is, Democrats win
>> by 8-10% most of the time.
>>
>> Step 1) A "Progressive" party starts up that thinks the Democrats have
>> gotten complacent and are not ambitious enough.  This resonates with people
>> but they're scared to vote for third parties.
>>
>> Step 2) IRV supporters tell everyone it's safe to rank your favorite
>> first.  Some people rank the Progressives first, and nothing bad happens!
>>  People gain confidence in IRV and ranking your favorite first.  More
>> people start ranking the Progressive first.
>>
>> Step 3) Eventually the Progressive party overtakes one of the top two
>> parties to make it into the final round.  The party overtaken is almost
>> certainly the Democrats (because the Progressive party wasn't taking any
>> votes from the Republicans).  So who did the Democrats put for their second
>> choice?  If even a small fraction of the Democrats put the Republican
>> second, then the Republican will win, and we have had a successful spoiler
>> scenario.  (Yes the Progressive was the spoiler even though they made it to
>> the final round.)  Voting for the Progressive caused the Republican to win.
>>  Progressives should've put the Democrat first.
>>
>> Step 4) Progressives and Democrats get very angry at each other and
>> everyone is angry at the Republicans.  A majority is angry at IRV.
>>
>
> Or what if the Dems get smart instead of angry and decide to work things
> thru with the Progs?  It's not IRV, it's the fact that the Dems weren't
> progressive enuf so as to make the Progs gain popularity and risk spoiling
> things for the Dems.  This is the same dynamic that exists today for FPTP.
>

Yes, ideally that would happen.

But as you say, the same dynamic exists today with FPTP.  And what has it
led to?  Total marginalization of third parties.  Everyone knows you only
should vote for the top two parties, otherwise you're wasting your vote.
 Two-party domination.  I'm not happy with that, and it seems to me that
IRV is prone to the same equilibrium.

On the other hand, the Tea Party movement has shown that the major parties
are movable, to some degree.  So I see what you're saying.  Maybe they
would be more movable with IRV.  But now you're talking about the whole
electoral/political landscape compensating for faults in IRV.  Wouldn't it
be better just to pick a better voting system to base the system on in the
first place?

Also, you made a remark at one point that the United States political
landscape is naturally highly-polarized into two parties so we should try
to work within that landscape.  But I believe Duverger's Law (
http://en.wikipedia.org/wiki/Duverger's_law).  That is, the US has
two-party domination _because_ we use plurality voting.  I believe the
political landscape would quickly re-configure itself if we had a better
voting system.

~ Andy

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Re: [EM] IRV3/AV3

[Andy Jennings]

>
> I believe there have to be only 3 candidates  and it has to be a close
> 3-way election for the 20% to be valid.
> As long as the odds are low enuf, it doesn't matter that much.  It just
> says that in some cases, some folks will have sour grapes.
>

As Jameson says, it depends how you simulate the voters.

But there are ways in which I think IRV encourages spoiler scenarios.
 Consider a city that has a slight Democratic bias.  That is, Democrats win
by 8-10% most of the time.

Step 1) A "Progressive" party starts up that thinks the Democrats have
gotten complacent and are not ambitious enough.  This resonates with people
but they're scared to vote for third parties.

Step 2) IRV supporters tell everyone it's safe to rank your favorite first.
 Some people rank the Progressives first, and nothing bad happens!  People
gain confidence in IRV and ranking your favorite first.  More people start
ranking the Progressive first.

Step 3) Eventually the Progressive party overtakes one of the top two
parties to make it into the final round.  The party overtaken is almost
certainly the Democrats (because the Progressive party wasn't taking any
votes from the Republicans).  So who did the Democrats put for their second
choice?  If even a small fraction of the Democrats put the Republican
second, then the Republican will win, and we have had a successful spoiler
scenario.  (Yes the Progressive was the spoiler even though they made it to
the final round.)  Voting for the Progressive caused the Republican to win.
 Progressives should've put the Democrat first.

Step 4) Progressives and Democrats get very angry at each other and
everyone is angry at the Republicans.  A majority is angry at IRV.

Yes, it's sour grapes, but it's not hard to see that it's a really bad
outcome.  A city that starts 45% Republican and 55% Democrat and then the
only change is that some of the Democrats put the Progressive first and the
Democrat second should not cause the Republican to win.  (Even if a few
Democrats put the Republican second.)

This was described from the perspective of the left, but it could have been
done just as easily in terms of Republicans and a "Libertarian" or "Tea"
party.  All that's required is that the growing third party be a little
more extreme than the two major parties (or, as Jameson put it, that the
three parties basically fall on a one-dimensional spectrum).  Then these
steps become natural, even probable.

The worst part is that IRV, and IRV supporters by telling people that it's
safe to rank your favorite first, encourage the progression down this
path-to-spoilers.

~ Andy

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[EM] IRV3/AV3

[Andy Jennings]

David,

My strongest feeling about your recently proposed system is that the
"three" is so arbitrary.

What if there are eight candidates running, and I really like five of them?
 Then approving three might not be enough.  I know you said that real
elections only seem to have four strong candidates, but the current
republican primary seems to have at least seven totally legitimate
candidates in the race.  Both 2008 primaries were the same way.  Sure, the
press is constantly trying to whittle it down to about four.  But why
should we let the press do the whittling?  Shouldn't that be done by the
voting system in some way?  Should we use a different system for these
larger elections?

If there are only three candidates running, then the AV step does nothing.
 If there are four candidates running, then the AV step is really
anti-plurality.

And as Kathy pointed out, you'd still better tell people that it's not safe
to put their favorite first.

~ Andy

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Re: [EM] how strong is support for IRV on this mailing list?

[Andy Jennings]

>
>  It would probably be an acceptable compromise for many of the Condorcet
>> supporters here.  But it has gotten no traction among IRV supporters.
>>
>
> are these staunch IRV supporters here on this list?


I was thinking of the vast FairVote contingent that's not on this list.

~ Andy

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Re: [EM] hello from DLW of "A New Kind of Party":long time electoral reform enthusiast/iconoclast-wannabe...

[Andy Jennings]

>
> 6b. I think that IRV3 can be improved upon by treating the up to three
>> ranked choices as approval votes in a first round to limit the number of
>> candidates to three then the rankings of the three can be sorted into 10
>> categories and the number of votes in each category can be summarized at
>> the precinct level.
>>
>
> I am not a big fan of IRV, though I find it better than plurality. Your
> "improvement", however, would remove its primary selling points. There
> would be incentives to truncate --- not use lower rankings --- and to bury
> --- use the lower rankings to dishonestly promote easy-to-beat turkeys. I
> suspect your proposed system would be opposed by many here as well as by
> many inside FairVote --- two groups which don't agree on much.
>

David, thanks for bringing up this idea.  Sounds interesting.  I'm willing
to consider it.  If you want to convince us on this list, then determining
which mathematical criteria it passes and focusing on specific voter
profiles where other methods do poorly would be a good strategy.

I would elaborate on Jameson's sentiment here.  I think this e-m list will
be very willing to discuss your method, but most of us will probably end up
not supporting it in the end.  That's just the law of averages, since the
vast majority of methods ever designed have serious problems and we're
pretty good at picking holes in methods here.  We're also biased toward
simplicity.  And we know that hybrid methods have a particularly bad track
record.  If you did get some of us to support it, it would probably take
months of light discussion and constant revisitation to do so.

On the other hand, I think you would have a very hard time getting IRV
supporters to even consider this method.  They don't seem very open to ANY
changes to IRV at all.  Someone once proposed a small change to IRV called
IRV-BTR where the step of eliminating the one candidate with the fewest
first place votes was replaced with taking the two candidates with the
fewest first place votes and eliminating the one that would lose in a
one-on-one race between those two.  It stands for IRV-Bottom Two Runoff and
it actually meets the Condorcet criterion.  It would probably be an
acceptable compromise for many of the Condorcet supporters here.  But it
has gotten no traction among IRV supporters.

~ Andy

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Re: [EM] Strategy and Bayesian Regret

[Andy Jennings]

On Fri, Oct 28, 2011 at 2:43 AM, Jameson Quinn wrote:

> What makes a single-winner election method good? The primary consideration
> is that it gives good results. The clearest way to measure the quality of
> results is simulated voter utility, otherwise known as Bayesian Regret (BR).
>
> This is not the only consideration. But for this message, we'll discount
> the others, including:
>
>- Simplicity/voter comprehension of the system itself
>- Ballot simplicity
>- Strategic simplicity
>- Perceived fairness
>- Candidate/campaign strategy incentives
>
>
> Calculating BR for honest voters is relatively simple, and it's clear that
> Range voting is best. But how do you deal with strategy? Figuring out what
> strategies are sensible is the relatively easy part; whether it's
> first-order rational strategies (as James Green-Armytage has worked 
> out)
> or n-order strategies under uncertainty (as Kevin Venzke does) or even just
> simple rules of thumb justified by some handwaving (as in Warren Smith's
> original BR work over 10 years ago), we know how to get this far. But once
> you've done that, you still have to make some assumptions about how many
> voters will use strategy. There are several ways to go about this. In order
> of increasing realism, these are:
>
>1. Assume that voters are inherently strategic or honest and do not
>respond to strategic incentives. Thus, the number of voters using strategy
>will be the same across different systems. Warren Smith's original BR work
>with IEVS seems to have shown that Range is still robustly best under these
>conditions. Although I am not 100% convinced that his definition of 
> strategy
>was good enough, the results are probably robust enough that they'd hold up
>under different definitions.
>2. Avoid the question, and just look at strategic worst cases. I count
>this as more realistic than the above, even though it's just a special case
>of 100% strategy, because it doesn't give unrealistically-precise numbers.
>But of course, if I say that method X has a BR score somewhere between Y 
> and
>Z, and method A has a BR between B and C, if YX is better than A. So you lose the ability to answer the important
>question, "which method is better?"
>3. Try to use some rational or cognitive model of voters to figure out
>how much strategy real people will use under each method. This is hard work
>and involves a lot of assumptions, but it's probably the best we can do
>today.
>4. Try to get real data about how people would behave in high-stakes
>elections. This is extremely hard, especially because low-stakes polls may
>not be a valid proxy for high-stakes elections.
>
> As you might have guessed, I'm arguing here for method 3. Kevin Venzke has
> done work in this direction, but his assumptions --- that voters will look
> for first-order strategies in an environment of highly volatile polling data
> --- while very useful for making a computable model, are still obviously
> unrealistic.
>
> What kind of voter strategy model would be better? That is, what factors
> probably affect a voters' decision about whether to be strategic? I can
> think of several. I'll give them in order from easiest explanation to
> hardest; the order below has nothing to do with the relative importance.
>
> First, there's the cognitive difficulty of strategizing versus voting
> honestly. In a system like SODA, an honest bullet vote is much simpler than
> a strategic explicit truncation, so we can expect that this factor would
> lead to less strategy. In a ranked system, it is arguably easier to
> strategically exaggerate the perceived frontrunners (Warren's "naive
> exaggeration strategy" or NES) than to honestly rank all the candidates, so
> we might expect this factor to increase strategizing. Note that the
> cognitive burden for strategy is reduced if defensive and offensive
> strategies are the same. For instance, under Range, exaggeration is always a
> good idea, whether it's offensively or defensively.
>
> (Note: This overall cognitive factor is probably most important for "lazy
> voters", and such "lazy voters" are also probably open to strategic and/or
> honest advice from peers, so the cognitive factor is perhaps not too
> important overall.)
>
> Second, there's offensive strategy. The more likely it is that strategy
> will be advantageous against honest opponents, and the more advantageous it
> is likely to be, the more strategy people will use. The first question has
> been addressed by the Green-Armytage 
> paper;
> it appears that IRV is relatively strategy-resistant, Condorcet is middling,
> and Range and Approval are likely to be subject to strategy. But remember,
> the whole point of this discussion is that strategy is not so much a problem
> in itself, as an input to the model for det

Re: [EM] Help naming a new method

[Andy Jennings]

Hi Kristen,

I'm having trouble understanding what your goal is in re-posting the first
four paragraphs from this April post of mine.
http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-April/027194.html

Is this some new kind of mailing list spam?  Or did you have some questions
about the method?

In any case, thank you for bringing up this method again.  I still like it
and like to discuss it.  I still haven't decided whether to call it "mutual
median" or "chiastic voting" or something else.

~ Andy



On Mon, Oct 24, 2011 at 6:17 AM, Kristen Eisenberg <
kristen.eisenb...@yahoo.com> wrote:

> Hi all,
>
>
> I have a new voting method and I think I need some help naming it. Let me
> say, first of all, that I admit it may be too complicated for use by the
> general public. It's a score aggregating method, like Score Voting.
>
>
> Each voter scores each candidate on a scale of 0-100. Each candidate's
> votes are aggregated independently, with their societal score given by
> finding the largest number, x, such that x percent of the voters gave that
> candidate a grade of x or higher.
>
>
> So a candidate where 71% of the people gave a grade of 71 or higher (but
> the
> same can't be said of 71+epsilon) will get a final score of 71.
>
>
> It shares a strategy-resistance property with the median that any voter
> whose score was above the societal score, if he were allowed to change his
> vote, could do nothing to raise the societal score. (Also, a voter whose
> score was below the societal score could do nothing to lower the societal
> score.) This means that if you're only grading one candidate (e.g. choosing
> an approval rating for the sitting president), then there is a strong
> incentive for everyone to submit an honest vote.
>
>
> Kristen Eisenberg
>
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>
>

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] Proposed experiment

[Andy Jennings]

Jameson's email actually came through fine for me.

But I have definitely seen enough mangled emails to agree that fixed-width
can be problematic.


On Fri, Oct 21, 2011 at 12:13 PM, Warren Smith  wrote:

> I suspect you intended some careful formatting which the web posting has
> obliterated, rendering this proposal essentially unreadable.
> You can use dots
> to.make...sure
> things...are...aligned
> at least if reader uses a constant width font.
>
> --
> Warren D. Smith
> http://RangeVoting.org  <-- add your endorsement (by clicking
> "endorse" as 1st step)
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>

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Re: [EM] majority judgement question

[Andy Jennings]

Good points, Ross and Jameson.

Section 4.3 of my dissertation (http://ajennings.net/dissertation.pdf) talks
about this very thing.

The Ac-Bc rule was proposed by David Gale (
http://en.wikipedia.org/wiki/David_Gale) before his passing, to Balinski and
Laraki directly.  I proposed a rule very similar to Jameson's (Ac - Bc)/(Mc
+ |Ac - Bc|).  Mine was (Ac - Bc)/(2*Mc).  Both are continuous everywhere
(assuming fractional voters), even at the junction where the median changes
from one grade to another.  (See graphs in the pdf.)  Also in my
dissertation, I gave examples for the other two rules where a small change
in the voter profile could cause a candidate to fall multiple rankings.

On the other hand, Balinski and Laraki's rule is constant with respect to
either Ac or Bc almost everywhere.  I think this might make it a little more
resistant to strategic voting.  Plus, the remove-one-median-rating-at-a-time
method has a certain simplicity and elegance to it, especially for very
small electorates, even if it gets a little convoluted for large ones.

~ Andy



On Wed, Oct 19, 2011 at 9:12 AM, Jameson Quinn wrote:

> Great suggestion. I've been thinking along those lines, but I hadn't
> expressed it as clearly.
>
> And now that Ross has given me this idea, I can make it even simpler.
>  Ross's suggested process is of course equivalent to, and harder to explain
> than, using (number above median grade)-(number below median grade) as a
> score. The only disadvantage of my version is that it could give negative
> numbers. But almost all people over the age of 10 (and a lot of people under
> that age) can handle negative numbers just fine, so I think that's OK.
>
> This tiebreaker process is good. It will also tend to agree with the MJ
> one, as long as the tied candidates have approximately the same number of
> votes at the median grade - which will generally be true for two candidates
> whose strengths are similar enough to tie the median grade in the first
> place.
>
> Here's another "tiebreaker" which I've developed. The advantage is that it
> gives a single real-number grade to each candidate, thus avoiding the issue
> of "ties" in the first place. I call it "Continuous Majority Judgment" or
> CMJ.
>
> Rc= Median rating for candidate c (expressed numerically; thus, letter
> grades would be converted to grade-point-average numbers, etc.)
> Mc= Number of median ratings for candidate c
> Ac= Number of ratings above median for candidate c
> Bc= Number of ratings below median for candidate c
> |x| = standard notation for absolute value of x
>
> CMJ rating for c = Rc + ((Ac - Bc)/(Mc + |Ac - Bc|))
>
> For approval (that is, binary ratings), the CMJ rating works out to be
> equal to the fraction of 1s, as you'd expect. Note that the adjustment
> factor is always in the range of -0.5 to 0.5, because the difference |Ac -
> Bc| can never be greater than Mc or it wouldn't be the median.
>
> I prefer either of these methods to the MJ method - not for results, but
> for simplicity. (Ac - Bc) is simplest to explain, while CMJ is simplest to
> compare candidates / post results. All three of them should give the same
> results in almost all cases. But Balinski and Laraki preferred the
> remove-one-median-rating-at-a-time method because they could prove more
> theorems about it, and they wrote the MJ book, so until I write my own book
> about it I'm fine with promoting their method.
>
> JQ
>
>
> 2011/10/19 Ross Hyman 
>
>>  It seems to me that there is a simpler way to compare candidates with
>> the same median grade in majority judgement voting than the method described
>> in the Wikipedia page for majority judgement.  Why isn't this simpler way
>> used?
>>
>> Every voter grades every candidate.  Elect the candidate with the highest
>> median grade (the highest grade for which more than 50% of voters grade the
>> candidate equal to or higher than that grade.)  If there are two or more
>> candidates with the same highest median grade, elect the candidate with the
>> highest score of those with the highest median grade.  A candidate's score
>> is equal to the the number of voters that grade the candidate higher than
>> the median grade plus the number of voters that grade to candidate equal to
>> or higher than the median grade.  This is equivalent to giving one point to
>> each candidate for each voter who grades the candidate its median grade and
>> two points for each voter who grades the candidate higher than its median
>> grade.  Motivation:  voters who vote median grade instead of something lower
>> should increase the score for the candidate by the same amount as voters who
>> vote above the median grade instead of equal to the median grade.  With this
>> scoring, going from less than median to median increases the candidate score
>> by one point and going from median to higher than median also increases the
>> candidate score by one point.
>>
>> Example using same example from Wikipedia's majority judgement entry:
>> 

Re: [EM] Declaration Status

[Andy Jennings]

>>
>>  reading this mail here. No response yet.
>>* I haven't contacted Nicholas Tideman. He may be reading this too,
>>
>>  but if he's not, I would like to get as many high-powered names
>>  such as those above to sign on before we talk to him.
>>* If we had a big-name author, I have a contact with the editor of
>>  /Science/, so we might be able to get an editorial published.
>>* As you can see on the declaration, Warren Smith has already signed.
>>
>>
>> Meanwhile, I agree that a good css stylesheet would dramatically improve
>> the look of the declaration on 
>> http://www.votefair.org/**declaration.html<http://www.votefair.org/declaration.html>
>> .
>>
>> Jameson
>>
>> 2011/10/18 Andy Jennings > <mailto:elections@**jenningsstory.com >>
>>
>>
>>So the declaration is all done, right?  Ready to send out to
>>everyone we think might be interested?
>>
>>I have a bunch of people I want to notify, but for some reason I
>>don't feel like sending them to either the Google Doc or to
>>Richard's page 
>> (http://www.votefair.org/**declaration.html<http://www.votefair.org/declaration.html>).
>>  Niether
>>seems appropriate for a first impression.
>>
>>Anyone else feel the same way?
>>
>>~ Andy
>>
>>
>
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>

Election-Methods mailing list - see http://electorama.com/em for list info

[EM] Declaration Status

[Andy Jennings]

So the declaration is all done, right?  Ready to send out to everyone we
think might be interested?

I have a bunch of people I want to notify, but for some reason I don't feel
like sending them to either the Google Doc or to Richard's page (
http://www.votefair.org/declaration.html).  Niether seems appropriate for a
first impression.

Anyone else feel the same way?

~ Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] Help requested: rankings corresponding to pairwise array

[Andy Jennings]

If all you care about are margins, then you can build up the pairwise array
from "atomic" pairs of voters.

For example, I consider ABCD and DCAB to be an atom for A>B because all
other pairwise races cancel out, yielding the following margins matrix:

  |  A  |  B  |  C  |  D  |
===+=+=+=+=+
 A |   0 |  +2 |   0 |   0 |
---+-+-+-+-+
 B |  -2 |   0 |   0 |   0 |
---+-+-+-+-+
 C |   0 |   0 |   0 |   0 |
---+-+-+-+-+
 D |   0 |   0 |   0 |   0 |
---+-+-+-+-+

But I don't know how this fits in with the way you calculate approval.

~ Andy Jennings




On Mon, Oct 10, 2011 at 2:51 PM, Ted Stern wrote:

> Hi,
>
> Say I have a pairwise array that looks like
>
>   |  A  |  B  |  C  |  D  |
> ===+=+=+=+=+
>  A |  60 |  45 |  46 |  60 |
> ---+-+-+-+-+
>  B |  55 |  55 |  55 |  49 |
> ---+-+-+-+-+
>  C |  54 |  45 |  54 |  52 |
> ---+-+-+-+-+
>  D |  40 |  51 |  48 |  51 |
> ---+-+-+-+-+
>
> For this example, I assume that a tie between candidates is counted as
> one vote for each candidate, and the diagonal entry is equal to the
> maximum non-diagonal entry on that row.  This is a way to extract
> Approval from the pairwise array.
>
> The exact numbers are not important.  What really matters to me is
> that the candidates in descending order of approval are A, B, C, D,
> and the pairwise outcomes look like
>
>   |  A  |  B  |  C  |  D  |
> ===+=+=+=+=+
>  A |  -  |  L  |  L  |  W  |
> ---+-+-+-+-+
>  B |  W  |  -  |  W  |  L  |
> ---+-+-+-+-+
>  C |  W  |  L  |  -  |  W  |
> ---+-+-+-+-+
>  D |  L  |  W  |  L  |  -  |
> ---+-+-+-+-+
>
> The reason I'm looking for a set of ranked ballots that lead to this
> outcome is that I believe it might be a counterexample to Forest
> Simmons' Enhanced DMC proposal.
>
> If there is a set of rankings that lead to this array, then B would be
> the winner under Schulze, Ranked Pairs, River and DMC, but Enhanced
> DMC would pick either A or C.
>
> Ted
> --
> araucaria dot araucana at gmail dot com
>
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>

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Re: [EM] Is there any profile where IRV is worse than Plurality?

[Andy Jennings]

Very good example.  Thanks.



On Fri, Sep 23, 2011 at 4:32 PM, Toby Pereira  wrote:

> Andy
>
> Candidates can go up the rankings or down when a candidate is eliminated in
> IRV, and it's possible to do both in different rounds. A plurality winner
> could slip down and be eliminated in a case where they would have still gone
> up again and won had they not been eliminated. So:
>
>  30: A>B>C>D
> 26: B>A>C>D
> 24: C>A>B>D
> 10: D>B>A>C
> 10: D>C>A>B
>
>  Round 1:
> A: 30
> B: 26
> C: 24
> D: 20
>
>  D eliminated
>
>  Round 2:
> B: 36
> C: 34
> A: 30
>
>  A eliminated
>
>  Round 3:
> B: 66
> C: 34
>
>  B wins the IRV election whereas A would have been the plurality winner
> and the (quite strong) Condorcet winner.
>
>  A>B: 64-36
> A>C: 66-34
> A>D: 80-20
>
> Toby
>
>
>   *From:* Andy Jennings 
> *To:* EM 
> *Sent:* Saturday, 24 September 2011, 0:13
> *Subject:* [EM] Is there any profile where IRV is worse than Plurality?
>
> Since we're discussing IRV quite a bit lately, here's a question:
>
> - Is there any voter profile where IRV gives a worse result than plurality?
>
> I can't seem to think of one.  So is it true that, mathematically, IRV
> dominates Plurality, that is IRV is always at least as good as plurality and
> sometimes strictly better?
>
>
> Even if that is true, I still believe that IRV is harmful, socially.  By
> successfully avoiding the traditional spoiler problem (where spoilers are
> very weak), it leads people to believe that it is immune to the spoiler
> problem.  Then it leads them directly into the second-tier spoiler scenarios
> where a large group of voters will, by voting honestly, cause their least
> favorite candidate to win.
>
> ~ Andy
>
> 
>

Election-Methods mailing list - see http://electorama.com/em for list info

[EM] Is there any profile where IRV is worse than Plurality?

[Andy Jennings]

Since we're discussing IRV quite a bit lately, here's a question:

- Is there any voter profile where IRV gives a worse result than plurality?

I can't seem to think of one.  So is it true that, mathematically, IRV
dominates Plurality, that is IRV is always at least as good as plurality and
sometimes strictly better?


Even if that is true, I still believe that IRV is harmful, socially.  By
successfully avoiding the traditional spoiler problem (where spoilers are
very weak), it leads people to believe that it is immune to the spoiler
problem.  Then it leads them directly into the second-tier spoiler scenarios
where a large group of voters will, by voting honestly, cause their least
favorite candidate to win.

~ Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] Title for the Declaration

[Andy Jennings]

On Mon, Sep 19, 2011 at 1:09 PM, Richard Fobes  wrote:


> "Declaration of Election-Method Reform Advocates -- Let's Move Democracy
> Beyond Plurality and First-Past-the-Post Voting"
>

I like this, or maybe (as you suggest):

"Declaration of Election-Method Reform Advocates -- A Call to Move Democracy
Beyond Plurality and First-Past-the-Post Voting"

I do think "demand" is too strong.

~ Andy

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Re: [EM] Weak Condorcet winners

[Andy Jennings]

Some general comments about the "weak Condorcet" concern:

- The one time I mentioned "better voting systems" to our city's vice-mayor
(who was actually running for mayor at the time), her first question was,
"In those systems couldn't someone win who was everyone's second choice but
nobody really liked?"  So I think this concern definitely resonates with
people, especially politicians.  Even though that specific election was
non-partisan, I do tend to agree that perhaps our two-party landscape
polarizes people and strengthens this "weak Condorcet" concern.

- It seems like the real question that should be asked is "how many voters
think this candidate is fit to govern", and it seems like "number of first
place votes" is an awfully poor proxy for that.  If there are more than a
few candidates, then I may think that my top two or three candidates are
completely fit to govern, or I might think none of them are.  The ranked
ballot doesn't really give us enough information to answer the fit-to-govern
question.  You need a cardinal ballot to answer it.  The approval ballot
would be good.  The MJ ballot, with words for the grading levels, would be
even better.  You could even use a ranked ballot with an approval cutoff and
automatically eliminate any candidate who didn't get 33% approval.

- Even if the criterion is "we want a winner with broad support who also has
deep support, or a core of passionate voters", how can we evaluate that with
a ranked ballot?  I might be passionate about my top two or three choices,
or I might not really like any of them.  A cardinal ballot is still the
proper way to make that evaluation.

Maybe I'll try to formulate this into some talking points...

Andy





On Fri, Sep 23, 2011 at 5:09 AM, Jameson Quinn wrote:

> Juho is right that the term "weak CW" is not inherently clear. The point
> is, that we're defining the meaning of this term for the purposes of
> discussion. The paradigmatic case is something like:
> 45: A>C
> 40: B>C
> 15: C
>
> C is only "weak" in the sense of first-choice support. The narrowest
> pairwise defeat is 55:45, which is not a weak result. So "weak" should not
> be understood to mean weak in every way.
>
> Also, in discussing this problem, we've repeatedly said that the principal
> problem is not the result itself, which may in many cases be perfectly
> correct in any meaningful sense; but the fear of the result. A method which
> could potentially elect a weak-CW, could theoretically thereby elect a
> relatively-unknown candidate; voters can be convinced to fear that.
>
> It is perfectly true that sometimes the weak-CW is the correct answer, but
> it's also beside the point.
>
> Jameson
>
> 2011/9/23 Juho Laatu 
>
>> I think term "weak CW" should not be used as a general term without
>> referring to in what sense that winner is weak. There are different
>> elections and different needs. In some of them weak CW is a good choice, in
>> some others not.
>>
>> 51: A
>> 49: B
>>
>> As you can see A is a weak CW here. Not so if you measure the number of
>> first preferences, but very much so if you compare the strength of the
>> winner to the strength of its competitors.
>>
>> 45: A>B>C
>> 5: B>A>C
>> 5: B>C>A
>> 45: C>B>A
>>
>> Here B is a strong CW since the alternatives are
>>
>> A = set tax level to 20%
>> B = set tax level to 19%
>> C = set tax level to 18%
>>
>> It is obvious that B is the alternative that should be chosen. Other end
>> results would be plain wrong. B is not a weak candidate in any way.
>>
>> Term "weak CW" seems to be heavily linked to the understanding that the
>> winner should have lots of first preference support (or it should often
>> belong to the most preferred subgroup of the candidates). This is a
>> viewpoint that is quite strong in two-party countries (that want to stay as
>> two-party countries) since in those countries whoever is in charge has
>> typically more than 50% support among the voters. But what is weak in this
>> kind of thinking need not be weak in some other set-up.
>>
>> > Failing the majority criterion is, in my view, a similar flaw to
>> electing a weak CW.
>>
>> I think electing a weak CW is a flaw only in some set-ups with some
>> specific requirements that make weak CW a bad choice. Majority criterion is
>> a requirement far more often, but not always. There are also elections where
>> majority is not a requirement. And there are also elections where it is
>> sometimes a requirement to elect against the majority opinion.
>>
>> Juho
>>
>>
>>
>>
>> On 23.9.2011, at 12.26, Jameson Quinn wrote:
>>
>>
>>
>> 2011/9/23 James Gilmour 
>>
>>> Warren Smith  > Sent: Friday, September 23, 2011 1:53 AM
>>> > At the present time, Jon Huntsman gets only a tiny
>>> > fraction of the USA-republican-presidential-nomination votes,
>>> > according to polls. For this reason, certain media people
>>> > have been saying it is a travesty Huntsman continues to run
>>> > and is allowed in debates, etc.
>>> >
>>> > However...
>>> > it

[EM] Title for the Declaration

[Andy Jennings]

The current title for the declaration is "Declaration of Election-Method
Experts and Enthusiasts".  I'm wondering if we can improve on this.
 Jameson, Richard, and I were discussing this in the comments and it was
suggested to take it to the group.

First, let me say that it's not a bad title, and I'm fine if this ends up
being the final title.  My main complaint is that it seems so passive.  I
think it would be better with the word "reform" in there.  Maybe something
like this:

"A Call for Election-Method Reform - A Declaration of Election-Method
Experts and Enthusiasts"

Anyone have any thoughts or suggestions?

~ Andy

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Re: [EM] Dodgson and Kemeny "done right"?

[Andy Jennings]

On Fri, Sep 16, 2011 at 5:27 PM, Warren Smith  wrote:

> On Fri, Sep 16, 2011 at 8:21 PM,   wrote:
> > You're right, I forgot that Kemeny only needed the pairwise matrix.  And
> according to Warren
> > Dodgson is summable. I don't see how.
>
> --if "Dodgson" minimizes the total travel distance for all candidates
> on all ballots to "travel" from their current position to the
> output-permutation's position,
> and "position" means "rank" then all you need to know is the total
> number of times candidate X is in rank Y on any input ballot, for all
> (X,Y).
>
> That count-info is publishable by each precinct.  For N candidates this
> is N^2 different counts published by each precinct.
>
> Right?


I think we just have to find the minimal travel distance to make someone a
Condorcet winner.

We don't have to make all of the ballots identical.

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Re: [EM] [CES #3605] Re: Kemeny Condorcet method. Apparently not a good choice for those of us who want to know who won in our lifetimes.

[Andy Jennings]

Kemeny has a couple things going for it:

1. Peyton Young argues here (
http://www.econ.ucsb.edu/~tedb/Courses/UCSBpf/readings/PeytonYoungCondorcet.pdf)
that it is probably the rule that Condorcet himself had in mind.

2. It is mathematically simple and elegant, so it is easier to prove things
about it than the other Condorcet methods.  Hence, it appears in lots of
theoretical papers.

In my opinion, these are the reasons that it is one of the "frontrunners"
among the Condorcet methods.  It is interesting that neither of these
reasons relates to its performance (either in terms of worst-case runtime or
criterion compliance), so I am fine that we question it here.  However, I
don't know that we can ever dethrone it as one of the "frontrunners", so
maybe it's worth leaving in the declaration on those grounds alone...

I, personally, feel that Warren's points are well-made and that NP-complete
worst case behavior is of some concern, but it's not a deal-killer for me.
 Also, Kemeny is not cloneproof, but I think the fault is sufficiently
difficult to exploit that it will be very rare.  Famous last words, right?
 So my mind can be changed on these opinions.  I'm just saying at this point
that I, personally, feel that Kemeny is good enough.

But I'm interested to hear from others...

Andy





On Mon, Sep 12, 2011 at 10:07 AM, Toby Pereira  wrote:

> How much support does the Kemeny method actually have? I know Richard Fobes
> supports it obviously. But as far as I understand, is problems run deeper
> than runtime. Like not being cloneproof.
>
> When I first found out about Condorcet methods, I thought it looked like
> the most "natural" one and seemed the best to me. It has a "maximum
> likelihood estimator" property, but that doesn't apply to real life. It
> assumes that there is "an objectively 'correct', but unknown preference
> order over the alternatives, and voters receive noisy signals of this true
> preference order" (from Wikipedia). In real life, people aren't all working
> towards trying to find the "objectively best" candidate in this way.
>
> It may be the best (ignoring runtime) at finding a winner when voters are
> "neutral" and not all with their own opinions, and also I've heard that it's
> good at producing a full order. But in single-winner elections those don't
> apply. Other Condorcet systems can find a full order anyway, even if they
> aren't as "good" at it. And you wouldn't want to decrease the quality of the
> winner in a single-winner method just to improve the rest of the order.
>
> Also, I wonder where Kemeny and others (such as Schulze) differ in the
> winner, why they differ. Is it in most cases because Kemeny-Young is not
> cloneproof? If so, that's a point against Kemeny-Young. Is it to do with
> margins/winning votes? That's probably not an important factor anyway,
> because methods can generally be converted from winning votes to margins or
> vice versa.
>   *From:* Jameson Quinn 
> *To:* electionscie...@googlegroups.com
> *Cc:* Kristofer Munsterhjelm ; election-methods <
> election-meth...@electorama.com>
> *Sent:* Monday, 12 September 2011, 16:00
> *Subject:* Re: [CES #3605] Re: [EM] Kemeny Condorcet method. Apparently
> not a good choice for those of us who want to know who won in our lifetimes.
>
> I wonder if there aren't also Kemeny optimizations similar to IRV's
> multiple-elimination, which would work well for real data.
>
> That is to say, that in real life, with enough candidates to make the
> problem hard, there are even more likely to be Condorcet losers (also-rans)
> than Condorcet winners. By successively peeling off the Condorcet loser, you
> could quickly reduce the problem. This much is a clear, easy optimization,
> and could easily bring an untractable 60 candidates down to a tractable 20.
>
> The analogy with the IRV case is that if you had a Smith set of condorcet
> losers, but they all (by some measure similar to IRV's summing) were "far
> enough behind" all other candidates, then it might be safe to treat them as
> a bloc, enabling a divide and conquer of the Kemeny problem. Or even if it
> weren't 100% safe, it would certainly be a good first guess. This part is
> just an intuition of mine, and it would certainly take further thought
> before you could use this idea.
>
> Jameson Quinn
>
>
>
> 2011/9/12 Warren Smith 
>
> one very simple algorithm for Kemeny ranking
> is the "quicksort" method.
>
> That is, you pick a random candidate X.  You then
> partition the others into two sets: above and below Xm,
> by consulting random voters.
> You then recursively sort the two resuitling subsets of candidates.
>
> This method produces random ordering of the candidates selected from a
> non-uniform distribution, which is biased in a good direction.  In
> particular if the votes
> all agree then it will get the best permutation immediately.
> The point is that this bias means, that if you keep trying this over
> and over, you will find the best permutation faster th

Re: [EM] Election Methods Code Repository Proposal

[Andy Jennings]

On Sun, Sep 11, 2011 at 9:15 PM, Greg Nisbet wrote:

> Anyway, IEVS is in C, RubyVote and PythonVote are obviously in Python,
> and my old code is in Java. If the community could settle on a single
> language for reference implementations (speed being less important
> here than clarity and familiarity) of various voting methods and maybe
> a quick language such as C, C++, D, or Java when additional speed is
> required, and possibly an efficiently parallelizable language (e.g.
> Erlang, Haskell) to allow for distributed computation and greater
> scalability.
>

I definitely agree on the "reference implementation" part.  I vote for
Python, but maybe someone should set up an approval-style poll.

As for a "fast language implementation" and a "parallel language
implementation", that's not a bad idea, but I don't know that we're ready to
maintain three different code repositories, yet.

~ Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] Last call for edits to consensus statement

[Andy Jennings]

On Sun, Sep 11, 2011 at 9:23 AM, Jameson Quinn wrote:

> For instance, for range voting, the equipment could count how many people
> gave each rating to candidate A, from a simple array of choices such as 0,
> 1, 50, 98, 99, or 100. Most choices are bunched near the ends of the scale,
> as this helps range voters get near to the maximum power from their ballot.
>

I'm glad these sentences have been removed.  I think this point is way too
confusing for the intended audience.

~ Andy

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Re: [EM] Executive Summary for Declaration

[Andy Jennings]

On Thu, Sep 8, 2011 at 11:01 AM, Richard Fobes  wrote:

> Removing the names of the "good" Condorcet methods is not acceptable. (We
> can change the word "good" if that's the issue.)
>
> Already we dropped "Condorcet-Tideman" (ranked pairs) from the list because
> Tideman himself prefers Condorcet-IRV (according to what I understand from
> Jameson Quinn).
>
> Originally the statement said that all the supported methods have been used
> to elect officials in organizations, but I had to change that to "our four
> supported methods" because Condorcet-IRV and Condorcet-Approval have not
> been used to elect officials (if I understand Jameson Quinn correctly).
>
> Listing specific Condorcet methods is essential. (As an exaggerated
> similarity, imagine expressing support for Bucklin methods and then not
> mentioning Majority Judgement as a specifically supported method.) The
> differences between the Condorcet methods are significant, especially in
> terms of how easy or hard they are to explain. The fact that they produce
> very similar results is just part of the picture.
>
> And we don't want someone taking the words "any of the Condorcet methods"
> literally, choosing an obscure Condorcet method that no one really supports,
> trying to get an organization to adopt it, and then having to answer the
> question "has it ever been used to elect officials?" with a "no". We want to
> fully support what we say we support.
>
> Personally I'd be happy to drop the reference to Condorcet-Approval, but
> I'm assuming that Approval advocates would not approve.



This is a good argument, and I don't disagree.  But still it feels like the
tone dives from conversational to technical right there.

Also, I feel like I know Condorcet-Kemeny and Condorcet-Schulze very well,
but I don't have a good feeling for Condorcet-Approval or Condorcet-IRV, and
I'm pretty informed about this stuff.  Those two aren't even listed on the
wikipedia page for Condorcet
Method.
 It doesn't seem like we've discussed them that much on this list, either.
 I guess I am fine with pretty much any Condorcet method, so it just seems
arbitrary to list these four.

But if everyone else is fine with it, that's fine.  It's really just minor
for me.  It won't keep me from signing.

Andy

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Re: [EM] Executive Summary for Declaration

[Andy Jennings]

I do like the executive summary.  Maybe it's a little too long?

I think we could do without the sentence "Some good Condorcet methods
are:..."

I do think the PR section could be significantly shortened.

I made a few changes.  Feel free to review, roll back, and discuss if you
think I have erred.

~ Andy Jennings



On Wed, Sep 7, 2011 at 9:25 PM, Richard Fobes
wrote:

> On 9/7/2011 2:09 PM, Peter Zbornik wrote:
> > I still think the 12 page declaration (incl table of contents) needs an
> > executive summary. The table of contents does not in my honest opinion
> > give good enough information.
>
>
> I agree that the declaration needs an executive summary.  Here is what I've
> come up with as a first draft:
>
> - Executive Summary -
>
> This declaration, which has been signed by election-method experts from
> around the world, publicly denounces the use of plurality voting in
> governmental elections.  Plurality voting mistakenly assumes that the
> candidate who receives the most ballot marks – on single-mark ballots – is
> the most popular.  Plurality voting also suffers from vote splitting, which
> is what forces political parties to offer only a single choice in each
> election.
>
> As replacements for plurality voting, this declaration recommends four
> significantly fairer election methods, namely, in alphabetical order:
> Approval voting, any Condorcet method, Majority Judgment voting, and Range
> voting.  These methods use better ballots – namely the Approval ballot,
> Ranked ballot, and Score ballot – to collect much more preference
> information compared to plurality's primitive single-mark ballot.
>
> The lack of awareness about plurality voting's unfairness arises from its
> use of single-mark ballots, which not only fail to collect enough
> information to correctly identify the most popular candidate, but also fail
> to collect enough information to produce proof or evidence of the unfair
> results.
>
> Computer technology now makes it easy to count better ballots and correctly
> identify who deserves to win.  All the supported methods are based on the
> fact that a majority of voters, not just a plurality of voters, must approve
> or prefer the winning candidate in order to produce fairer results.
>
> In spite of the academically recognized, well-known unfairness of plurality
> voting, it is used throughout Canada, the United Kingdom, the United States,
> and to some extent nearly every democracy around the world.  As a
> consequence of adopting fairer election methods, this declaration's signers
> expect the benefits to include a dramatically reduced gap between voters and
> government, more easily -- and fairly -- resolved political conflicts, and
> significantly increased economic prosperity for any region that adopts
> fairer election methods.
>
> Significantly the election-method experts do not support the use of
> instant-runoff voting, which is also known as the alternative vote. This
> method is based on the mistaken belief that the candidate with the fewest
> plurality votes is the least popular candidate.
>
> The four supported methods also can be adopted for use in non-governmental
> situations, such as electing an organization's officers, making democratic
> decisions, and electing corporate board members.
>
> The signers of this declaration do not share any common political beliefs,
> and are confident that the recommended election reforms will not favor any
> particular political parties or political orientations. Their clearly stated
> goal is to improve election fairness by replacing primitive plurality voting
> with any of the fairer supported methods. Their expectation is that a higher
> level of democracy will lead to higher standards of living, reduced
> conflicts, and widespread greater economic prosperity, just as replacing
> monarchies and dictatorships with plurality voting has produced dramatic and
> widespread benefits.
>
> The signers urge everyone to learn more about how voting should be done –
> using Approval voting, Condorcet methods, Majority Judgment voting, or Range
> voting – and begin adopting the supported voting methods in whatever
> situations currently, yet inappropriately, use plurality voting.
>
> - end -
>
> It mentions some concepts that currently aren't in the declaration itself,
> so if this executive summary is liked, adjustments will need to be made in
> either this summary or in the declaration.
>
> Also note that this summary does not mention PR. We still need to decide
> what to do about that section. It is long yet just says we like PR but
> oppose closed-list PR.
>
> Richard Fobes
>
>
> On 9/7/2011 2:09 PM, Peter Zbornik wr

Re: [EM] Lp-ball range

[Andy Jennings]

>
> > The unit ball for method two has no corners or bulges (which all other
> values of p involve), so the strategy is not so obvious. But if Samuel
> Merrill is right, then in the zero information case, the optimum strategy
> for method two is to vote appropriately normalized sincere utilities.
>
> --wrong.
> Your best strategy for any of these methods is, you identify the two
> "frontrunners", you vote max for one and min for the other, and then
> if you have any freedom left, you start considering the other N-2
> candidates.


He said "in the zero information case".  I think this means you can't know
who the frontrunners are.

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Re: [EM] Proportional parliamentary and government elections with proxies

[Andy Jennings]

I found this paper by James Green-Armytage very interesting:
http://www.econ.ucsb.edu/~armytage/proxy2010.pdf

He doesn't cover all of the issues you mention, but it's a good start.



On Sun, Sep 4, 2011 at 2:27 PM, Peter Zbornik  wrote:

> Dear all,
>
> has a direct proportional election system with proxies been considered
> before?
>
> Each voter is granted a vote in parliament, either personally or through a
> proxy (as in stock companies). The voter could change his representative in
> parliamet when she/he likes (or at a specific date to avoid identification
> of the voter). The voter could have several representatives, each of them a
> specialist in a different issue (health care, tax, education, business and
> so on), or split his vote on several representatives in each area. There
> would be no elections, just a continuous switching of proxies. The
> representative of the voter would not know who supports him/her to avoid
> coercion.
>
> The voter who chose to represent himself would have the right to speak and
> be present "virtually" or (less practical) physically in the parliament and
> to vote on all issues and so on. For the time being I would like to put
> aside such practical details, like how a milion parlamentarian would vote
> and so on. Such problems can be solved through remote voting or similar.
>
> The government could (but need not) be formed through proportional
> elections by the citizens too.
> Each voter would vote for each department, i.e., if there were 10
> ministries, then the voter would cast a ranked ballot for each of the 10
> ministries.
> Some weights could be applied, i.e. if the voter could only care for one
> ministry instead of all 10, then he could put all of his votes on this
> ministry and none for the others.
> In addition to this, each ministry could be weighted according to the share
> of the public budget it uses.
> I.e some ministries would take more of the vote than others. I.e. if one
> ministry has half the budget, then a "standard" vote for this would require
> half of the votes the voter has (i.e. 5 votes in the case of 10 ministries).
> I.e. the voter has a constant number of votes (say V votes), each vote for
> a specific seat "costs" A1,...,AS, where S is the number of ministries, and
> A1+...+AS=V. A vote for ministry s, 1>=s>=S, would be normalised by the
> "cost", i.e. if the voter would like to vote only for one minstry s, then he
> would get V/As votes.
> Furthermore, the voter would need to specify the rank-order of the
> ministries themselves, so that all of the vote is used, even if the minister
> in the "favorite minstry" becomes someone else than the candidates preferred
> by the voter or if the preferred candidate is elected but the vote is not
> fully exhausted.
> The elections would then proceed as a normal STV election.
> This got a bit complicated, I will provide a simple example upon request.
>
> An election system as described above would blur the difference between
> proportional representation and direct democracy and allow for direct
> elections of a government.
>
> A question I am not sure of, is how the approach above should be applied
> for budget allocation for each ministry, i.e. how big part of the cake each
> ministry should get. I guess each voter could make his budget allocation
> between the ministries, and the resulting budget would be the arithmetic
> mean of the submitted allocations. I guess there are better or more
> sophisticated systems for optimal budget allocation.
>
> Does anyone on this list have more information on similar methods to the
> ones described above?
> I guess such methods have been discussed on this list before.
> A recommended book or paper or a reference to previous posts on this list
> would be appreciated.
>
> Best regards
> Peter Zborník
>
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>
>

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Re: [EM] This mailing list as a forum?

[Andy Jennings]

Toby,

I agree that it is a pain to try to reply to the digest.  I've switched to
receiving every message as a separate email and it seems much easier.  The
downside, as you say, is that there are a lot of messages sometimes.

I would support moving to Google Groups because I think it would be a strict
improvement over what we have now: after the adjustment period, life would
be worse for no one and strictly better for some.  But there would, no
doubt, be a learning curve for some people.

And then there's the risk of what happened on the range voting list.
 Someone created a Google Group with the intent of moving from Yahoo Groups
to Google, but then some people didn't want to move and so now there are two
lists to follow.  One on Yahoo and one on Google.

~ Andy



On Fri, Sep 2, 2011 at 10:40 AM, Toby Pereira  wrote:

> I don't know if this has been discussed before, but most discussion groups
> on the internet (certainly the ones I use) use forums with separate threads
> for topics, rather than a mailing list. I think forums are easier to use and
> the threads are easier to follow. It's awkward to reply to topics on here
> unless you have individual e-mails sent to your inbox and it's a full-time
> job to put them into a separate folder. You can't reply via the central
> "hub". Mailing lists are the FPTP of the internet discussion world! Any
> thoughts?
>
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>
>

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Re: [EM] Voting reform statement

[Andy Jennings]

I like it, and would sign on to these general ideas.  Thanks for writing it,
Jameson.

It's not bad as is, but I'm sure we can find ways to improve it as we work
together.  I'll try to help as much as I can, but I can't promise I'll be
fast.

~ Andy


On Mon, Aug 15, 2011 at 7:09 AM, Jameson Quinn wrote:

> A few months ago, we had a discussion where several people supported the
> idea of writing a common statement for people on this list to sign on to. I
> said that I would write such a statement, but until now, I haven't. I
> believe that, with the Rhode Island Voter Choice Commission about to be
> seated, now is an opportune time to do so.
>
> The statement below is my attempt to write something that I think will get
> broad consensus here.* It is only a first draft and I expect it to change
> significantly before we start to sign on to it.* I am probably being
> overoptimistic about how much we can agree on. I'd welcome discussion of any
> of the points below. Remember: the main objective here is not to convince
> others to agree with you, but to find the most-useful statement on which you
> can already agree. So once people have heard each side of a debate, if we
> still don't agree on something, we just remove that from the statement or
> present both sides; we should try to avoid getting sidetracked in endless
> debates on specific points.
>
> 
>
> The study of voting systems has made significant progress over the last
> decade, and our understanding is even farther beyond what it was 20 years
> ago. One important place where that has happened is on the election methods
> mailing list. This mailing list is likely to include the largest and most
> diverse group of voting systems theorists in the world. It is a place where
> opinions vary and debate is vigorous. Thus, we think that the broad, though
> imperfect, consensus on the following ideas is worth paying attention to.
>
> We believe that the voting systems currently used in most of the
> English-speaking world, including single-round plurality voting (also termed
> First Past the Post, FPTP) and single-member districts (aka seats, ridings,
> or electorates), represent some of the worst voting systems known. We
> believe that reforming these systems would provide important societal
> benefits, and that there are clearly not corresponding reasons to oppose
> such reform from the perspective of the public interest. We may disagree
> about which specific reforms might provide the absolutely optimum results,
> but we can nevertheless agree that there are a number of options which would
> represent worthwhile improvements.
>
> *Single-winner reform*
>
> There are various criteria, both formally-defined and informal, by which
> one can judge a voting system. These criteria can be divided into several
> classes:
>
> 1. Honest-results-oriented criteria. These include such measures as
> Bayesian regret (that is, simulated societal satisfaction), the majority
> criterion, and the Condorcet criterion, which focus on whether the "correct"
> candidate, according to some definition, is elected. Although these criteria
> in some cases can favor different candidates as being "correct", in most
> practical cases they agree.
>
> 2. Strategy-resistance criteria. Voting is a complex process, and
> inevitably there are some cases where some group could get an advantage by
> changing their votes.  It is desirable to keep such cases to a minimum. For
> one thing, it's fairer not to reward such strategic voting behavior. But
> it's not just that. Perhaps more importantly, a voting system which gives
> too much of an incentive to strategic voters, can lead to widespread
> strategy which systematically distorts the results.
>
> 3. Process-oriented criteria. These include such measures as simplicity of
> the ballot, simplicity of the ballot-counting process, and feasibility of
> auditing or other fraud-prevention measures.
>
> 4. Candidate-incentive criteria. Systems which encourage or discourage
> "clone candidates"; give too much power to parties, as opposed to voters;
> have problems here. These criteria also include less strictly-defined
> concerns about the type of candidates and campaign strategies a system
> encourages; for instance, systems which effectively reduce the field to 2
> major candidates could encourage negative advertising.
>
> There is a broad consensus among researchers plurality voting is among the
> worst systems for honest results, for strategy-resistance, and for candidate
> incentives. Honest voting can split votes among similar candidates,
> "spoiling" the election and leading opposing candidates to win. Voters
> respond by strategically choosing the "lesser evil" among the two major
> candidates, which can lead to complacent candidates because even corrupt,
> widely-disliked candidates can win. The system discourages candidates from
> entering the race, and encourages negative advertising. Although plurality
> has good simplicity an

[EM] Maximal Bucklin PR (was: Record activity on the EM list?)

[Andy Jennings]

On Wed, Aug 3, 2011 at 5:22 AM, Jameson Quinn wrote:

>
>
> 2011/8/3 Juho Laatu 
>
>> I noticed that there was a lot of activity on the multi-winner side.
>> Earlier I have even complained about the lack of interest in multi-winner
>> methods. Now there are still some interesting but unread mails in my inbox.
>>
>> Multi-winner methods are, if possible, even more complicated than
>> single-winner methods. Maybe one reason behind the record is that there are
>> still so many uncovered (in this word's regular non-EM English meaning)
>> candidates to cover.
>>
>> Juho
>>
>
> OK, on the theme of simple multi-winner systems I haven't seen described
> before, here's a simple Maximal (that is, non-sequential) Bucklin PR, MBPR.
> Now that the sequential bucklin PR methods have been described, it's the
> obvious next step:
>
> Collect ratings ballots. Allow anyone to nominate a slate. Choose the
> nominated slate which allows the highest cutoff to assign every candidate at
> least a Droop quota of approvals. Break the tie by finding the one which
> allows the highest quota of approvals per candidate (the slate whose members
> each satisfies the most separate voters). If there are still ties
> (basically, because you've reached the Hare quota, perfect representation,
> aside from bullet-vote write-ins) remove the approvals you've used, and find
> the maximum quota per candidate again (that is, look to for the slate whose
> members each "double satisfies" the most separate voters).
>
> Obviously, this needs to use the contest method to beat its NP-complete
> step. But all the rest of the steps are computationally tractable. Except
> for the NP-completeness, this or some minor variation thereof (diddling with
> the order of the tiebreakers between threshold, quota, and double-approved
> quota) seems like the optimal Bucklin method. I'd even go so far as to say
> that it seems so natural and "right" to me that, if it weren't NP-complete,
> I'd consider using it as a metric for other systems, graphing them on how
> well they do on average on the various tiebreakers.
>

Sounds like a good system to me.  Keep bringing it up so I'll remember to
keep thinking about it.  :)

Seems similar to Monroe in some ways...

Is there any sense lowering the cutoff for the tie-breaker phase?  Maybe if
you can't find any slates that "double satisfy" all the voters with the
original cutoff, you could with a lower cutoff.  Just thinking out loud...

Andy

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Re: [EM] SODA

[Andy Jennings]

On Mon, Aug 8, 2011 at 6:35 AM, Warren Smith  wrote:

> http://wiki.electorama.com/wiki/SODA
>
> SODA is slightly more complicated for the voter since voter needs to
> check box saying she delegates her vote, or not.  Also more
> complicated in the sense that there is more information shoved in the
> voter's face.
> But those deficits are probably amply compensated for...
>
> I think this is a very nice voting method.
>
> It also can be used both as a single-winner method, and as a PR
> multiwinner method
> (in the sense it acts like "asset voting"), right?
> Another very elegant point.  It also has ideas in common with "DYN"
>   http://www.rangevoting.org/DynDefn.html



SODA is definitely a descendant of DYN.  In my opinion, it comes down to
three improvements that are basically orthogonal.

1. Ballot design - The most important thing here is that the ballot
basically looks like it always has and that voters who bullet vote like they
always have are casting a delegated vote for one candidate, which is an
effective vote.  (Yes there is one extra question at the bottom, but I find
that preferable to forcing people to write in "Do not delegate".)

2. Candidates must exercise their ballots in a way consistent with a
preference order they declared before the election - Helps voters understand
how their ballot might get "extended" and vastly decreases opportunities for
strategy in the delegation phase.

3. Candidates exercise their ballots one-at-a-time in a specific order -
Avoids candidates trying to mislead each other about how they will exercise
their delegated ballots (if they all go simultaneously).  Can eliminate the
"chicken" paradox.

You could apply these improvements to DYN in isolation or in other
combinations, or even mix in other improvements, but together I think they
make quite a strong system.



> On the "sample ballot" on the SODA web page, I do not like the use of
> the word "share."
> I think that word is not the right word.  But I admit I'm unsure how
> best to re-word it.
> "Delegate your remaining approvals" is not the same as "share," is my
> linguistic point.



I agree.  At one point I reworded it to "candidates exercise their delegated
ballots".  But I don't think this is perfect.  Jameson wanted to unify the
language on the whole page, which is good, and went with "share" likely
because it is the most succinct, but I do think it can be confusing for
someone learning about SODA for the first time.

~ Andy

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Re: [EM] connection between multiwinner voting systems & districting problems

[Andy Jennings]

On Thu, Jul 28, 2011 at 6:50 AM, Warren Smith wrote:

> To draw districts using a multiwinner voting system:
> Let there be V people, whose coordinates are known.
> Let the "candidates" be the same set as the people (V candidates).
> Each voter "votes" by ranking the "candidates" in order of increasing
> distance
> away from her, or somehow scoring them (in a score-based voting
> system) using some decreasing function of distance.   (Actually, all
> these votes are fake in the
> sense that they are automatically generated from the coordinates; no
> humans actually vote.)  We then "elect" W winners.
> These winners will be the centers of the districts.  [Once the
> district centers are selected there is a known polytime algorithm for
> finding the best assignment of the people to the districts such that
> the sum of the distances (or squared distances) to the district
> centers is minimized subject to the equipopulousness constraint.]
>

Good idea.  Hadn't thought of it that way before.


> We can now attempt to evaluate various multiwinner voting systems by
> asking how well they would perform for districting purposes.
>
> Consider, e.g, Andy Jennings' "greedy algorithm"
> which selects the candidate whose Tth highest score is greatest (where
> T is the district target population) and removes the T voters who
> scored him with the T highest scores, as "district #1" -- then
> continues on with the remaining voters.
>   It would work pretty well at first, removing chunks of people in
> dense cities, each chunk having population equal to a district target
> population.  However, as it proceeded, eventually your country would
> start to look like swiss cheese, with many removed "holes."
> The late districts Jennings produced, would necessarily be quite bad,
> large,
> containing a lot of scattered people, and with a lot of holes in the
> middle of those districts.
>

Interestingly enough, people in Arizona wanted it that way at one point.
 Some people think Arizona's 1st district (
http://en.wikipedia.org/wiki/Arizona's_1st_congressional_district) is the
way it is because of gerrymandering, but I'm pretty sure it was a
non-partisan committee who designed it that way so rural interests could be
combined and have their own representative.

Then again, it was the district that elected Rick Renzi, accused of being
one of the most corrupt congressmen at the time.  Does this reflect
negatively on the swiss cheese idea?  In any case, I agree that most people
would reject swiss cheese districts.


> Now consider (Lewis Carroll's form of) "asset voting."
> Here each voter names, e.g. their 3 favorite candidates.  Candidate with
> least votes (assets) is eliminated and transfers his assets to whomever he
> likes (according to his own vote).   Continue on.
> Eventually we have only W candidates left,
> who win.   In the districting application, "favorite" means "nearest."
> I actually suspect this method would work quite well as a districting
> method.
> There would be a lot of random tiebreaking going on, though, making its
> results depend to a large extent on random chance.
> But if each voter cast weighted votes for their top three (weightings
> chosen using
> distances according to some suitable scheme so the sum is 3 and they
> decrease with distance) then there would generically be no ties and no
> randomness.
>
> To boil that down to a simple districting algorithm:
> 1. input locations of all P people in country.
> 2. compute for each person v, its nearest neighbor NN(v).
> 3. for(v=1 to P){ asset(v)=1; }
> 4. for(v=1 to P){ increment asset(NN(v)); }
> 5. while(P>W){
> 5a.find v minimizing asset(v);
> 5b.eliminate v (decrementing P)  and transfer her assets to NN(v);
> }
> 6. the W remaining people are the winners, i.e. become district centers.
>
> In step 5a, ties could be broken deterministically using some function
> of distances,
> or just randomly.
> It is possible to implement the above algorithm to run in O(PlogP) time by
> using fast all-nearest-neighbor algorithms in step 2 and implementing
> step 5 with the aid of a "heap" (also called "priority queue") data
> structure.
> Those improve over the naive runtime which would have been O(P^2).
>
> With this algorithm, if the people in step 1 come in "census blocks" then
> it is easy to start out with "weighted people" where each block is
> replaced by a person at its center with weight (i.e. assets) equal to
> the block population
> in step 3, and in step 4 you increment by the weight of v not just by +1.
>
> So this has been a simple, efficient, and flexible districting
> algorithm, which probably usually doesn't perform horribly badly.
>

I agree that it definitely deserves to be simulated.  Might do quite well...

- Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] Single Contest Method

[Andy Jennings]

On Wed, Jul 27, 2011 at 4:32 PM, Kevin Venzke  wrote:

> Hi Forest,
>
> --- En date de : Mer 27.7.11, fsimm...@pcc.edu  a
> écrit :
> > Andy's chiastic method is a way of
> > utilizing range ballots that has a much more mild incentive
> > than
> > Range itself to inflate ratings.  He locates the
> > method in a class of methods each of which is based on a
> > different increasing function f from the interval [0,1 ]
> > into the same interval:
> >
> > Elect the candidate with the highest fraction q such that
> > at least the fraction f(q) of the ballots rate the
> > candidate at fraction q of the maxRange value (assuming
> > that minRange is zero).
>
> Hmmm. So, noting that I cannot test more than 4 slots due to the design
> of the simulation, I want to take each candidate and ask:
> Did 100% of the voters rate him 3/3?
> Or else did 67+% of the voters rate him 2/3 or higher?
> Or else did 33+% of the voters rate him 1/3 or higher?
> And then the last possible question is trivial.
>
> That I believe is if f(q)=q. So what I want is this:
>
> >f(q)=q/2, and f(q)=(q+1)/2,
>
> So the first one asks:
> 50% rated 3? 33.3% rated a 2+? 16.7% rated a 1+?
>

This is correct.


> It is curious to me that the 50% figure should decrease.
>
> I'm not really sure how to interpret the second one. I was interpreting
> the range of q to be 0-100%. I guess I will interpret (q+1) for a
> four-slot ballot to mean 133.3%. So then I get:
> 66.7% rated 3? 50% rated 2? 33.3% rated 1+?
>

It would be 100% rated 3?  83.3% rated a 2+?  66.7% rated a 1+?

But you are right that it would probably work better with more grade levels.

- Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] Monroe's Clustering Method (was PR methods and Quotas)

[Andy Jennings]

On Tue, Jul 26, 2011 at 12:03 AM, Kristofer Munsterhjelm wrote:

> Andy Jennings wrote:
>
>>
>> If you want a clustering PR method, then I would highly recommend Monroe.
>>  In Monroe, the score of each slate is equal to the sum of each voter's
>> score of his assigned candidate.  I think that, for a given slate, finding
>> the optimal way of assigning the voters to the winners is polynomial.  (See
>> Warren's page for more information: http://rangevoting.org/**
>> MonroeMW.html <http://rangevoting.org/MonroeMW.html>)
>>
>> I think this is the method I called CFC-Range, for "continuous forced
> clustering, Range".


Thanks for the clarification.  I remember looking through your list and not
having time to understand all of the methods you simulated.  I even wondered
if some of them were methods I knew by a different name.


> This method assigns voters, or fractional voters (so we can handle weighted
> votes) to one of a number of clusters, where each cluster is assigned to a
> candidate, so as to maximize the score that is the sum of scores to the
> assigned candidates in each cluster. This is done subject to the constraint
> that each cluster must have the same weight (sum of votes' weights), so one
> doesn't end up with one cluster representing 99% of the people and others
> less than 1%. Then it tries each possible slate to find the one that has a
> max sum, and that one wins.
>

Another option, instead of using fractional voters, is to make sure each
winner is assigned either floor(N/W) voters or ceil(N/W) voters, where N is
the number of voters and W is the number of winners.


> I do that assignment per slate by using linear programming, but I guess it
> could be done faster by more specialized algorithms, as Warren states. It
> might also be the case that Monroe's original integer programming
> formulation will relax easily to linear programming and so in practice be
> solvable quickly, similarly to how I usually can find the Kemeny and Dodgson
> winners quickly.
>

I think linear programming is fine for the fractional solution, but Warren
prefers the integral solution, so he prefers using the
constrained-degree-subgraph problem and solutions, though you can do the
same thing with integer programming.

I did some experiments at finding the optimal slate, for both the fractional
case and the integral case, using a general integer programming package.
 One thing I noticed was that the solution to the fractional case only
divided up as many voters as was necessary, no more.  Almost all of the
voters were assigned in whole to one of the candidates.  Did you notice
anything similar?  This makes it seem like the solution to the fractional
problem might be an excellent starting point for finding the integral
solution.


> I also made a Kemeny version of this - actually, the Kemeny version was the
> one I tried first. Here, one assigns orderings (rankings of candidates) to
> each cluster, and then allocates voters to the different clusters to
> maximize the Kemeny score of the assigned ordering wrt the cluster in
> question. The orderings are constrained so that there is a different first
> place candidate for each cluster's ordering, and then the candidates at
> first place of the orderings whose Kemeny scores' sums are maximum, win.
> However, this is *very* slow, because now one doesn't only have to find the
> right slate, but the right combination of orderings. Thus, it's impractical,
> though it seems to work to some degree as a multiwinner method (were it not
> so slow...).
> Therefore, I've been interested in Condorcet methods that give reasonable
> results under a variant of margins where the X against Y score is always
> (number of votes where X is above Y) - (number of voters where Y is above
> X), not either this or 0, whichever is more. If I could find such a method,
> it might be incorporable into linear programming and then I could make a
> clustering Condorcet method that would only be per-slate combinatorial
> instead of worse.


Is there some way in which the CFC-Kemeny method is better than
CFC-Range/Monroe?  It doesn't seem that useful to use the Kemeny scores that
the voters give to the ranking for the cluster they appear in only to
discard the entire ranking except for the first candidate.

- Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] A multiwinner voting method based on graph-matching theory

[Andy Jennings]

On Tue, Jul 26, 2011 at 7:21 PM, Warren Smith wrote:

> This voting method will be for V voters, C candidates, and W winners,
> 0 There will also be an integer parameter K with 0 For simplicity we shall assume W exactly divides V (although we do not
> really need to assume that, and it is easy to avoid assuming it, I
> just want to bother complicating things by explaining how).
>
> 1. All voters supply scores in some fixed range (e.g. 0 to 9) for all
> candidates
> [as in "range voting"]
>
> 2. Consider a bipartite graph whose V red vertices are the voters, and
> whose W blue
> vertices are the winners.   Associated with each voter-candidate edge
> is that voter's score for that candidate.  Assume each voter has
> valence K, that is,
> is joined by graph edges to exactly K winners for some constant K with
> 0 Further, assume each candidate is joined to exactly V*K/W voters.
>

Don't you mean "each candidate is joined to EITHER ZERO OR V*K/W voters"?

Then, I believe, the problem is no longer polytime.  Your own analysis is
here: http://rangevoting.org/MonroeMW.html

I've decided that it's still tractable enough for my taste, but it is
NP-hard in the very worst case and that's a fatal flaw to some.

With K=1, this is the same system I've been calling Monroe, and Kristofer
calls "CFC-Range".

- Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] PR methods and Quotas

[Andy Jennings]

On Sun, Jul 24, 2011 at 6:30 AM, Jameson Quinn wrote:

>
> 2011/7/24 Andy Jennings 
>
>> Like Jameson and Toby, I have spent some time thinking about how to make a
>> median-based PR system.
>>
>> The system I came up with is similar to Jameson's, but simpler, and uses
>> the Hare quota!
>>
>> Say there are 100 voters and you're going to elect ten representatives.
>>  Each representative should represent 10 people, so why not choose the first
>> one by choosing the candidate who makes 10 people the happiest?  (The one
>> whose tenth highest grade is the highest.)  Then, take the 10 voters who
>> helped elect this candidate and eliminate their ballots.  (There might be
>> more than ten and you'd have to choose ten or use fractional voters.  I have
>> ideas for that, but lets gloss over that issue for now.)  You can even tell
>> those 10 voters who "their" representative is.
>>
>
> Glossing-over noted. I'd like to hear your ideas, but I agree that they
> should not be part of the basic definition of the system.
>

The main idea I had was to eliminate first the ballots which don't rate any
of the remaining hopefuls above zero, then the ballots which rate one
remaining hopeful above zero, and so on.  Where there are ties, I would
probably prefer fractional de-weighting to random discards.

Suppose I'm seating candidate A and need to eliminate 10 ballots and there
are
7 voters who rated all the rest of the hopefuls at zero
5 voters who rated only one other hopeful above zero

Then I would eliminate all seven of the first class and de-weight the other
5 by 60% (multiply by 0.4).

The idea is to prevent degeneration in the final round as much as possible,
we give priority to ballots which give non-zero scores to the most
candidates.  Even to the point of incentivizing them.

This might incentivize turkey-raising, but only to the first non-zero level.
 And with Hare quota, there's a real chance that it WILL make a difference
in the final round, so instead of raising turkeys, hopefully voters will
give a non-zero score to anyone they can live with.

Of course, we'll still probably have a tie at zero in the final round, so
we'll elect the candidate with the fewest zero votes, a form of
lowest-denominator approval.


  Which got me thinking...  Is there anything that special about the 50th
>> percentile in the single-winner case anyways?  I can imagine lots of
>> single-winner situations where it's more egalitarian to choose a lower
>> percentile.  In a small and friendly group, even choosing the winner with
>> the highest minimum grade is a good social choice method.  It's like giving
>> each person veto power and still hoping you can find something everyone can
>> live with.  This is the method we tend to use (informally) when I'm in a
>> group choosing where to go to lunch together.
>>
>
> The Droop quota reduces to the median. The Hare quota reduces to the
> highest minimum grade. You could also use any number in between. (I note
> that "modified Saint-Lague" is, I think, actually used in some places, and
> amounts to a similar compromise idea.)
>
> The higher the quota (up to Hare), the smaller a group of strategic voters
> can be and still determine the result (if everyone else is honest). I'd
> argue that this makes pure Hare a poor solution. I am open to compromises.
> 2/(2N+1), the quota half way between Droop and Hare (I bet it already has a
> name, but I don't know it), reduces to the ~33rd percentile in the
> single-winner case. From what I've seen of supermajority requirements in
> contentious high-stakes contexts (California tax hikes, US senate
> filibusters), 2/3 is the highest reasonable supermajority requirement, and
> may already be too high. But, as you say, a higher requirement may make
> sense for smaller, friendlier decision-making.
>
> In sum: I like your method. It is certainly similar to, but simpler than,
> AT-TV. I prefer it with the Droop quota. What do you call it? (It would be
> good if you had terms for both the Droop and Hare versions).
>

I don't know what to call it.  Maybe one of:

Sequential Hare Favorite
Successive Hare Favorite
Sequential Favorite Voting (SFV-Hare)

Are those acronyms taken?


- Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] PR-SODA? Try 2 (and 3)

[Andy Jennings]

Jameson Quinn wrote:
>
>   Suggestions:
 - When a candidate is elected and you need to discard ballots, you could
 specify a more detailed preference order:
 1. Ballots which delegated to that candidate
 2. Ballots which bullet voted that candidate and didn't delegate
 3. Ballots which approved two candidates
 4. Ballots which approved three candidates
 5. Ballots which approved four candidates
 6. And so on.
 This eliminates ballots first which approve fewer candidates.  You may
 still have to select randomly within these tiers, but it gives an incentive
 for people to approve more candidates, which helps the method work better.
  Right?

>>>
>>> Well, up to a point. The problem would be if people approved a "no-hope"
>>> candidate, just to puff up the number of approvals on their ballot. This is
>>> a form of "Woodall free riding", and it could lead to DH3-type pathologies
>>> in the worst case. I'd rather not go there.
>>>
>>
>> Good point.  Although if there do happen to be any voters who bullet voted
>> for that candidate but didn't delegate to him, then you should definitely
>> eliminate those first (even before the delegated ones, I think).  Once that
>> candidate is elected, ballots which don't approve any other candidates are
>> pretty useless, so you might as well get rid of them.
>>
>> But after that, I can see why you would be reluctant to incentivize
>> approving more candidates.
>>
>>
> Here's an idea. When you have elected a candidate, choose which of their
> ballots survive, not which are eliminated; and do so in proportion to the
> number of remaining hopeful candidates approved per ballot. This naturally
> eliminates bullet votes.
>

You're still choosing randomly, right?  So the probability of surviving will
be proportional to the number of remaining hopeful candidates left on that
ballot.

I like it.  (I'm still kind of wary of non-deterministic methods, though.
 Not for myself, actually, but for selling them to the public.)

- Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] PR-SODA? Try 2 (and 3)

[Andy Jennings]

Jameson Quinn wrote:

> - Would it work just as well with the Hare quota?
>>
>
> Yes, but see my other message about your median-based system. For
> contentious elections, I prefer the Droop quota. With the Hare quota, the
> last candidate elected is likely to have about half the support of all the
> rest.
>

I don't think that's necessarily true.  It all depends how the voters are
divided, how many candidates they approved, and the order in which they are
eliminated.  If we're electing ten candidates, there's really no reason
that, out of the last two-elevenths of the population, exactly 50% will be
happy with the last candidate and 50% won't.  And I don't think we can
decide beforehand that each candidate should represent one-eleventh of the
population and one-eleventh of the population should be left unrepresented.

Droop quota is natural in STV because it is the smallest number that can
elect no more than the desired number of candidates.  With a cardinal method
I think Droop is just arbitrary.  With one-winner approval voting, even 50%
doesn't have any special significance.  We just take whoever is the
candidate with the most approvals.

I guess I prefer a method like Monroe, that tries to get as close to Hare as
it can, and if not, it does the best it can.  Of course, it's not perfect...



>  Suggestions:
>> - When a candidate is elected and you need to discard ballots, you could
>> specify a more detailed preference order:
>> 1. Ballots which delegated to that candidate
>> 2. Ballots which bullet voted that candidate and didn't delegate
>> 3. Ballots which approved two candidates
>> 4. Ballots which approved three candidates
>> 5. Ballots which approved four candidates
>> 6. And so on.
>> This eliminates ballots first which approve fewer candidates.  You may
>> still have to select randomly within these tiers, but it gives an incentive
>> for people to approve more candidates, which helps the method work better.
>>  Right?
>>
>
> Well, up to a point. The problem would be if people approved a "no-hope"
> candidate, just to puff up the number of approvals on their ballot. This is
> a form of "Woodall free riding", and it could lead to DH3-type pathologies
> in the worst case. I'd rather not go there.
>

Good point.  Although if there do happen to be any voters who bullet voted
for that candidate but didn't delegate to him, then you should definitely
eliminate those first (even before the delegated ones, I think).  Once that
candidate is elected, ballots which don't approve any other candidates are
pretty useless, so you might as well get rid of them.

But after that, I can see why you would be reluctant to incentivize
approving more candidates.

- Andy

Election-Methods mailing list - see http://electorama.com/em for list info

[EM] Monroe's Clustering Method (was PR methods and Quotas)

[Andy Jennings]

Kristofer Munsterhjelm wrote:

> Andy Jennings wrote:
>
>> Like Jameson and Toby, I have spent some time thinking about how to make a
>> median-based PR system.
>>
>> The system I came up with is similar to Jameson's, but simpler, and uses
>> the Hare quota!
>>
>
> How about clustering logic? Say you have an electorate of n voters, and you
> want k seats. The method would be combinatorial: you'd check a prospective
> slate. Say the slate is {ABC...}. Then that means you make a group of n/k
> voters and assign A to this gorup, another group of n/k other voters and
> assign B to that group, and so on.
> The score of each slate is equal to the sum of the median scores for each
> assigned candidate, when considering only the voters in the assigned
> candidate's group.


Kristofer,

If you want a clustering PR method, then I would highly recommend Monroe.
 In Monroe, the score of each slate is equal to the sum of each voter's
score of his assigned candidate.  I think that, for a given slate, finding
the optimal way of assigning the voters to the winners is polynomial.  (See
Warren's page for more information: http://rangevoting.org/MonroeMW.html)

I consider it to be a very promising method.

If I recall, when you did your PR simulations and graphed them on two axes
(total satisfaction vs. proportionality), you said you weren't completely
happy with your metric for proportionality.  I think you should consider
using Monroe's metric.  That is, no matter how a given method chooses it's
slate, you run the algorithm on that slate to optimally assign the voters to
that slate and then you compute the sum of the voters' grades of their
assigned candidates.

Of course, to actually find the optimal slate is an NP problem.  People
often show this by embedding the "exact cover by 3-sets problem" in it.  But
that requires having one-third as many candidates as voters!  In fact,
finding the optimal slate is NP in the number of candidates and seats to
fill, not in the number of voters.  If there are not too many candidates or
not too many seats to fill, it should be tractable to iterate over all
possible winning sets of candidates.  In reality, I think an integer
programming algorithm should be able to find the optimal slate fairly
quickly.  Or you can always dodge the question by having a public contest to
find the best slate.

If we are choosing 15 winners from 30 candidates, there are 155 million
possible slates to try.  Seems tractable to me.

I do wonder if it will be underconstrained.  That is, there will be many
possible slates all tied for first.  If so, then we'll need to have some
tie-breaker method.

Monroe's method reduces to score voting in the one winner case, though his
original paper talked mostly about voters submitting ratings and generating
the scores from the ratings (which reduces to Borda Count).  His paper
mentioned an Approval Voting variant also, which Brams expounded on at one
point.

There is some free-rider incentive, I suppose.  If you know your favorite
candidate will get elected even without your vote, then you can rate him at
zero, making sure that your vote is not assigned to him, which will help you
have more influence on the rest of the election. I still don't think it can
help a faction get more than their fair share of seats, though.

- Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] PR for USA or UK

[Andy Jennings]

Jameson Quinn wrote:

> 2011/7/23 Andy Jennings 
>
>> On Sat, Jul 23, 2011 at 7:45 AM, Jameson Quinn 
>> wrote:
>>
>>> And so I'd like to suggest that we should be looking for a PR system
>>> which satisfies the following criteria:
>>>
>>> c1. Truly proportional (of course). I would be willing to support a
>>> not-truly-proportional system, but I'm not everyone. Egregious compromises
>>> on this issue will simply reduce the activist base, to no benefit.
>>> c2. Includes a geographical aspect. People are attached to the "local
>>> representation" feature of FPTP, whether that's rational or not.
>>> c3. No "closed list". A party should not be able to completely shield any
>>> member from the voters. In general, voter power is preferable to party
>>> power, insofar as it's compatible with the next criterion.
>>> c4. Simple ballots. A reasonably-thorough voter should not have to mark
>>> more than, say, 5 candidates or options, and an average ballot should not
>>> list more than 20 candidates or options. Those are extreme limits; simpler
>>> is better, all the way down to around 7 options (of which only around half
>>> will be salient and/or viable).
>>> c5. Ideally, the smoothest transition possible. If existing single-winner
>>> districts can be used unchanged, all the better.
>>> c6. Insofar as it's compatible with the criteria above, greater freedom
>>> in voting is better. For instance, if ballots are printed with only
>>> in-district candidates, a system which allows out-of-district write-ins is
>>> better than one which doesn't, all other things being equal.
>>>
>>
>> I'm interested both in systems which satisfy 2 and those that don't.  If
>> we could identify a good, truly proportional, at-large system, then a state
>> with a bicameral legislature (like Arizona) could leave one house as
>> geographical and change one to be at-large proportional.
>>
>
> I agree that if you were designing a democracy from scratch,
> non-geographical systems deserve attention. My purpose here is to support a
> system or systems that have some chance of passage in the US or UK. In my
> experience, that means that activists should unify behind a system which
> represents a minimal change. Whatever reform you propose will have
> opposition, both from people who are honestly and naturally skeptical of
> anything new, and from whichever major party currently benefits from the
> distortions of the current system. It's better to push a smaller reform
> which gives such people fewer arguments to use against you, than a
> more-complete one which can never pass. That's why I included criteria 2 and
> 5, and I stand behind them.
>
> This same argument applies to Kathy Dopp's suggestion that states like AZ
> could have their bicameral legislatures function using one PR body and one
> geographical body. It's a great idea, and I'd happily and enthusiastically
> support it; but it's a more-radical reform, so I think something which meets
> my criteria would be more attainable. At least, I'd like to settle on
> something which meets my criteria, so that if I'm right, we still have a
> chance.
>

Agree on both counts, but I live in AZ so the bicameral option doesn't seem
so radical.  :)



>
>>
>> My proposal for SODA-PR satisfies and surpasses all 5 criteria. Other
>>> systems which do reasonably well:
>>> -I've seen a proposal for single-member districts and open party lists.
>>> This is similar to my SODA-PR system, except that it requires that all
>>> candidates in a party approve the same party set. As such, it is strictly
>>> worse on criterion 3, without being notably better on any of the other
>>> criteria. It is more conventional, though.
>>> -Multimember districts, with some system inside each district.
>>> -Mixed member systems.
>>>
>>
>> We should add Fair Majority Voting, by Balinski.  (
>> http://mathaware.org/mam/08/EliminateGerrymandering.pdf)  Here's the
>> summary:  Parties run one candidate in each district and voters vote for one
>> candidate in the race in their district.  The votes are totaled nationwide
>> by party and an apportionment method is used to decide how many seats each
>> party deserves.  Each party is assigned a "multiplier" and the winner in
>> each district is the one whose (vote total times party multiplier) is
>> highest.  The multipliers can be chosen so that the final total seats won by
>> each p

Re: [EM] Single Contest

[Andy Jennings]

Jameson Quinn wrote:

> The ranked majority criterion is: if one candidate is top-ranked by a
> majority of voters, that candidate must win.
>
> To me, the natural extension of that to rated systems is: if only one
> candidate is top-rated by any majority of voters, that candidate must win.
>

That must be the definition Forest is using.  Thanks.  Any "strategic
median" which assigns the MaxGrade if at least 50% of the electorate rated
the candidate at MaxGrade will indeed pass this criterion.



> You are suggesting that we use the ranked majority criterion for rated
> systems. If we do so, you are right that broad classes of rated systems
> (including range, median, and chiastic) can never pass.
>
> But if we use my definition of the criterion, then median systems pass,
> trivially.
>

You are probably aware the median systems pass a stronger criterion:  If for
some grade X, only one candidate is rated at X or above by any majority of
voters, then that candidate must win.

In other words, it doesn't just have to be "top-rated", it can be any grade.

- Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] PR methods and Quotas

[Andy Jennings]

Kristofer Munsterhjelm wrote:

> Andy Jennings wrote:
>
>> Kristofer Munsterhjelm wrote:
>>
>>Andy Jennings wrote:
>>
>>Like Jameson and Toby, I have spent some time thinking about how
>>to make a median-based PR system.
>>
>>The system I came up with is similar to Jameson's, but simpler,
>>and uses the Hare quota!
>>
>>
>>How about clustering logic? Say you have an electorate of n voters,
>>and you want k seats. The method would be combinatorial: you'd check
>>a prospective slate. Say the slate is {ABC...}. Then that means you
>>make a group of n/k voters and assign A to this gorup, another group
>>of n/k other voters and assign B to that group, and so on.
>>The score of each slate is equal to the sum of the median scores for
>>each assigned candidate, when considering only the voters in the
>>assigned candidate's group. That is, A's median score when
>>considering the voters of the first group, plus B's median score
>>when considering the voters of the second group, and so on. The
>>voters are moved into groups so that this sum is maximized.
>>
>>
>> The median is not what you want for clustering like this, because it
>> basically ignores the scores of half the voters assigned to each candidate.
>>  That is, if I'm assigning 11 voters to each candidate, I can assign 6
>> voters who love that candidate and 5 voters who hate the candidate and still
>> have a very high median.
>>
>
> Well, yes, but the same thing holds for median ratings in general. If you
> want to find someone who represents the whole population, median ratings can
> pick someone who is loved by 51% and hated by 49%, rather than someone that
> 80% think are okay (and I think Warren have made arguments to the effect
> that this makes Range better than median).
>

Exactly.  This is why I'm questioning the median even for single-winner
elections.  Maybe you're right and we should be using the 20th percentile,
which would give us the candidate that some 80% of the population liked
best.  I tried to point out some arguments that highest minimum might be a
good method even in some single-winner environments.  It does give everyone
veto power.  But that's okay if everyone is committed to finding a solution
that's acceptable to everyone.  (In a public method, obviously, you'd have
to have some tie-breaker, like electing the candidate vetoed by the fewest
voters.)


> The question then is: what makes that logic okay when you're electing a
> single representative for the whole population, but not okay when you're
> electing one of ten representatives for 10% of the population? Is it the
> fluid nature of the clustering - that the optimizer could try to
> artificially inflate the scores by packing "hate A" voters into the A-group?


Yes, the fluid nature makes it much worse.  Say there are 110 voters and
we're choosing 10 winners.  Here's the voter profile:
50 people love A and noone else
6 people love B and noone else
6 people love C and noone else
...
6 people love K and noone else

If A were a political party, it would be entitled to at least 4 out of the
ten seats.  As a candidate, you would expect A to get a seat.  But we can
cluster the voters into:
6 voters who love B and 5 voters who love A
6 voters who love C and 5 voters who love A
...
6 voters who love K and 5 voters who love A

And then we elect B,C,..., and K, each with a perfect median in their
cluster.

Clustering with the median in each cluster is way too under-determined.

   Then the last candidate is only the one with the best worst votes in
>>the sense that there are only ten voters left.
>>
>>How about using the midpoint? That is, you find the 5th voter down,
>>not the 10th. Then when you're down to the last 10 voters, the 5th
>>voter down is the median. Doing so would seem to reduce it to median
>>ratings in the single-winner case, since 100/1 = 100, so you'd pick
>>the midpoint, i.e. at the 50th voter, which is the median.
>>
>>
>> True, but in filling the first seat, I don't think we should take a
>> candidate loved by 5 and hated by 95 as the first choice to represent
>> one-tenth of the population.
>>
>
> I guess you could be more gentle by placing the point at 50% (1/2) for one
> winner, 1/3 for two, 1/4 for three ... 1/11 for ten. That would be more
> Droop-like and less Hare-like. But then you can't simply eliminate those who
> contributed to the voting, I think.


Yes, it is much more Droop-like.  It seems arbitrary, though, to leave one
eleventh of the

Re: [EM] PR methods and Quotas

[Andy Jennings]

Kristofer Munsterhjelm wrote:

> Andy Jennings wrote:
>
>> Like Jameson and Toby, I have spent some time thinking about how to make a
>> median-based PR system.
>>
>> The system I came up with is similar to Jameson's, but simpler, and uses
>> the Hare quota!
>>
>
> How about clustering logic? Say you have an electorate of n voters, and you
> want k seats. The method would be combinatorial: you'd check a prospective
> slate. Say the slate is {ABC...}. Then that means you make a group of n/k
> voters and assign A to this gorup, another group of n/k other voters and
> assign B to that group, and so on.
> The score of each slate is equal to the sum of the median scores for each
> assigned candidate, when considering only the voters in the assigned
> candidate's group. That is, A's median score when considering the voters of
> the first group, plus B's median score when considering the voters of the
> second group, and so on. The voters are moved into groups so that this sum
> is maximized.
>

The median is not what you want for clustering like this, because it
basically ignores the scores of half the voters assigned to each candidate.
 That is, if I'm assigning 11 voters to each candidate, I can assign 6
voters who love that candidate and 5 voters who hate the candidate and still
have a very high median.


 Say there are 100 voters and you're going to elect ten representatives.
>>  Each representative should represent 10 people, so why not choose the first
>> one by choosing the candidate who makes 10 people the happiest?  (The one
>> whose tenth highest grade is the highest.)  Then, take the 10 voters who
>> helped elect this candidate and eliminate their ballots.  (There might be
>> more than ten and you'd have to choose ten or use fractional voters.  I have
>> ideas for that, but lets gloss over that issue for now.)  You can even tell
>> those 10 voters who "their" representative is.
>>
>
> I imagine you could eliminate the voters directly, though that would have
> some path dependence problems (which was why I suggested the above). Say you
> make use of highest tenth grade. Then you know which voters voted the
> candidate in question that high. Eliminate these. Find the highest tenth
> with those voters elminated, among uneliminated candidates. Again, you know
> the 10 voters who voted the next winner at that level or higher. Eliminate
> *them*. And so on down.
>
> Is that what you're suggesting?


Yes, this is what I'm suggesting.


> Then the last candidate is only the one with the best worst votes in the
> sense that there are only ten voters left.
>
> How about using the midpoint? That is, you find the 5th voter down, not the
> 10th. Then when you're down to the last 10 voters, the 5th voter down is the
> median. Doing so would seem to reduce it to median ratings in the
> single-winner case, since 100/1 = 100, so you'd pick the midpoint, i.e. at
> the 50th voter, which is the median.


True, but in filling the first seat, I don't think we should take a
candidate loved by 5 and hated by 95 as the first choice to represent
one-tenth of the population.



> But this system doesn't reduce to median voting.  Which got me thinking...
>>  Is there anything that special about the 50th percentile in the
>> single-winner case anyways?  I can imagine lots of single-winner situations
>> where it's more egalitarian to choose a lower percentile.  In a small and
>> friendly group, even choosing the winner with the highest minimum grade is a
>> good social choice method.  It's like giving each person veto power and
>> still hoping you can find something everyone can live with.  This is the
>> method we tend to use (informally) when I'm in a group choosing where to go
>> to lunch together.
>>
>
> I think the median is used because it's robust. If you assume unlimited
> ratings, the maximum and minimum could be altered by a single voter
> (whoever's at the min or max), as could the mean (by any outlier). However,
> the median is robust to distorted values - quite a number of voters would
> have to change their votes to alter the median.
>

With any finite number of voters, the median is still the score of one
voter, who can change the median by changing his vote.  But you are right
that if the scores follow a normal distribution, then he probably can't
change the median very much before he crosses another voter's score and is
not the median vote anymore.   But that's not true for a bimodal
distribution.

- Andy

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] Single Contest

[Andy Jennings]

On Sat, Jul 23, 2011 at 11:28 AM,  wrote:

> If one of the finalists is chosen by a method that satisfies the majority
> criterion, then you can skip step
> one, and the method becomes smoother.
>
> Here are some possibilities for the method that satisfies the majority
> criterion:  DSC, Bucklin, and the
> following range ballot based method:
>
> Elect the candidate X with the greatest value of p such that more than p/2
> percent of the ballots rate X at
> least p percent of the maxRange value.
>

Forest,

Can you clarify your definition of the majority criterion?  I don't think
this method satisfies it.

As a general example, suppose there are two candidates, A and B.  The voting
range is 0-100 and there are 5 voters:
1 voter: A=10 B=30
1 voter: A=30 B=50
1 voter: A=50 B=70
1 voter: A=70 B=90
1 voter: A=90 B=10

B is strictly preferred to A by 4 out of 5 voters, but these two candidates
have the exact same set of votes.  Any method which forgets which voter gave
which vote must consider them exactly tied.  This includes score (range)
voting, majority judgement, the chiastic median, and any of the other
generalized medians.  Thus, with only some minor perturbation, A can defeat
B in any of these methods.

In the chiastic median (or the majority judgement), both candidates have
societal grades of 50, but if you change A=50 to A=51 for the third voter,
A's societal grade becomes 51 and A defeats B, despite strong majority
opposition.

In the p/2 system, 40% of the voters gave grades of 70 or above and 20% of
the voters gave grades strictly above 70, so both candidates get a societal
grade of 70.  But if you change A=70 to A=71 for the fourth voter, A's
societal grade becomes 71 and A defeats B, again despite a strong majority
opposition.

I think any method which forgets which voter gave which vote will never
satisfy the majority criterion.

- Andy

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Re: [EM] PR-SODA? Try 2 (and 3)

[Andy Jennings]

On Thu, Jul 21, 2011 at 9:45 AM, Jameson Quinn wrote:

> So, here's the simpler procedure:
>
> While there are more uneliminated candidates than empty seats:
>
> Divide each ballot by the number of uneliminated candidates it approves
> If there are any candidates with more than a Droop quota:
>
> Elect the one with the highest score (previously "unique ballots")
> Discard a Droop quota of randomly-chosen ballots which approve the elected
> candidate, starting with the ones delegated to that candidate
> Assign that candidates pre-declared approvals on any undiscarded delegated
> ballots for that candidate
>
> Otherwise:
>
> Eliminate the candidate with the lowest score
> Assign that candidates pre-declared approvals on any delegated ballots for
> that candidate
>
> Elect all remaining candidates to fill the seats.



Okay, I really love how simple this is.  From the description, it sounds
like it would be explainable and would work well.  I wonder how it does in
simulations and if we can find any problematic scenarios.

Questions:
- Is there a "bullet vote but don't delegate" option like normal SODA?

- Would it work just as well with the Hare quota?

- Without the delegation, is it the same as any other
PR-with-approval-ballots method in existence?

Suggestions:
- When a candidate is elected and you need to discard ballots, you could
specify a more detailed preference order:
1. Ballots which delegated to that candidate
2. Ballots which bullet voted that candidate and didn't delegate
3. Ballots which approved two candidates
4. Ballots which approved three candidates
5. Ballots which approved four candidates
6. And so on.
This eliminates ballots first which approve fewer candidates.  You may still
have to select randomly within these tiers, but it gives an incentive for
people to approve more candidates, which helps the method work better.
 Right?


- Andy

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[EM] PR methods and Quotas

[Andy Jennings]

Like Jameson and Toby, I have spent some time thinking about how to make a
median-based PR system.

The system I came up with is similar to Jameson's, but simpler, and uses the
Hare quota!

Say there are 100 voters and you're going to elect ten representatives.
 Each representative should represent 10 people, so why not choose the first
one by choosing the candidate who makes 10 people the happiest?  (The one
whose tenth highest grade is the highest.)  Then, take the 10 voters who
helped elect this candidate and eliminate their ballots.  (There might be
more than ten and you'd have to choose ten or use fractional voters.  I have
ideas for that, but lets gloss over that issue for now.)  You can even tell
those 10 voters who "their" representative is.

Electing the next seat should be the same way.  Choose someone who is the
best representative for 10 people.  Repeat.

The only problem is when you get down to the last representative.  If you
follow this pattern, the last candidate is the one whose LOWEST grade among
the remaining ballots is the highest, which is rather unorthodox.  You could
change the rules and just use the median on the last seat, but using the
highest minimum grade does have a certain attraction to it.  You're going to
force those last ten voters to have some representative.  It makes some
sense to choose the one who maximizes the happiness of the least happy
voter.  (Though ties at a grade of 0 may be common.)

But this system doesn't reduce to median voting.  Which got me thinking...
 Is there anything that special about the 50th percentile in the
single-winner case anyways?  I can imagine lots of single-winner situations
where it's more egalitarian to choose a lower percentile.  In a small and
friendly group, even choosing the winner with the highest minimum grade is a
good social choice method.  It's like giving each person veto power and
still hoping you can find something everyone can live with.  This is the
method we tend to use (informally) when I'm in a group choosing where to go
to lunch together.

Thoughts?

Andy

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Re: [EM] PR for USA or UK

[Andy Jennings]

On Sat, Jul 23, 2011 at 7:45 AM, Jameson Quinn wrote:

> And so I'd like to suggest that we should be looking for a PR system which
> satisfies the following criteria:
>
> 1. Truly proportional (of course). I would be willing to support a
> not-truly-proportional system, but I'm not everyone. Egregious compromises
> on this issue will simply reduce the activist base, to no benefit.
> 2. Includes a geographical aspect. People are attached to the "local
> representation" feature of FPTP, whether that's rational or not.
> 3. No "closed list". A party should not be able to completely shield any
> member from the voters. In general, voter power is preferable to party
> power, insofar as it's compatible with the next criterion.
> 4. Simple ballots. A reasonably-thorough voter should not have to mark more
> than, say, 5 candidates or options, and an average ballot should not list
> more than 20 candidates or options. Those are extreme limits; simpler is
> better, all the way down to around 7 options (of which only around half will
> be salient and/or viable).
> 5. Ideally, the smoothest transition possible. If existing single-winner
> districts can be used unchanged, all the better.
> 6. Insofar as it's compatible with the criteria above, greater freedom in
> voting is better. For instance, if ballots are printed with only in-district
> candidates, a system which allows out-of-district write-ins is better than
> one which doesn't, all other things being equal.
>

I'm interested both in systems which satisfy 2 and those that don't.  If we
could identify a good, truly proportional, at-large system, then a state
with a bicameral legislature (like Arizona) could leave one house as
geographical and change one to be at-large proportional.


My proposal for SODA-PR satisfies and surpasses all 5 criteria. Other
> systems which do reasonably well:
> -I've seen a proposal for single-member districts and open party lists.
> This is similar to my SODA-PR system, except that it requires that all
> candidates in a party approve the same party set. As such, it is strictly
> worse on criterion 3, without being notably better on any of the other
> criteria. It is more conventional, though.
> -Multimember districts, with some system inside each district.
> -Mixed member systems.
>

We should add Fair Majority Voting, by Balinski.  (
http://mathaware.org/mam/08/EliminateGerrymandering.pdf)  Here's the
summary:  Parties run one candidate in each district and voters vote for one
candidate in the race in their district.  The votes are totaled nationwide
by party and an apportionment method is used to decide how many seats each
party deserves.  Each party is assigned a "multiplier" and the winner in
each district is the one whose (vote total times party multiplier) is
highest.  The multipliers can be chosen so that the final total seats won by
each party matches the number of seats assigned by the apportionment method.

It definitely satisfies your criteria 1,2,4, and 5.  I'd say it mostly
satisfies 3.  Don't know how to evaluate 6.  The main thing I don't like
about it is that it conflates voting for a candidate with voting for his
party.  What if I like the candidate but not the party, or vice versa?  But
since so many things in the legislature happen on a party basis, I've
decided that this is not as bad as it first seems.



> Still, I would argue that SODA-PR sets a high water mark on all the
> criteria I mentioned, and is therefore the system to beat. I'm somewhat
> surprised that it hasn't gotten more comments.
>

I still have it starred in my inbox to look at more in depth.  Sorry.  I'm
drowning in things at the moment.


Andy

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[EM] General PR question

[Andy Jennings]

Forest and I were discussing PR last week and the following  situation came
up.  Suppose there are five candidates, A, B, C, D, E.  A and B evenly
divide the electorate and, in a completely orthogonal way, C, D, and E
evenly divide the electorate.  That is:

One-sixth of the electorate approves A and C.
One-sixth of the electorate approves A and D.
One-sixth of the electorate approves A and E.
One-sixth of the electorate approves B and C.
One-sixth of the electorate approves B and D.
One-sixth of the electorate approves B and E.

It is obvious that the best two-winner representative body is A and B.  What
is the best three-winner representative body?

CDE seems to be the fairest.  As Forest said, it is "envy-free".

Some methods would choose ABC, ABD, or ABE, which seem to give more total
satisfaction.

Is one unequivocally better than the other?

I tend to feel that each representative should represent one-third of the
voters, so CDE is a much better outcome.  Certain methods, like STV, Monroe,
and AT-TV (I think) can even output a list of which voters are represented
by each candidate, which I really like.

I also note that if there was another candidate, F, approved by everybody,
it is probably true that ABF would be an even better committee than CDE.  Is
there a method that can choose CDE in the first case and ABF in the second
case?

Andy

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Re: [EM] Correspondences between PR and lottery methods (was Centrist vs. non-Centrists, etc.)

[Andy Jennings]

On Mon, Jul 18, 2011 at 6:00 PM,  wrote:

> Andy and I were thinking mostly of Party Lists via RRV.  His question was
> that if we used RRV, either
> sequential or not, would we get the same result as the Ultimate Lottery
> Maximization.  I was able to
> show to our satisfaction, that at least in the non-sequential RRV version,
> the results would be the
> same.  It seems like the initial differences between sequential and
> non-sequential RRV would disappear
> in the limit as the number of candidates to be seated approached infinity.
>
> Would that imply P=NP?In other words, sequential RRV might be an
> efficient method of
> approximating a solution (for large n) of non-sequential RRV (which is
> undoubtedly NP hard).  What
> would be analogous in the Traveling Salesman Problem?  Don't hold your
> breath, but it would be
> interesting to sort out the analogy, if possible.
>


I am still hopeful that sequential RRV with a large number of seats, leaving
each candidate in as if they were their own party, would be a good and
tractable way to choose legislators and give them each a different amount of
"voting power".  I'm hoping it would be possible to calculate the
proportions in the limit as n goes to infinity.

But sequential RRV is completely ignorant about how many seats need to be
filled, so it's not really going to find the globally optimum N-winner
representative body like ULM and non-sequential RRV aim to do.  This
"infinite sequential RRV" might be good  when there is no pre-determined
number of seats to fill but instead we want the method to choose the number
of winners.  For real elections, however, I suspect that it will give some
voting power to every candidate, so maybe it's not that good for choosing a
representative body.

Here's an example, on the other hand, where this method chooses too few
winners:
10 voters approve A and C
10 voters approve A and D
10 voters approve A and E
10 voters approve B and C
10 voters approve B and D
10 voters approve B and E

If you're choosing two winners, I think the obvious winners are A and B.
 But if you want to choose three winners, I think the obvious choice is C,
D, and E.  Only a method that knows how many winners you're going to choose
can make the correct decision here.  In this case, RRV will choose A and B.
 If A and B are "left in" (pretending they are parties even if they are
candidates) then RRV will continue to alternate between A and B.  In the
limit, it will give half of the voting power to A and half to B.  This is
just not helpful if you wanted to choose three winners.

ULM and non-sequential RRV evaluate each possible combination of winners and
can do the right thing in the three winner case.

Andy

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Re: [EM] Has this idea been considered?

[Andy Jennings]

I agree with Kevin that the existing SODA page on the wiki is _not_ for
novices.

I created a simplified page:
http://wiki.electorama.com/wiki/Simple_Optionally-Delegated_Approval_(simplified)

Feel free to edit, but let's add to it as little as possible, or even take
some away if we can.

Andy



On Fri, Jul 8, 2011 at 4:27 PM, Kevin Venzke  wrote:

> --- En date de : Ven 8.7.11, Toby Pereira  a écrit :
> The thing about SODA is that it's harder to "get" than Approval Voting.
> I haven't exactly read through all the posts on it here thoroughly but
> I've looked at the page - http://wiki.electorama.com/wiki/
> Simple_Optionally-Delegated_Approval - and I do find myself
> thinking "What?"
> [end quote]
>
>
> Well hmm. I'm kind of looking at this article as a collection of things
> that have been said by SODA people. As a neutral intro to the method
> for people who don't know whether the inventors have any idea what they
> are talking about, it's kind of terrible.
>
> In particular that intro paragraph... I didn't want to go on.
>
> "I'm going to abandon the neutral voice and talk as myself."
>
> Ahaha.
>
> Maybe the article should be forked. Have one concise, neutral version
> (like neutral neutral), and then the exciting one.
>
> Kevin
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>

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Re: [EM] Has this idea been considered?

[Andy Jennings]

On Fri, Jul 8, 2011 at 3:56 AM, Jameson Quinn wrote:

>
> So, I guess the question is: is there anyone who would support Approval but
> not SODA? Respond in text. Also, I made a poll on betterpolls - go vote.
> http://betterpolls.com/v/1425
>
>
Wow, that results page is hard to read when the poll is about voting systems
and the results are analyzed with lots of different voting methods.  Very
"meta".

In any case, I went and voted.

I was pretty hard on SODA.  Even though I like where it's going, I, like
Kristofer, don't think it's been analyzed enough to become our endorsed
system at this point.

Let's keep working on it...

Andy

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Re: [EM] Learning from IRV's success

[Andy Jennings]

>
> Also, I think IRV's seemingly intuitive nature has something to do with it.
> For those who *did* investigate more deeply, IRV seemed sensible, too:
> instead of holding a bunch of expensive runoffs, collect all the required
> information at once and then act as if there were runoffs. That fails to
> account for the dynamics between the rounds, but that's a subtle detail and
> might easily be missed.
>

I, too, must admit that IRV has a natural feeling to it.  I had a friend who
described to me a system he thought of "on his own" and he ended up
describing IRV.

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Re: [EM] SODA

[Andy Jennings]

Here's an off-the-wall idea.  Haven't fully thought through the strategic
implications, but here goes:

What if, instead of requiring the candidates to vote sequentially, they all
have to go at the same time, but we introduce another level between
"approve" and "don't approve" which is "conditional approval" or "approve
this candidate only if he approves me".  (I don't yet know how this fits in
with the candidates' pre-specified rankings.)

These are resolved on a pairwise basis.  If A approves B and B conditionally
approves A, then that is converted into full approval.  If A and B both
conditionally approve each other, then that should be converted into mutual
full approval.

Thoughts?

Andy

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Re: [EM] SODA

[Andy Jennings]

This is not an answer to the question of how to arrange them into a tree,
but here is an idea for how to compare factions of different sizes:

If there are N total candidates, then the score of a faction (a subset of
candidates) of size M could be the voter count of that faction (the number
of voters who ranked those candidates strictly above all other candidates)
divided by the expected size of a faction of size M (total number of voters
divided by "N choose M").

Then you could identify the weakest candidate in the strongest faction and
make him go first, or something like that.


In general, since it seems like an disadvantage to go first, to me it
doesn't seem right to make the strongest candidate go first.  Jameson, is
the main thing you're trying to avoid the game of chicken between two
clones?  Or are you trying to avoid the game of chicken and the kingmaker
problem at the same time?

Andy

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Re: [EM] SODA clarification

[Andy Jennings]

On Thu, Jul 7, 2011 at 8:33 AM, Jameson Quinn wrote:

> Andy, I like both of your suggestions. Why don't you try putting them on the
> page<http://wiki.electorama.com/wiki/Simple_Optionally-Delegated_Approval>yourself?
>  I don't want this system or that page to be "mine", I just want
> them to be good.
>
>
Okay, I changed the Wiki.  I'll try to give it a second look tomorrow to see
if I want to re-word anything.



>
> 2011/7/7 Andy Jennings 
>
>> Jameson,
>>
>> I'm really liking the SODA method that is evolving.  I have a couple of
>> cosmetic suggestions:
>>
>> First, in the description of SODA, I dislike using the term "delegate" for
>> step 3, candidate-to-candidate transfers.  I would only use the word
>> "delegate" for step 2, the bullet voters' votes getting delegated to their
>> candidates.  I prefer to think of step 3 as the candidates "casting" their
>> votes (which includes all the delegated votes they control).  It's a much
>> simpler mental model for me.  Since they aren't passing anything on to
>> another candidate which can be changed or controlled, I don't consider it
>> delegation.  Also, it decreases the implication of smoke-filled rooms (for
>> me) to have as little "delegation" as possible.  I think this terminology
>> was why I was confused about step 3 in a prior email.
>>
>> Second, I find it incredibly confusing to say you have to write in "do not
>> delegate" if you bullet vote and you don't want your vote delegated.  I
>> realize that you want delegation to be the default for bullet voters.  Why
>> not organize the ballot with that as a separate question (as follows)?
>>
>> 
>> "Vote for as many candidates as you approve:"
>>
>> [ ] Candidate A
>> [ ] Candidate B
>> [ ] Candidate C
>> [ ] Candidate D
>> [ ] ___(write-in)_
>> [ ] ___(write-in)_
>> [ ] ___(write-in)_
>>
>> "If you only vote for one candidate, he can choose to transfer his vote to
>> one or more alternate candidates in the event that he cannot win, UNLESS you
>> check the box below:"
>>
>> [ ] Do not let the candidate I voted for transfer my vote to other
>> candidates
>> 
>>
>> Andy
>>
>>
>>
>>
>> On Wed, Jul 6, 2011 at 8:54 AM, Jameson Quinn wrote:
>>
>>>
>>>
>>> 2011/7/6 Andy Jennings 
>>>
>>>> Jameson,
>>>>
>>>> I have become confused about one point of operation in SODA.  Take this
>>>> scenario:
>>>>
>>>> 35 A>B>C
>>>> 34 B>C>A
>>>> 31 C>A>B
>>>>
>>>> If A delegates to A,B then does B have 69 votes he can delegate to B,C
>>>> or does he have only 34 he can play with?
>>>>
>>>> In other words, can votes delegated from one candidate to another be
>>>> re-delegated to a third candidate?
>>>>
>>>
>>> B has 34. Delegable votes are only bullet votes. In fact, a real SODA
>>> scenario would probably be more like:
>>>
>>> 25 A (>B)
>>> 5 A,X
>>> 5 A,B
>>>  26 B (>C)
>>> 4 B,X
>>> 4 B, C
>>> 29 C (>A)
>>> 1 C,X
>>> 1 C,A
>>> Initial totals: 36A, 39B, 35C
>>> Delegable: 25A, 26B, 29C
>>>
>>> Note that in this example, C has the most delegable votes and would
>>> decide delegation first, even though B has the most total initial votes. In
>>> this case - a Condorcet cycle - the result would be the same no matter who
>>> delegates first, as long as all candidates use correct strategy. But there
>>> are cases where it wouldn't be:
>>>
>>> 25: Left (>X)
>>> 15: Left, Center
>>> 5: Left, Right
>>> 25: Center (>Right)
>>> 30: Right (>Center)
>>>
>>> The candidate Left has not declared any delegable preferences, but the
>>> left voters clearly tend to prefer Center over Right. Center is the
>>> Condorcet winner, but Right would get the chance to delegate before Center,
>>> and thus would be the strategic winner under SODA. If delegation order went
>>> in order of total votes instead of delegable votes, Center would win.
>>>
>>> Hmm... now that I look at this scenario in black and white, I'm starting
>>> to think that delegation order should be in order of total, not delegable,
>

Re: [EM] SODA clarification

[Andy Jennings]

Jameson,

I'm really liking the SODA method that is evolving.  I have a couple of
cosmetic suggestions:

First, in the description of SODA, I dislike using the term "delegate" for
step 3, candidate-to-candidate transfers.  I would only use the word
"delegate" for step 2, the bullet voters' votes getting delegated to their
candidates.  I prefer to think of step 3 as the candidates "casting" their
votes (which includes all the delegated votes they control).  It's a much
simpler mental model for me.  Since they aren't passing anything on to
another candidate which can be changed or controlled, I don't consider it
delegation.  Also, it decreases the implication of smoke-filled rooms (for
me) to have as little "delegation" as possible.  I think this terminology
was why I was confused about step 3 in a prior email.

Second, I find it incredibly confusing to say you have to write in "do not
delegate" if you bullet vote and you don't want your vote delegated.  I
realize that you want delegation to be the default for bullet voters.  Why
not organize the ballot with that as a separate question (as follows)?


"Vote for as many candidates as you approve:"

[ ] Candidate A
[ ] Candidate B
[ ] Candidate C
[ ] Candidate D
[ ] ___(write-in)_
[ ] ___(write-in)_
[ ] ___(write-in)_

"If you only vote for one candidate, he can choose to transfer his vote to
one or more alternate candidates in the event that he cannot win, UNLESS you
check the box below:"

[ ] Do not let the candidate I voted for transfer my vote to other
candidates
----

Andy




On Wed, Jul 6, 2011 at 8:54 AM, Jameson Quinn wrote:

>
>
> 2011/7/6 Andy Jennings 
>
>> Jameson,
>>
>> I have become confused about one point of operation in SODA.  Take this
>> scenario:
>>
>> 35 A>B>C
>> 34 B>C>A
>> 31 C>A>B
>>
>> If A delegates to A,B then does B have 69 votes he can delegate to B,C or
>> does he have only 34 he can play with?
>>
>> In other words, can votes delegated from one candidate to another be
>> re-delegated to a third candidate?
>>
>
> B has 34. Delegable votes are only bullet votes. In fact, a real SODA
> scenario would probably be more like:
>
> 25 A (>B)
> 5 A,X
> 5 A,B
>  26 B (>C)
> 4 B,X
> 4 B, C
> 29 C (>A)
> 1 C,X
> 1 C,A
> Initial totals: 36A, 39B, 35C
> Delegable: 25A, 26B, 29C
>
> Note that in this example, C has the most delegable votes and would decide
> delegation first, even though B has the most total initial votes. In this
> case - a Condorcet cycle - the result would be the same no matter who
> delegates first, as long as all candidates use correct strategy. But there
> are cases where it wouldn't be:
>
> 25: Left (>X)
> 15: Left, Center
> 5: Left, Right
> 25: Center (>Right)
> 30: Right (>Center)
>
> The candidate Left has not declared any delegable preferences, but the left
> voters clearly tend to prefer Center over Right. Center is the Condorcet
> winner, but Right would get the chance to delegate before Center, and thus
> would be the strategic winner under SODA. If delegation order went in order
> of total votes instead of delegable votes, Center would win.
>
> Hmm... now that I look at this scenario in black and white, I'm starting to
> think that delegation order should be in order of total, not delegable,
> votes. Not that there isn't a case to be made for Right in this election; if
> Center were really a better result, then they should get either Left's
> delegation or more delegable votes from the nominally voters who chose
> [Left, Center] here. This argument like FairVote's handwaving arguments
> about "strength" of support - which is not necessarily invalid just because
> it's imprecise and easy to reduce ad absurdem. But... I think that having
> this scenario go to Right puts too much of a burden of strategic calculation
> on the [Left, Center] voters.
>
> So, yet another adjustment to SODA, I think. Delegation choice goes in
> descending order of total votes; the person with the most total votes gets
> the "first move". If my grounded intuition is correct, this should not
> matter when there's a 3-way cycle, only when there's a pairwise champion
> (CW).
>
> Hopefully this will be the last time I have to adjust SODA. Also note that
> all the adjustments so far have been minor tweaks; any of the versions so
> far would work well, though I believe they have been steadily improving.
> Current rules, as always, are at
> http://wiki.electorama.com/wiki/Simple_Optionally-Delegated_Approval
>
> JQ
>
>
>> I looked at

Re: [EM] SODA

[Andy Jennings]

On Wed, Jul 6, 2011 at 6:06 PM,  wrote:

>
> Of course, with too many factions, the optimal strategy computation would
> be intractable.
>

With twenty candidates, there are about a million different possible subsets
to consider.  Seems like it could be tractable.

I'm not exactly following how the tree is organized.  If there are N
candidates and every voter ranks all candidates, then the biggest N-1 size
faction will be the one that omits the candidate who is ranked last by the
most voters, right?  Can't you apply that recursively to build the tree?

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[EM] SODA clarification

[Andy Jennings]

Jameson,

I have become confused about one point of operation in SODA.  Take this
scenario:

35 A>B>C
34 B>C>A
31 C>A>B

If A delegates to A,B then does B have 69 votes he can delegate to B,C or
does he have only 34 he can play with?

In other words, can votes delegated from one candidate to another be
re-delegated to a third candidate?

I looked at the wiki and still am unclear on this.  I still have the
original SODA proposal in my head (where votes could not be delegated
multiple times) and I can't remember if we've changed this detail at some
point.

Thanks,

Andy



On Tue, Jul 5, 2011 at 12:39 PM, Jameson Quinn wrote:

> Russ, you said that SODA was too complicated. In my prior message, I
> responded by saying that it was actually pretty simple. But thanks for your
> feedback; I realize that the SODA page was not conveying that simplicity
> well. I've changed the procedure there from 8 individual steps to 4 steps -
> simple one-sentence overviews - with the details in sub-steps. Of these 4
> steps, only step 1 is not in your proposal. And the whole of step 4 is just
> three words.
>
> The procedure is exactly the same, but I hope that this 
> versiondoes
>  a better job of communicating the purpose and underlying simplicity of
> the system.
>
> Thanks,
> Jameson
>
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>
>

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Re: [EM] A secure distributed election scheme based on Bitcoin's Proof-of-Work protocol

[Andy Jennings]

I bet inTrade could be persuaded to sell BitCoin futures.

A future that pays out if BTC falls below a certain dollar amount could
serve the same purpose as shorting BitCoins.

- Andy


On Sat, Jun 18, 2011 at 4:02 PM, Mike Frank  wrote:

> Shorting essentially just means borrowing the item to short, and then
> selling the borrowed item below market price.
>
> You could certainly borrow bitcoins from someone (if they were willing to
> loan them to you), and then sell the borrowed coins on an exchange.
>
> However, the existing exchanges don't support "naked short selling," which
> would means posting an "ask" to sell bitcoins that you don't actually have
> on deposit in your exchange account.
>
> But, there is nothing to prevent someone from making such an exchange, or
> just posting a Craigslist ad that says, "I have 1 million Bitcoins which I
> am willing to sell to anyone for $0.001 cents each," when you don't have the
> actual coins yet, just some friends who have agreed to loan you their coins.
>
> That would essentially be a retro-tech equivalent of a naked short sell.
>
> -Mike
>
>
> On Sat, Jun 18, 2011 at 6:16 PM, Warren Smith wrote:
>
>> By the way, re Jameson Quinn saying he'd short-sell bitcoins...
>> is it actually possible to short them?
>>
>> --
>> Warren D. Smith
>> http://RangeVoting.org  <-- add your endorsement (by clicking
>> "endorse" as 1st step)
>> and
>> math.temple.edu/~wds/homepage/works.html
>> 
>> Election-Methods mailing list - see http://electorama.com/em for list
>> info
>>
>
>
>
> --
> Full name:   Michael Patrick Frank
> Email addr.: michael.patrick.fr...@gmail.com (pers. email)
> Snail mail:  820 Hillcrest Ave., Quincy, FL,  32351-1618
> Phone/voicemail: (413) 842-6670 (main number, uses Google Voice)
> Webpage URL: http://www.facebook.com/M.P.Frank (pers. profile)
>
>
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>
>

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Re: [EM] A secure distributed election scheme based on Bitcoin's Proof-of-Work protocol

[Andy Jennings]

On Sat, Jun 18, 2011 at 7:50 AM, Mike Frank  wrote:

> Even if the total resources deployed on the Bitcoin network were to someday
> fall to such a low level that a single attacker could easily produce a
> forged chain of transactions, that would only mean that this attacker could
> double-spend their own coins from that point onwards, not that they could
> nullify the established chain that was already in existence and accepted by
> all nodes on the network.
>

If the attacker truly had disproportionate computing resources, couldn't he
go back to the chain as it was a year ago and start extending from there?

If he could make the forged chain longer than the real chain, wouldn't that
invalidate every bitcoin mined and every peer-to-peer transaction in the
last year?

Andy

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Re: [EM] MRSODA (Mr. Soda), a SODA-inspired PR method (NP-complete???)

[Andy Jennings]

Jameson,

On Fri, Jun 10, 2011 at 6:53 AM, Jameson Quinn wrote:

> I'm not aware of many approval-based PR systems, though. Perhaps it's my
> own ignorance, but the only ones I know of are RAV and the two-ranked case
> of a complicated, unpublished Bucklin-based system I've come up with, based
> on the concept of assigning individual votes and electing candidates one at
> a time. Since I don't really even understand my own system (I've decided
> it's too complex to be worth publishing until I've at least explored its
> properties computationally) that leaves just RAV (reweighted approval
> voting, the approval simplification of RRV).
>

You may want to Google "Brams Kilgour Approval Committee".  In early 2009, I
saw Marc Kilgour give a talk that surveyed MANY different methods of
resolving a multiwinner election from approval ballots.  He considered many
different permutations and parameters.I think this is a similar "survey"
paper: http://www.springerlink.com/content/r173p72n6l1q6880/

But it's not free...  :(

It seems the method that Kilgour and Brams like best is called Satisfaction
Approval Voting.  There is some material about this in Brams' book
"Mathematics and Democracy".



> Remember, the RAV procedure is:
> 0. While there are still open seats, repeat the following two steps:
> 1. Elect the highest-approval candidate
> 2. Reweight all ballots to 1/(n+1), where n is the number of elected
> candidates they approve
>
> I would propose a variant of this, Minimum Remainder RAV. The slate elected
> is the one which leaves the lowest average final weight over all ballots.
> This is an optimizing, not a procedural system, and so I do not know how
> hard it is in practice to calculate the result; as far as I know right now,
> it could be NP-complete. In that case, to make it decidable, the rule could
> be to allow anybody to submit a slate for some period after the election,
> and the winning slate is the optimum out of those submitted. With modern
> computers, it would be possible to submit all possible slates for up to a
> few dozen serious candidates; past that, it may be impossible to find a
> provably-optimum solution, but you could be certain to come close.
>
> Here's a simple example of when it comes out different from RAV:
> 11: AB
> 10: AC
> 6:D
>
> RAV elects A,D. MRRAV elects B,C
>


Can you explain what it means that "the slate elected is the one which
leaves the lowest average final weight"?

I thought it meant to minimize SUM(1/(N_i + 1)) over all voters, i, where
N_i is the number of winning candidates approved by voter i.

But in your example, electing B and C would leave 21 voters with one
approved candidate and 6 voters with zero approved candidates, which gives
an average final weight of 0.6111.  Electing A and D would give all 27
voters exactly one approved candidate, for an average final weight of 0.5.
 So wouldn't A and D be the winner in MRRAV?

Andy

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Re: [EM] Defensive strategy for Condorcet methods

[Andy Jennings]

On Wed, Jun 8, 2011 at 8:58 AM, Jameson Quinn wrote:

> From my experience talking to normal people not already interested in
> voting or math, I think that it is very important to keep your list of
> proposals short. 1 is good, 2 is tolerable, 3 is approximately pointless,
> and anything more is clearly counterproductive.
>
> Since I understand that I'm probably not going to convince the condorcet
> supporters here, I'm willing to include a Condorcet proposal. Since I value
> offering a simple option, I think that proposing (Some Condorcet) or SODA is
> better than just advocating (Some Condorcet). Still, I strongly urge that
> our statement should not go beyond two well-explained proposals, though it
> should endorse by simple mention a number of other systems (Schulze, Range,
> MCA, MJ...).
>

I strongly believe that plain Approval, plain Range, some Condorcet method,
and a median-based method (perhaps MJ?) should be tried in real political
elections to see what happens, so I would hate to see any of these not get
mentioned at all.  Now I can't guarantee that each method's nightmare
scenario won't happen, but I would surely like to see each one tried.  Maybe
mentioning these systems in passing is good enough.

I do agree that the shorter we can keep the list of proposals, the better.
 But are we ready to settle on SODA and something else?  To me, SODA seems
like a pretty good system so far, but it seems like we should analyze it for
a while more before we decide to endorse it.  After all, it was only
invented a couple of weeks ago and it seems like we're still adjusting the
details.

Also, do we need to worry about endorsing methods that nobody has ever heard
of?  I'm afraid that if we endorse SODA, then nobody will take us seriously
because they've never heard of it before.  Just as an example, Schulze seems
to have some name-recognition on the internet.

Maybe a necessary first step is to write up SODA in the Electorama wiki, to
write up a blog post about it, and to try to get it featured on some news
sites.  Slashdot and HackerNews seem like good targets, since programmers
seem disproportionately interested in voting systems.

Andy

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[EM] List of acceptable methods (and some wiki questions)

[Andy Jennings]

On Sat, May 28, 2011 at 5:53 PM,  wrote:

> From simplest to less simple but still simple enough:
>
> 1. Asset Voting
> 2. Approval
> 3. DYN
> 4. MCA
> 5. The Bucklin Variant of Venzke and Benham
>
>
Forrest,

Can you remind me what "the Bucklin Variant of Venzke and Benham" is?  If
it's that good, we should name it and make an entry on the wiki.

Also, I didn't find a wiki entry for DYN.  We should add one.

When you mention MCA, are you thinking specifically of the three-grade
version, or are you open to different grading scales?

A couple more thoughts about the wiki:

- We should make sure there are entries for the Ultimate Lottery Method and
any other good methods that get seriously discussed on the list.

- To the MCA page, we should add the tie-breaking method used in the
Majority Judgement (drop one copy of the median grade and then compute the
new median.)  Maybe Majority Judgement is different enough to deserve its
own page.  I can probably make those changes if you want me to.  If I just
add it as another tie-breaking method, should I call it "MCA-MJ"?

- It looks like "Condorcet//Approval" might have a page on the wiki, but all
the incoming links are broken.  Do you think it's because of the slashes in
the name?

Andy

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Re: [EM] Statement by this list (was Remember toby Nixon)

[Andy Jennings]

I think an official statement by this list is a great idea.

Andy


On Fri, May 27, 2011 at 12:01 AM, Jameson Quinn wrote:

> This thread, like this list, has two purposes - practical advocacy and
> mathematical exploration.
>
> On the practical advocacy front, I'd propose a process:
> 0. We discuss get some degree of informal consensus on this process itself
> - I imagine it will take about a week, so say, before Sunday June 5th.
> 1. We draw up a statement which details the serious problems with plurality
> in the US context, and states that there are solutions. Leave a blank space
> for a list of acceptable solutions. This statement, when finished (after
> step 3) would be "signable" by any members of this list, completely at their
> own option.
> 2. We take a vote on what options to list. We can use betterpolls.com,
> remembering that the scores there are -10 to 10, and negative/positive is
> mapped to approval/disapproval.
> 3. We list the options and the winner(s) in the statement and sign it.
> 4. When we have a good number of signatures, we put out a "press" release
> to some bloggers who've shown an interest in the issue (e.g. Andrew
> Sullivan)
>
> My hope is that, despite the varied opinions, we could say something
> clearly and strongly enough to have an impact.
>
> JQ
>
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>
>

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Re: [EM] electing a variable number of seats

[Andy Jennings]

Isn't Jameson right?  In the non-sequential version of RRV, if there are
only two seats to be awarded and C gets niether of them, then the sum of the
C voter's grades of the elected candidates is zero, which will contribute a
huge negative value to the sum of the logs.

But if C is given one of the two seats, even though only one voter out of
100 liked C, then the C voter will have a positive sum and all the A voters
will have a positive sum, so the sum of the logs will be higher.

I guess you can try to pick a large enough epsilon so that a small group of
voters doesn't have veto power.  Has a good formula been given for choosing
the appropriate epsilon?  If you're considering the limit as epsilon goes to
zero, then it seems to be vulnerable to one voter bullet voting.

Andy



On Wed, May 18, 2011 at 12:15 PM,  wrote:

>
> Jameson Quinn  wrote ...
>
> Wait a minute so under non-sequential RRV, there is no "leftover Hare
> quota" of unrepresented voters? If 99 voters vote A100 B99 and one voter
> votes C100, then C will be in the 2-member parliament? That seems broken.
>
> FWS replies:
>
> Your question has the same answer regardless of which version of RRV is
> used
> (sequential or non):
>
> If there are only two seats, A gets the first and B the second.
> If there are only two seats and repetition is allowed, A gets both of them.
> If there are 100 seats with repetitions allowed, then A gets 99 of them and
> C
> gets one of them.
>
> We allow repetition only if A , B, C, etc represent parties (or if the
> elected
> body uses a weighted voting system).
>
> So the primary interpretation of "A gets two seats" would be two seats come
> from
> the party A.
> 
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>

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