date:20070314

At 01:23 PM 3/14/2007, Chris Benham wrote:
>I reject this on the same grounds that I reject the "candidate
>withdrawal option" (in say IRV) and
>"Asset Voting":  I am only interested in single-winner methods where the
>result is purely determined (as far as possible) by voters voting, 
>and not by the machinations of candidates/parties.

To be consistent, Chris should likewise reject deliberative process, 
and he should reject proxy voting. Asset Voting is merely proxy voting.

Further, he should reject all pre-election process, including the 
processes by which candidates are nominated, as they are likewise 
"the machinations of candidates/parties." Only pure voting would be 
allowed. No consultation through coalitions of voters.

Public elections without such pre-election process are rather 
difficult to imagine as being something desirable.

Further, Chris should reject parliamentary government, where leading 
governmental officers are elected by representatives of the people 
rather than directly.

Asset Voting allows voters total freedom. As Asset has been 
described, any voter can either vote for a proxy or can vote for 
himself or herself and thus participate directly in the next stage. 
While Asset has typically been described as using candidates as 
proxies (which seems reasonable to me, particularly if ballot access 
is relatively easy), if write-in votes are allowed, the freedom of 
the voter is totally unrestricted.

Given how desirable this would seem (and, as proxy voting, it must be 
noted that the precedent is firmly established: it is what people do 
when they have choices, as did investors when corporations were 
originally formed), the objection would seem to be technical: Asset 
is not a complete "election method," it begs the question as to how 
the final determination is made. Thus, it might be argued, it is 
irrelevant here, we should only talk about "election methods."

Yet, of course, Asset *would* be a procedure whereby a society can 
select from a multitude of choices, the one (or more) to be adopted.

What would Chris think about Asset used for multiwinner elections? In 
particular, we have proposed using Asset to create full proportional 
representation, and have suggested that this could be used to create 
an assembly which would have nearly all voters with a known 
representative (known to the voter, and chosen by the voter directly 
or indirectly), whom the voter's vote elected, and who would usually 
represent a geographic district, completely independently of "party 
machinations," unless the voter elects to chose candidates who are 
party-affiliated. Because Asset wastes no votes, *anyone* can run and 
receive votes without harm.

(The only "harm" would be if the candidate only gets one vote, his or 
her own vote, and the harm is that the canddidate has wasted his 
time: he will have to participate further, or waste the vote.)

Frankly, I find it difficult to imagine an objection to this process 
used to create a fully representative assembly beyond one like "It 
will never fly, people won't go for something so different from what 
they know."

And it would seem that Chris' objection to Asset is basically an 
objection to representative democracy entirely. Yet the very concept 
of a single-winner election, where the winner is to represent or make 
decisions on behalf of the voters, is that of representative 
democracy, though boiled down to a single winner (and single-winner 
district-based assemblies are a series of such elections).

What's the problem? Is it the pedantic one of "Asset isn't an 
election method as I define it," or is it more substantial?

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Re: [EM] Trees and single-winner methods

On Mar 14, 2007, at 19:23 , Chris Benham wrote:

> Juho wrote:
>
>> Here's one more election method for you to consider
>>
>> Let's start from a Condorcet method (it doesn't matter much which   
>> one). Then we allow the candidates to form groups. Each group will  
>> be  handled as if it was a single candidate.
>>
>
> I reject this on the same grounds that I reject the "candidate  
> withdrawal option" (in say IRV) and
> "Asset Voting":  I am only interested in single-winner methods  
> where the result is purely determined
> (as far as possible) by voters voting, and not by the machinations  
> of candidates/parties.
>
> Chris Benham

That sounds quite strict. The voters still have all the power  
although the algorithm threats different candidates slightly  
different (depending on what the candidate tree looks like). A  
majority of the voters can pick any candidate they want.

Note that it is very typical in elections that the parties will  
decide on what candidates will be offered to the voters to choose  
from in any case. So the parties will have some impact in most  
elections anyway. They may arrange preliminaries, decide if they  
nominate more than one candidate etc.

How about multi-winner elections - do you say that open and closed  
list elections are no good and only flat candidate structures like in  
STV, are ok?

I see candidate withdrawal related problems to be quite different  
from what I see in the proposed three based method. The biggest  
problem I see in candidate withdrawal is that if the person/group  
that makes the decision on withdrawal already knows the given votes,  
then it is possible to decide the winner in a small group, partially  
bypassing the opinions that the voters expressed in the ballots. This  
also opens the door to horse trading or even blackmailing. The  
proposed method at least is based on giving full information to the  
voters already before the election and letting the voters decide.

Maybe you have some examples where the proposed method would behave  
in some unacceptable way. That would help evaluating what the method  
is good for.

Note that the main reason for proposing this method is to try to  
study methods that would bypass the strategy and method alternative  
jungle of the Condorcet group in a more radical way so that Condorcet  
like ranking based methods would be usable even in some badly  
strategic environments. For this reason I'l like to invite you all to  
point out also the potential strategic problems of the method.

Juho

P.S. The proposed candidate tree structure allows candidates to be  
arranged in many different ways. They could be grouped simply into  
parties in a two layer structure or the structure could be deeper. It  
is also possible that the structure would stay flat if no strategic  
voting is expected. One approach would be to arrange the candidates  
of one party into a list. We could mark the list [A B C D] and that  
would mean a binary tree structure A B) C) D). This structure  
would favour the beginning part of the list (unless the voters  
clearly express that D is the best). Since the structure of the tree  
is visible to the voters they may make their decision on what to vote  
based on what the tree is like. => If some candidate is bundled with  
another one that I don't like, maybe I won't give my support to  
either of them. Probably the candidates are similar minded after all.  
The structure gives also useful information to the voters.

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Re: [EM] divided house problem of close vote (50%+1)

On Mar 14, 2007, at 16:07 , Howard Swerdfeger wrote:

> You are correct, It was not originally intended to choose between two
> similar alternatives.
> but I believe it could serve this purpose. You wouldn't actually  
> send it
> to mars or Venus until the "score" reached a super majority, and then
> you would stop voting.

I just commented in another mail that the method could be also  
modified so that it would make the decision in either direction if  
the accumulated deviation from 50% to either direction exceeds some  
threshold value. In this case the method should behave in a symmetric  
way in both directions / towards both alternative options.

> As for debate, Typically I would Imagine a situation where a decision
> making body (legislature or citizens) exists in a currently almost
> evenly divided state. I would further imagine that the division of  
> this
> body would change over time at some rate. possibly because of  
> debate and
> people changing there minds, or possibly because of the actual  
> people in
> the decision making body changing (Bi-Election, full new elections,
> demographic change of citizens).
> I would guess that enough time needs to pass to typically allow 1-3%
> total state changes in decision making body, But that is just a guess.
> You need time to allow for honest debate. In a legislature this  
> could be
> 1 week or 1 day with debate and backroom deals in the middle. In a
> referendum this could be months or years to allow for some small
> demographic shift, or to account for some random variation in voter  
> opinion.

One could in principle also have voting chains that go on forever. If  
the timing and threshold parameters are well designed it would be ok  
to vote once every year or every month on whether it makes sense to  
send a rocket somewhere. No problem if the "yes" decision would never  
come. Maybe it would be too expensive to send the rocket.

Your original description included the possibility of reaching a  
conclusion that no additional round is needed (support below an  
agreed threshold, but no cumulative effect in the downwards direction  
(the symmetric method that I mentioned above would have similar  
cumulative effect in both directions)). It is possible to combine  
somehow also the length of the delay between elections in the  
equation ("try again after x hours/days"). Then the method would not  
only say if other votes are needed but it could also say something  
about when the next vote should be held. Maybe this would not be  
symmetrical. Maybe getting only 5% support would mean that new vote  
would be arranged earliest after some relatively long time. A  
concrete decision on time could be needed if there was a tendency to  
propose a new election with similar content right after the previous  
one led to a "don't try again" conclusion. (This is getting a bit  
complex => maybe recommendations and good practices and/or chairman's  
discretion would be enough :-).)

Juho

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Re: [EM] divided house problem of close vote (50%+1)

On Mar 14, 2007, at 12:15 , [EMAIL PROTECTED] wrote:

Doubtless this won't thread correctly.

Juho said
> Some observations.
>
> The description talks only about the "yes" votes. Is the assumption
> that the "no" votes mean "no action will be taken"?
>
> If we are talking about approving a new law then this is quite
> typical, but if we vote for example about whether we should send our
> rocket to Mars or Venus, then both sides should be treated in the
> same way.
>
> In the described method repeated 45% yes, 55% no results do not lead
> to final "no" (assuming super majority and new referendum levels  
60%/
> 40%). If we have only one rocket to send, voting first on sending  
the
> rocket to Mars, then on sending it to Venus, then to Mars etc. is  
not

> fair either. But maybe the method is not intended for this kind of
> elections with two similar alternatives to choose from.
>

I get the impression the vote would go something like:

Initial scores = 0

Round 1

Mars: 45%  +0 = 45 (-50 = -5)
Venus: 55% +0 = 55 (-50 = +5)

Round 2
Mars: 45%  -5 = 40 (-50 = -10)
Venus: 55% +5 = 60 (-50 = +10)

Round 3
Mars: 45%  -10= 35 (-50 = -15)
Venus: 55% +10= 65 (-50 = +15)

Round 4
Mars: 45%  -15= 30 (-50 = -15)
Venus: 55% +15= 70 (-50 = +15)

Venus wins as >2/3

Yes. You seem to assume that the Mars and Venus votes would take  
place more or less simultaneously.

Howard Swerdfeger's xls sheet btw doesn't behave exactly the same way  
as the written description of the method says. It doesn't let the  
Mars results drop below 45%. Thanks to Howard Swerdfeger for  
providing the sheet. Tthat is a good method to give clear  
(operational) definitions to the methods.

Note that it is possible that the sum of Mars and Venus votes need  
not be 100%. It is possible for example to have a faction that is  
eager to send a rocket to any planet. As a result both planets may  
get !50% results. In this case I don't know what happens if both  
planets reach the super majority limit at the same round.

One could also make the rules such that there is only one Mars vs.  
Venus vote at each round and the decision will be made when the  
balance will go from 50% to some threshold % to either direction.  
This way the election would be a symmetric election between two  
similar options (not a status quo vs. change type of election as in  
the original version).

This means that a majority can get anything past if they stick to  
their

guns, however, it will take lots of votes (spaced say 1 day apart).

It also naturally scales the time spent debating based on how
controversial the decision is.

Handling multiple choices could be handled with approval voting.   
Using

multiple rounds means that the tactics for approval are easier to use.

Yes. Even Condorcet could be used - just keep increasing/decreasing  
the elements of the comparison matrix.

I think there could be also electronic election methods where results  
are calculated in real-time and voters may change their vote when  
they see what the current results are. The behaviour of a method in  
this situation could be also used as one criterion to evaluate the  
stability of the method. This kind of situations could make also the  
Nash equilibrium of strategic voting states more meaningful (I have  
earlier criticized them as not being a good measure for typical ("non  
real-time feedback") elections).

Juho

For example, if you could use the following formula

New Approval = 2/3 * ( Old Approval*3/4 + approval from vote )

if 50% approve of an option, it will get

Round 1:
2/3*( 0 + 50) = 33%

Round 2:
2/3*(25+50) = 50%

Round 3:
2/3*(38+50) = 59%

Round 4:

2/3*(44+50) = 63

At round N (with N -> inf)

Round N

2/3*(50+50) = 66 and 2/3

Round N+1

2/3*(50+50) = 66 and 2/3

I would suggest rounding upwards to the nearest percent.  Ignoring  
rounding

an option cannot get the supermajority unless it has 50%+ approval.

Alternatively, rounding down could be used and the supermajority  
could be

set to say 65% required.

Raphfrk

Interesting site
"what if anyone could modify the laws"

www.wikocracy.com
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Re: [EM] "Possible Approval Winner" set/criterion (was "Juho--Margins fails Plurality. WV passes.")

On Mar 14, 2007, at 8:31 , Chris Benham wrote:

I'm not suggesting that PAW be explicitly made part of the rules of
any method, and the PAW
criterion is met by most methods including the simplest. So I don't
see how it "adds complexity".

Ok, if the election method already meets the criterion and the
criterion is not used as part of the rules, then there is no impact.

The Plurality criterion is about avoiding common-sense, maybe
"simple-minded" but nonetheless
very strong and (IMO)sound complaints from a significant subset of
voters: the supporters of a candidate
that pairwise beats the winner: "X ranked alone in top place on
more ballots than Y was ranked above
bottom clearly equals 'X has more support than Y', so how can you
justify X losing to Y?!".

I think there are different kind of elections with different kind of
rationale behind selecting the winner. For example the Condorcet
winner could be different than the one with best average rating. =>
One has to decide which needs to respect. Similarly the complaints of
the voters could be based on different arguments. Some voters may
complain about the number of "above bottom votes" (as above) but
other voters might complain about the fact that the voters would like
to change the winner to another candidate with a large majority.
There are other other rational measures that can be used as a basis
for complaints.

The plurality criterion is thus just one way of tying to characterise
what kind of a candidate should be elected. It is typical that in the
presence of cycles some rules that look obvious when there are no
cycles, but things get more complicated and intuition easily fails
when the cycles are present, and one needs to violate some of the
criteria.

I liked the rationale you gave in support of the plurality criterion,
the description of the situation after the election has been held. I
think this is a good way to evaluate the methods (more natural than
e.g. winner changing path based arguments) since typically we are
seeking a candidate that would work well with the society and that
would lead to a stable and happy state.

Note that the corresponding "state after the election" based
justification of minmax(margins) (that fails the plurality criterion)
for its behaviour is that it minimises the level of interest to
change the winner to some other candidate (to one other candidate at
a time). I think that property can be seen as a benefit for the
society and as one possible justification to violate the plurality
criterion. I don't claim that this minmax(margins) style of measuring
utility is ideal, but at least it makes quite a lot of sense since it
clearly provides best possible protection against one type of "after
the election" risk/complaints.

I ended up again in discussing the benefits of different methods with
sincere votes. But so did you :-). (I didn't yet catch if there are
also some strategic issues that are closely linked to the plurality
criterion.)

Juho

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Re: [EM] DAMC

Hello,

when proposing DAMC, I also wrote:
> What I'm not sure about so far is ... what would happen
> when we used the "resorting" or the "definitively defaeted" version
> of DMC with absolute majority size defeats only.

Here's a "resorting" version which seems to be equivalent to DAMC(River) 
but which is, however, a bit more complicated to describe:

1. Sort the options from top to bottom by descending approval score and 
draw for each absolute majority defeat an arrow from the defeated to 
the defeating option.

2. Remove all arrows for which a second, upward arrow exists with the 
same source and a higher target.

3. If no more downward arrows exist, elect the topmost option.

4. Otherwise, pick a downward arrow from those with the topmost target 
option. If this arrow builds a cycle with some upward arrows, remove 
it. Otherwise move its source option from its current position to just 
below the current position of its target option (thereby turning the 
downward arrow into an upward arrow).

5. Go to step 2.

When leaving out step 2, we get another "resorting" method which 
probably is equivalent to DAMC(Ranked Pairs).

Yours, Jobst

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[EM] More re: FBCs

2007-03-14 Thread Michael Ossipoff



FBC/SF is just a shortcut for expectation FBC. FBC/SF is easier to 
demonstrate compliance with because it only looks for noncompliance in one 
place.


DAMC, it seems to me, passes FBC/SF. It also seems to me that the way in 
which DAMC can reward favorite burial is so unpredictable, and just as 
likely to hurt as harm the voter, that it cant be said to help the voters 
expectation, leaving the mistreatment of ones favorite to give the 
favorite-burial a negative expectation increment.


FBC/SF assumes that that can be said, for all methods, for the 
favorite-burials that FBC/SF doesnt look at. Maybe thats a good 
assumption. But expectation FBC is what its really based on. You dont want 
it to be knowable that the voter can improve his/her expectation by 
favorite-burial, without very improbable predictive information.


Mike Ossipoff



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Re: [EM] Trees and single-winner methods

2007-03-14 Thread Chris Benham

Juho wrote:

>Here's one more election method for you to consider
>
>Let's start from a Condorcet method (it doesn't matter much which  
>one). Then we allow the candidates to form groups. Each group will be  
>handled as if it was a single candidate. 
>
>  
>

I reject this on the same grounds that I reject the "candidate 
withdrawal option" (in say IRV) and
"Asset Voting":  I am only interested in single-winner methods where the 
result is purely determined
(as far as possible) by voters voting, and not by the machinations of 
candidates/parties.

Chris Benham

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Re: [EM] divided house problem of close vote (50%+1)

At 09:32 AM 3/14/2007, Howard Swerdfeger wrote:
>[it was written]
> > In general, I dislike indefinitely repeated elections because they
> > increase voting costs for both the society and the voters in propotion
> > to the number of rounds they require.
>
>agreed. This would only be appropriate for situation where, the cost of
>the decision of little importance, when compared to the importance of
>the decision it self.

I think that it should be understood that in small groups, "repeated 
elections" is the normal decision-making process. Robert's Rules, or 
similar parliamentary rules, proceed with frequent votes on 
relatively minor options, including amendments, motions to table or 
refer to committee, as well as votes on whether or not the assembly 
is ready to vote on a main motion.

My own opinion is that the majority, quite properly, has the right of 
decision and that rules which prevent the majority from exercising 
this right are oppressive, in the end.

However, that the majority properly has that power does not mean that 
it should routinely exercise it. Essentially, any society benefits 
from decisions being made with general support. The experience of 
many small societies has shown that it is often possible -- in such 
small groups (perhaps up to thirty people or even more) -- to find 
total consensus, and a decision which is supported by everyone will 
almost certainly be a better decision (as long as that decision was 
sincerely supported, not merely because the rules required consensus 
and, hey, we've got to do something!)

Essentially, the desirability of consensus is a social context issue. 
I'm uncomfortable with building it into a system, unless the rule 
created is merely a warning, an alarm. I.e., this would be true if 
any decision made by mere majority vote must be accompanied by a 
finding of emergency, i.e., a finding, by the majority, that the 
society would be harmed by delay.

Now, if the majority wants to lie about this, what can we say? If we 
have a society where the majority is willing to lie to get its way, 
at the expense of a substantial miniority, we have serious problems, 
entirely aside from majoritarian rules.

(By the way, suppose the "harmed by delay" vote is sincere? This 
would point out the danger of preventing the majority from making a 
decision. This is especially clear when the status quo favors a 
minority which can block changes due to consensus rules. And I have 
seen this happen.)

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Re: [EM] reply to venzke - range "random skewing" effect is not a problem

At 02:03 AM 3/14/2007, Juho wrote:
>On Mar 13, 2007, at 21:20 , Abd ul-Rahman Lomax wrote:
>I really think this should be realized: I expect, at least
> > initially, major party supporters to vote under Approval exactly
> > the same as they currently vote under Plurality. Almost all will
> > bullet vote.
>
>This sounds to me like you are close to the third style of using /
>seeing the Range method (that I defined in my mail). => "3) accept
>the elections to turn into Approval like elections as a result of
>widespread Approval style voting". With two major parties Approval
>and bullet voting are about the same thing.

Yes. But that does not mean that the "election has been turned into 
Approval." Because in a two-party system, the parties tend to parity, 
more or less, making election swing on independent voters. Who would 
*not* vote simple Approval in Range elections.

If even one voter votes an intermediate vote, and it turns out that 
the election hinges on this vote, would you still claim that it was 
an Approval election? In fact, my guess is that many Range elections, 
if you analyzed them into Approval style votes and ballots containing 
intermediate votes, would turn on the intermediate votes, even if a 
large majority of voters voted Approval style.

So why would you even call this an "Approval-like election." It would 
be an election that includes Approval votes, and it could be said 
that Range is like Approval in many ways, but clearly the behavior 
would be different.

I think, however, that Approval and Range in single winner elections 
will *usually* pick the same winner. I'd bet that Warren's 
simulations show this, it would be interesting to see how true it is.

>One could thus use the Range method in different ways: 1) use it in
>non-competitive elections, 2) allow strategic/exaggerating/"sincerely
>strong opinion" voters to have more say and make their favourite win
>with improved likelihood, 3) accept the elections to turn into
>Approval like elections as a result of widespread Approval style voting.

Those are not different ways. The first is a different context, the 
others both apply in a Range election, except, of course, that I 
don't accept that a Range elections have been turned "into Approval 
like elections" merely because Approval style voting is "widespread." 
Only if it could be seen that non-Approval votes were almost always 
moot would I agree that the election has become "Approval-like."

And I have no problem if the electorate decides not to use the 
flexibility of Range. But Warren's little experiment with Range as an 
exit poll, while certainly not conclusive as to how voters would 
behave in real elections, shows an indication that most voters will 
use the Range flexibility. Yes, in a real election, with substantial 
attempts to "educate" voters undertaken by partisans, I'd expect many 
voters to retreat for that. But many voters, significant numbers of 
them, would not be so influenced.

If I think of how I'd have voted in 2000, were it Range, and I have 
strong opinions and am not shy about trying to turn them into 
reality, I come up with this:

Gore 100
Green 100
Libertarian 50
"Conservatives" 0
Bush 0

(I've used faction names rather than candidates because, for example, 
my opinion of Nader drastically dropped because of his intransigence 
in 2000, but if not for that -- and it would not have been a problem 
had the election been Range -- my rating would be higher. I'm 
generally "Progressive" -- but with a libertarian streak that is less 
trusting of big government solutions than most progressives might be.)

Had, say, a conservative like Barry Goldwater been on the ballot, I 
might have rated him higher than 0.

Ultimately, I support, strongly, libertarian principles, but do not 
judge society as being ready for them (if, indeed, it is ever ready). 
However, the proper field for libertarian action is *outside* of 
government, the whole FA/DP concept is rigorously libertarian.

> > I don't know how many times this nonsense has been repeated. "Range
> > becomes Approval." No, Range will *never* become Approval unless
> > you can somehow get all the voters to not express intermediate
> > ratings.
>
>This however confused me. In the beginning of the mail you assumed
>that almost all will bullet vote (which I interpreted to be in line
>with Approval).

What I expected, and stated, is that supporters of the major parties, 
which by definition covers a majority of voters, even a 
supermajority, will largely vote Approval style.

But that is not the whole election. Largely, more or less by design, 
these two factions cancel each other out, and elections hinge on 
"swing voters," and these voters will quite frequently vote 
intermediate votes, using the Range flexibility.

Get it? Come on, it's not that difficult!

The Range voters are quite likely to turn the election. So how can 
you say that the election has reduced to Approval?

>  But here the interpretation is

Re: [EM] DAMC

Hello,

When proposing DAMC, I wrote:
> What I'm not sure about so far is whether using Beatpath or Ranked
> Pairs instead of River gives the same winner.

Now I'm sure all these would give different methods -- examples follow.

We define these methods:

DAMC(River), DAMC(Beatpath), DAMC(Ranked Pairs):

Define 
  defeat := absolute majority size defeat
and 
  defeat strength := approval score of defeating option.
Then use the River/Beatpath/Ranked Pairs method of cycle resolution.
Of those options remaining undefeated, elect the most approved.

My original proposal was DAMC(River).

The following example shows DAMC(Ranked Pairs) to be different from the 
other two:

Defeats: E>A>D>C>B>D 
Approval scores: A>B>C>D>E
DAMC(Ranked Pairs) locks in E>A>D and C>B>D and hence elects C.
DAMC(River) locks in E>A>D>C>B and hence elects E.
In DAMC(Beatpath), E has beatpaths against A,B,C,D, hence E wins.

The following example shows that DAMC(Beatpath) is also different:

Defeats: A>B>D>A,C>D
Approval scores: A>B>C>D
DAMC(Ranked Pairs) locks in A>B>D and C>D and hence elects A.
DAMC(River) locks in A>B>D and also elects A.
In DAMC(Beatpath), C has beatpaths against A,B,D, hence C wins here.

The following example shows that DAMC(Ranked Pairs) violates IPDA and 
ISDA (just as ordinary Ranked Pairs does):

Defeats: C>D>E>C>F>B>A>D, A>E, B>D, and D is Pareto-dominated by A.
Approval scores: A>B>C>D>E>F
DAMC(Ranked Pairs) locks in A>D,A>E, B>D,B>A, C>D,C>F, D>E, F>B, which 
gives the social order C>F>B>A>D>E. 
But when D is removed, it locks in A>E, B>A, C>F, E>C, which gives the 
social order B>A>E>C>F.

DAMC(River) has not this problem: It locks in A>D,A>E, B>A, C>F, E>C 
from the beginning, which gives the same social order B>A>E>C>F as 
without D, with only the defeat A>D added to it. Also DAMC(Beatpath) 
elects B in both cases.

The following example shows that also DAMC(Beatpath) violates IPDA and 
ISDA (just as ordinary Beatpath does):

Defeats: C>D>E>A>B>D, A>C, B>E, and D is Pareto-dominated by C.
Approval scores: A>B>C>D>E
Since C has a beatpath against A,B,D,E, it wins. Without D, also A 
remains undefeated after the cycle resolution, hence A wins.

Unlike ordinary Beatpath, DAMC(Beatpath) at least fulfils "immunity from 
absolute majority 2nd place complaints". This is because all defeats by 
an option have the same strength (namely the approval score of that 
option). Assuming X wins and is absolute majority defeated by Y, there 
must be a beatpath from X against Y leading thru more-approved options 
than Y. In particular, Y is then defeated by a more approved option 
other than X, and hence cannot win after X is removed.

So, just as in the winning-votes case, River seems to be a slightly 
better cycle resolution method for DAMC than Ranked Pairs and Beatpath 
since it fulfils IPDA and ISDA and is therefore less vulnerable to the 
addition of weak options.

Yours, Jobst

pgp4Rm3kLvrlW.pgp
Description: PGP signature

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Re: [EM] Are proposed methods asymptotically aproaching some limit of utility?

At 01:11 AM 3/14/2007, Kevin Venzke wrote:
>But is this all about changing what we mean by the terms "strategic"
>and "insincere"? Is that the point?

As the terms apply to Range and Approval, yes. The usage came from 
use with ranked systems, where the behavior of the system and 
implications for voters was different.

> > Yes. I think that if you vote Approval style, you are dividing the
> > candidates into two groups, and you are willing to support one group,
> > fully, and not the other. It is true that this might not reflect much
> > care, it might be simple disinterest, insufficient to go to the
> > effort of rating candidates intermediately.
>
>Am I supposed to put extra effort into something just because I can?

No. You do it if it serves you, and not otherwise. And we assume that 
if everyone behaves like this, the votes will generate a useful 
result. "Serves you" could include serving others, i.e., voters 
considering what they think others would be pleased with, if this 
matters to them. But in a "fully sincere" Range poll, I'd want voters 
to vote their personal preferences, and not consider the needs of 
compromise, but, quite for this reason, I dislike Range polls that 
automatically determine outcomes. They are far more useful as input 
to a deliberative process, or at least another poll for actual 
implementation (which might not be Range, it might be Condorcet 
compliant or at least majoritarian).

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Re: [EM] RE : Re: Are proposed methods asymptotically aproaching some limit of utility?

At 11:19 PM 3/13/2007, Michael Poole wrote:
>Take a voter who thinks candidate A is the best, B is bad, and C is
>the worst.  His best estimates of normalized utility might be A=1,
>B=0.2, C=0.

Why does he not vote his best estimate?

>If the ballot asks for scores based on how much a voter likes the
>candidates, then a vote with B=0 is insincere: the voter is not
>answering what the ballot asks for.

Don't blame Range Voting for faulty ballot instructions!

Yes, you could call such behavior "insincere," that is, the voter is 
not responding, allegedly, sincerely (Poole has assumed that it is 
insincere). But what those who write about this seem to consistently 
overlook is that if the voter wants to vote 0 rather than 0.2 for B, 
the voter must have some motivation to do so! (or is simply voting 
randomly, which tells us nothing).

Why would we claim that the voter "sincerely" would rate the 
candidate as 0.2 when the voter decides that *for whatever reason*, 
the candidate should get no votes!

Because the voter kinda likes the candidate, perhaps personally?

Present ballots don't tell voters how to vote. They simply say 
something like "Vote for One." They do not say, "Vote for the 
candidate you like."

And quite a few voters don't vote for the candidate they like -- that 
is, third party supporters or those who'd prefer, really, a write-in.

>   However, if the ballot asks for
>something else, it could be a sincere vote.  What instructions do you
>think a range voting ballot should give voters?

That's a good question. If it is summation Range (as distinct from 
average Range, which is a little trickier), it is as if the voter has 
100 votes to cast (or 99 or whatever), in an Approval election, as I 
wrote. So, without claiming that I've considered this carefully:

For each candidate, vote from 0 to 99, 0 giving the candidate no 
support whatever, and 99 giving full support. You may freely support 
as many candidates as you choose at whatever rating you choose. If 
you make no rating for a candidate, a rating of zero (0) will be assumed.

The last part is for summation range, the instruction for average 
range might be "If you make no rating of a candidate, your vote will 
not be considered in determining the overall rating of that candidate."

I highly recommend that Range *start* as summation Range. But there 
would be no harm in a provision which allows voters to explicitly 
abstain, though I'm not sure there is sufficient social benefit to 
justify the complication.

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Re: [EM] Beatpath(Unc, wv), a version of Beatpath that always picks from the Uncovered set

Dear Forest,

you wrote:
> Let N be the number of ballots. In Beatpath(Unc, wv) the strength of
> a pairwise victory of X over Y is N+1 if X covers Y, else it is the
> number of ballots on which X is ranked above Y.

I fear a "Beatpath" or "River" method based on this definition of 
strength will not be monontonic. Let's assume the defeats 
X>B>Y>A>B>C>A>X>C>Y>X with winning votes of the following relative 
sizes:

  over...
wvA  B  C  X  Y
of...
 A-  1 4
 B   -  1 5
 C1 - 2
 X   5  3  -   
 Y51  -

Since every defeat is on a 3-cycle, the covering relation is empty and 
the beatpath strengths are of these relative sizes:

beatpath  over...
strength  A  B  C  X  Y
of...
 A-  *  *  4  *
 B*  -  *  4  *
 C*  *  -  2  *
 X5  5  3  -  5
 Y*  *  *  4  -

Hence your Beatpath version will elect X.
(By the way, River would lock in the defeats X>B>Y>A and X>C, and Ranked 
Pairs would in addition lock in B>C>Y and C>A, both therefore also 
electing X.)

Now assume that weak defeat Y>X is reversed into a weak defeat X>Y, with 
winning votes like these:

  over...
wvA  B  C  X  Y
of...
 A-  1 4
 B   -  1 5
 C1 - 2
 X   5  3  -  1! 
 Y5   -

Then C covers Y and X covers B, hence the defeat strengths and beatpath 
strengths are now of these relative sizes:

defeatover...
strength  A  B  C  X  Y
of...
 A-  1 4
 B   -  1 5
 C1 - 9!
 X   9! 3  -  1 
 Y5   -

beatpath  over...
strength  A  B  C  X  Y
of...
 A-  *  3  4  *
 B*  -  3  4  *
 C5  4  -  4! 9
 X5  9  3  -  5
 Y*  *  3  4  -

That is, X has a weaker beatpath against C than C has against X. The new 
winner is C, proving that the method is not monotonic!

Using your definition of defeat strength with River instead would lock 
in C>Y>A>X>B, also electing C. 

However, using it with Ranked Pairs would lock in C>Y and X>B, then 
B>Y>A, then X>C>A and B>C, giving the same social order as before in 
this example. 

So, could it be in this case the Ranked Pairs cycle-resolution method 
works better than the Beatpath and River cycle-resolution methods??

Yours, Jobst

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Re: [EM] divided house problem of close vote (50%+1)

2007-03-14 Thread Howard Swerdfeger

Juho wrote:
> Some observations.
> 
> The description talks only about the "yes" votes. Is the assumption  
> that the "no" votes mean "no action will be taken"?

yes.

> 
> If we are talking about approving a new law then this is quite  
> typical, but if we vote for example about whether we should send our  
> rocket to Mars or Venus, then both sides should be treated in the  
> same way.
> 
> In the described method repeated 45% yes, 55% no results do not lead  
> to final "no" (assuming super majority and new referendum levels 60%/ 
> 40%). If we have only one rocket to send, voting first on sending the  
> rocket to Mars, then on sending it to Venus, then to Mars etc. is not  
> fair either. But maybe the method is not intended for this kind of  
> elections with two similar alternatives to choose from.

You are correct, It was not originally intended to choose between two 
similar alternatives.
but I believe it could serve this purpose. You wouldn't actually send it 
to mars or Venus until the "score" reached a super majority, and then 
you would stop voting.

> You also didn't set a rule on when the new election should be  
> arranged. Using term "referendum" refers to a situation where for  
> practical reasons there has to be at least one week time between two  
> consecutive elections. The proposed method might however be used also  
> in smaller elections like in the legislative body to accept laws  
> (maybe at its best in smaller scale elections due to the costs etc.).  
> There are countries where required super majority can be replaced  
> with simple majority and another simple majority after the next  
> elections. In this case the time span is months or years. You  
> mentioned allowing for debate and discussion in between votes. That  
> could mean 15 minutes. Any time is ok with me but probably the rules  
> need to be defined (to avoid e.g. 10 votes in one minute).

I agree with everything you say.
The time between votes would need to be decided by what ever body would 
implement it.

As for debate, Typically I would Imagine a situation where a decision 
making body (legislature or citizens) exists in a currently almost 
evenly divided state. I would further imagine that the division of this 
body would change over time at some rate. possibly because of debate and 
people changing there minds, or possibly because of the actual people in 
the decision making body changing (Bi-Election, full new elections, 
demographic change of citizens).
I would guess that enough time needs to pass to typically allow 1-3% 
total state changes in decision making body, But that is just a guess. 
You need time to allow for honest debate. In a legislature this could be 
1 week or 1 day with debate and backroom deals in the middle. In a 
referendum this could be months or years to allow for some small 
demographic shift, or to account for some random variation in voter opinion.

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Re: [EM] divided house problem of close vote (50%+1)

2007-03-14 Thread Howard Swerdfeger


>>For every vote there are 3 possible outcomes:
>>1. It passes with a super majority.
>>2. It fails with a super majority.
>>3. It is 'close', and a new vote is auto-magically triggered
>>  * scheduled to allow for debate and discussion in between votes.
> 
> 
> In general, I dislike indefinitely repeated elections because they
> increase voting costs for both the society and the voters in propotion
> to the number of rounds they require.

agreed. This would only be appropriate for situation where, the cost of 
the decision of little importance, when compared to the importance of 
the decision it self.

> As a real-world alternative, for votes within the Debian project,
> there is usually a "further discussion" option in addition to any
> specific candidates.  This option also replaces "no" options when the
> other proposals are changes to the status quo.  In an election to
> office, this could provide a sort of approval threshold in an
> otherwise Condorcet method, although I do not think the Debian
> elections use the option in this way.

I was trying to look at a situation that would always produce a majority 
of some kind. Every democracy I am aware of passes laws with a yes no 
ballot by the legislative body. Generally these votes take the form "Yes 
we will do X" or "No we will maintain the status quo."

Adding a 3rd option convolute the matter in my opinion.

> I say "ordinary" topics because changes to areas such as rules of
> procedure will generally require a supermajority to change, and a
> clear majority that falls short of the supermajority should not be
> able to effect the change even if the elections are repeated.  

Generally, in reality this is only sometimes true.
Israel has "Basic laws" but no constitution, They can be changed by a 
simple majority of parliament.

Parts of the Canadian constitution that only effect a specific province 
can be changed in some provinces with a simple majority of the 
provincial parliament.

Parts of the German Constitution can not legally be changed ever.


> could be addressed in your proposal by adjusting the -50% factor to be
> the necessary approval level for the proposal.)

adjusting the "Leak" rate simply adjust the longterm threshold. This may 
be appropriate for some situations.


> Michael Poole


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Re: [EM] DAMC meets reasonable FBC