Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Chris Benham]

Oops! Yes, thanks Abd.
 
I made an error. The A and B group was supposed to add up to 49, not 51. So it 
should be:
 25: A>Y>X
24: B>Y>X
17: C>D>X
17: E>F>X
17: G>H>X
 
100 ballots, Bucklin election.
 
The majority threshold is 51 and X wins in the third round. But if we add 
anywhere between 3 and 100
X>Y ballots then Y wins in the second round.
 
Chris Benham


 At 03:58 PM 6/17/2013, Chris Benham wrote:
>Benjamin,
>The criterion ("criteria" is the plural) you suggest is not new. It 
>is called Mono-add-Top, and comes from Douglas Woodall.
>
>It is met by IRV and MinMax(Margins) but is failed by Bucklin. In my 
>opinion IRV is the best of the methods that meet it.
>
>26: A>Y>X
>25: B>Y>X
>17: C>D>X
>17: E>F>X
>17: G>H>X
>
>The majority threshold is 51 and X wins in the third round. But if 
>we add anywhere between 3 and 100
>X>Y ballots then Y wins in the second round.

Some error there. Total votes are 102. Majority is 52 votes. 

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

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Abd ul-Rahman Lomax]

At 03:58 PM 6/17/2013, Chris Benham wrote:

Benjamin,
The criterion ("criteria" is the plural) you suggest is not new. It 
is called Mono-add-Top, and comes from Douglas Woodall.


It is met by IRV and MinMax(Margins) but is failed by Bucklin. In my 
opinion IRV is the best of the methods that meet it.


26: A>Y>X
25: B>Y>X
17: C>D>X
17: E>F>X
17: G>H>X

The majority threshold is 51 and X wins in the third round. But if 
we add anywhere between 3 and 100

X>Y ballots then Y wins in the second round.


Some error there. Total votes are 102. Majority is 52 votes. I just 
want it to be noticed how *crazy* this scenario is. Voting systems 
criteria can be like that. A totally insane situation, won't happen 
in a real election in a billion years, can be asserted to cause 
criterion failure. There is no *evaluation*, no consideration of harm 
or effect on social utility, just a raw definition of a criterion and 
an example showing failure. Or, sometimes, a proof that failure is 
not possible (with *any* scenario).


The deeper analysis is much more difficult. What are the conditions 
that allow mono-add-top failure? In the example above, X wins without 
the additional votes because X is the *unanimous* third choice of all 
the voters, while being the first or second choice of none. That's, 
for starters, preposterously unlikely. However, a somewhat more 
realistic version could be constructed.


The ballots that then shift the win to Y cross a minimal majority 
threshold for Y in the second round (With the 3 votes additional, 53 
votes is majority, so this would need to be two votes, not three).


I have generally suggested that in studying criteria performance that 
overall social utility be considered. Because Bucklin, especially 
Bucklin-ER -- which this election could be -- uses a Range ballot, 
that's what makes strategic voting sense -- it is possible to 
estimate social utility performance. In a hybrid system, which is 
what I've been coming to highly recommend as a more sophisticated 
reform, social utility and the Condorcet criterion can be tested, and 
problems, conflicts, can easily be handled with a runoff, and if the 
runoff *is the general election*, then the primary method is merely a 
nomination device. If the primary method never *eliminates* a 
Condorcet winner, then the overall method can fairly be considered 
Condorcet-compliant, with the final application of the criterion 
being *in the general election*. I.e., the Condorcet winner will win, 
*unless* the voters vary and that preference is not maintained. That 
pairwise majority will know the situation from the primary. How will they vote?


Now, X is the *social utility winner* if this is Bucklin. The voting 
pattern does not reflect -- at all -- real voting behavior with 
Bucklin, which we know. Many or even most voters will bullet vote. 
The frontrunners are A and B. A and B voters are unlikely to add 
lower preferences in second rank, in fact, they many not add them at 
all. And all of this reveals problems with the majority criterion and 
the multiple majority criterion.


I have pointed out that Bucklin uses a Range ballot to control voting 
in a series of approval elections. That is, the optimal Bucklin 
ballot will show utilities for candidates, as to those within the 
approved set, those where the voter is at all willing to support the 
candidate, to approve the candidate, and thus cause the election. 
Here, a deeper preference is revealed in the third rank. What does 
this do to a social utility estimate:


4 3 2
26: A>Y>X
25: B>Y>X
17: C>D>X
17: E>F>X
17: G>H>X
---
102 voters, max score 408

Totals, as percentage of maximum possible (i.e, 4 points per voter 
per candidate)


A: 25.4%
B: 24.5%
C,E,G: 16.7%
Y: 37.5%
D,F,H: 12.5%
X: 50%

X is *obviously* the social utility winner. However, that's a wimpy 
decision, 50% of maximum range. Voting third rank in Bucklin is *bare 
minimum approval,* which is why I interpret it as 50% range.


Now, we add

2: X>Y

The two votes, when the second rank is amalgamated, lead to 53 votes 
for Y, a bare majority, Y wins, in the second round, with only 2 
votes for X at that level. That's because Bucklin collapses to 
approval voting as higher ranks fail to find a majority. A and B are 
still two votes short of a majority. However, the full ballots show a 
different story.


In this case, the two additional votes caused a bare majority to 
appear in the second round, thus concealing the *full approval* for X 
that only comes up in the third round.


Notice that the A,B voters also approve Y, all of them. None of them 
approve each other. These votes, as far as I can tell, make no sense, 
they are preposterously unreal. While I can easily create preference 
profiles that match the votes -- they would be these preferences 
translated into Bucklin votes, which are then Range 4 utilities -- 
the voters are *uncorrelated* with each other, and are behaving as if 
purely and completely isolated. It's

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Abd ul-Rahman Lomax]

At 03:41 PM 6/17/2013, Jameson Quinn wrote:
2013/6/17 Abd ul-Rahman Lomax 
<a...@lomaxdesign.com>

At 01:23 PM 6/17/2013, Jameson Quinn wrote:

2013/6/17 Benjamin Grant <b...@4efix.com>

Is *this* an example of Bucklin failing Participation?

5: A>B>C

4: B>C>A

A wins

Right

But add these in:

2: C>A>B

 B wins.


Yes, with your "tiebreaker".


This is not participation failure. Adding ballots ranking C highest 
did not cause C to lose.



Abd, you're wrong. Adding B>A ballots caused A to lose; that is a 
participation failure.


I did err in my analysis. However, I would urge anyone tempted to 
write "you are wrong" to be very careful. It's a big red flag that 
one is, oneself, making some mistake. Would we not expect the 
addition of B>A ballots to have the possibility of causing A to lose?


No, the added ballots were A>B ballots, at a lower ranking. The 
failure comes from causing majority failure, thus pulling in deeper votes.


I had somehow failed to notice the B votes from the 5 voters. A wins 
in the first round without the added votes, with a simple majority. 
This is the  sequence, which Jameson did not explore specifically, 
merely stating his result.



5: A>B>C

4: B>C>A

A wins

Right

But add these in:

2: C>A>B

 B wins.



A wins in the 9-voter case, by a simple majority. However, the 
11-voter case has a new majority requirement, 6 votes instead of 5.


We have the situation here that a majority favoring A votes second 
rank for B. In Range equivalents, often proposed as examples of "bad 
Range behavior," we see the same kind of phenomenon asserted.


Under straight Bucklin, if there are two frontrunners, A and B, we 
would expect *very few* additional votes for B, because the election 
is very likely to reduce, then, to A vs B. So this is like examples 
of alleged majority criterion failure based on the majority 
suppressing its preference by voting for another candidate, who gets 
a greater majority once they do that.


First round: (majority is 6)
A:5, B:4, C:2

Second round:
A: 7, B:9, C:6

*All three candidates have a majority?* Who is the ideal winner of 
this election? The A voters elected to vote A>B rather than A>.>B or 
just A. The only reason B can win is because they set it up. By 
second-ranking B, which indicates weak preference, they gave the 
election to B. The C voters merely opened that box.


The back-up Bucklin system under discussion would still award the 
victory to A, because there was more than one majority, so the result 
would back up to the first rank and A would still win. Is that a 
desired result, or otherwise?


What do we see here WRT utilities? First of all, I don't know what is 
really meant by the .>.>X preferences? Are there more than three 
candidates in this election? Are those actually approvals? If so, 
every voter ultimately approved every candidate. Jameson and another 
seemed to assume Bucklin votes from a preference order, which is naive.


That's why I suggested that these might have been written the way 
below, if they were *not* approvals, i.e, if the third rank shown was 
the *worst* rating. Yeah, in analyzing ranked voting systems, this is 
common practice, to give the complete rankings. But Bucklin is *not* 
a simple ranked system, it uses an Range ballot, in the traditional 
form, with the range only covering the approved categories. You 
cannot translate sincere preferences to Bucklin votes, especially 
Bucklin-ER. There are *families* of sincere votes.


So Bucklin votes, perhaps:

5: A>B
4: B>C

If this is 3-rank Bucklin (standard), then the voters also had X>.>Y 
possibilities, or bullet votes. If they second-rank a candidate, that 
indicates *weak preference*. Bucklin analysis here only looks at the 
first rank, because a majority is found there.


Range analysis gives me this:

9-voter election
5: A,4; B,3
4: B,4; C,3

So full range analysis: A,20; B,31; C,12.

So the A win is actually weak, mere majority criterion compliant, an 
example of the failure of the majority criterion! This election is 
then *vulnerable* to more voter participation, and that is what happens.


5: A>B
4: B>C
2: C>A

This vote expresses, by default, A>B. However, the *primary 
expression* is a vote for C. The A vote is a subsidiary preference. 
Are these weak or strong preferences (Bucklin allows four levels of 
preference strength, i.e., a Range increment of 4, 3, 2, or 1. The 
voters here all elected to express weak preference with the top two 
and strong preference with the third candidate.)


5: A,4; B,3
4: B,4; C,3
2: C,4; A,3

A,26; B, 31; C, 20

B is *still the utility optimizer.*

Yes, there is technical participation failure. 2 votes that did 
express, as a lower preference, A>B, did cause A to lose to B.


Will the C voters be upset? On the face, yes. They got C, the worst 
candidate, because they voted. However, what they really did was to 
trigger a deeper consideration, that revealed that B

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Jameson Quinn]

2013/6/17 Benjamin Grant 

> *From:* Jameson Quinn [mailto:jameson.qu...@gmail.com]
> *Sent:* Monday, June 17, 2013 3:14 PM
>
> *Subject:* Re: Participation Criteria and Bucklin - perhaps they *can*
> work together after all?
>
> ** **
>
> Unfortunately, Bucklin systems fail that one too.
>
> ** **
>
> Hold on a sec. Let me think this through.  If we are using a Bucklin
> system, perhaps a strictly ranked one, and X is currently winning.  Adding
> a single ballot that has X ranked as the highest does two things: it
> changes the threshold, and it awards one more vote to X.  The only way it
> can hurt X – ie, cause X not to win, is if the harm in changing the
> threshold is greater than the benefit of getting another first place vote.
>

I think you're close to right here, but not quite. In Bucklin, an
additional top-rank vote does not hurt X; it always helps their individual
median score and/or tiebreaker. It's just that that same ballot might pull
the median for some Y upwards even further, so that Y leapfrogs ahead of X.

In what circumstances would this happen? First, the ballot's rating for Y
must be above Y's median. And second, Y must have dramatically fewer
ratings at or just above its median than X does. Considering the
psychology/politics of such a situation, we have reason to believe that it
would be rare, and also it is arguable that Bucklin (not Buckley) is
actually doing the right thing here.

Why would it be rare? For some reason, Y is a polarizing candidate, with a
bimodal grade distribution. Voters seem to either love them or hate them,
with few falling in between. Such candidates certainly do exist in reality.
For instance, a candidate with a compelling ethnic- or class-based
narrative of whom to blame for the country's problems usually excites such
reactions, with little middle ground. But voters who support such
candidates tend to do so exclusively. For instance, in Balinski and
Laraki's study of the 2007 French election, right-wing candidate Le Pen
showed that kind of appeal; Le Pen got few middle rankings, and Le Pen
voters gave relatively few high rankings to other candidates. Thus, a
ballot which fails participation, giving a high-but-not-top rating to a Y
like Le Pen, but also giving an even higher rating to some other X, would
be the rarest kind of ballot.

And in the rare cases where this happened, it is actually arguably the
right thing to do. The extra ballot only shifts the result because it puts
Y over the 50% threshold of "high" versus "low" ratings (where "high/low"
means "above/below X's median"). That's not an arbitrary threshold. If Y
has >50% of the electorate who think they deserve a high rating, chances
are that they could win the election if all such voters were strategic.

> 
>
> ** **
>
> That’s the key to why Buckley keep failing Participation!!  I think I
> finally grasped the essential Participation flaw with Buckley!!
>
> ** **
>
> Each added ballot changes the threshold. Changing the threshold will
> either have NO effect, or it will change how “deep” we have to go to find a
> winner.
>

This is, indeed, another way that Bucklin could fail participation: through
a ballot which gave below-median ratings to both X and Y, and thus caused X
to fail to meet a threshold. But it's the opposite of what you were
discussing above, which is a way that Bucklin fails mono-add-top.

>
>

>
> ** **
>
> In this case, even if we know ALL the ballot we are adding have X at the
> top, adding even a single on if it changes the threshold enough will
> suddenly bring into your totals all the next place rankings for the
> existing ballots.  In other words, Buckley fails Participation because it
> is not a “smooth” curve, it is a fragile one that can leap and lurch, if
> you see what I am saying.
>

Yes, your intuition is getting stronger, my young padawan. But there's
still something you're missing. As I argued above, there is sometimes a
good reason to leap or lurch when a 50% threshold is crossed. If the voting
system doesn't so lurch, the voters may take it upon themselves to do the
lurching strategically; and they, with imperfect knowledge, are almost
always likely to do a worse job at it than the voting system.

> 
>
> ** **
>
> In its own way, Buckley is as unpredictable as IRV.  Both have fractal
> moments where a very small change can completely swamp the system and
> produce a very different result.  Any system as – what’s the right word,
> jagged? sensitive? fragile? is going to have one or more issues with
> appealing to our common sense, because each has a point in which a tiny
> change can cause a system wide shift.
>
> ** **
>
> Am I right?
>

Not wrong; but as you can see, I find IRV's overreactions to be unjustified
and common, while I see Bucklin's as being justifiable and likely rare.
This is a contentious issue, though, and there are certainly those here who
disagree with me.


>
> ** **
>
> I don’t know what this kind of trait is ca

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Juho Laatu]

On 18.6.2013, at 4.24, Benjamin Grant wrote:

> From: Jameson Quinn [mailto:jameson.qu...@gmail.com] 
> Sent: Monday, June 17, 2013 3:14 PM
> Subject: Re: Participation Criteria and Bucklin - perhaps they *can* work 
> together after all?
>  
> Unfortunately, Bucklin systems fail that one too.
>  
> Hold on a sec. Let me think this through.  If we are using a Bucklin system, 
> perhaps a strictly ranked one, and X is currently winning.  Adding a single 
> ballot that has X ranked as the highest does two things: it changes the 
> threshold, and it awards one more vote to X.  The only way it can hurt X – 
> ie, cause X not to win, is if the harm in changing the threshold is greater 
> than the benefit of getting another first place vote.
>  
> That’s the key to why Buckley keep failing Participation!!  I think I finally 
> grasped the essential Participation flaw with Buckley!!
>  
> Each added ballot changes the threshold. Changing the threshold will either 
> have NO effect, or it will change how “deep” we have to go to find a winner.
>  
> In this case, even if we know ALL the ballot we are adding have X at the top, 
> adding even a single on if it changes the threshold enough will suddenly 
> bring into your totals all the next place rankings for the existing ballots.  
> In other words, Buckley fails Participation because it is not a “smooth” 
> curve, it is a fragile one that can leap and lurch, if you see what I am 
> saying.
>  
> In its own way, Buckley is as unpredictable as IRV.  Both have fractal 
> moments where a very small change can completely swamp the system and produce 
> a very different result.  Any system as – what’s the right word, jagged? 
> sensitive? fragile? is going to have one or more issues with appealing to our 
> common sense, because each has a point in which a tiny change can cause a 
> system wide shift.
>  
> Am I right?

Yes. This is a good approach to describing the problem.

I tend to categorize different methods also as heuristic and "more 
mathmatically exact" methods that try to describe the outcome or wanted 
features of the winner more directly. IRV is a good example of a method that is 
based on an algorithms that makes pretty much sense to us, but that is anyway 
just an approximation of what we want. Also Bucklin is based on a similar kind 
of algorithm that does pretty good job, but still is just a serial stepwise 
approximation based on guesses on what direction we want to take (and which 
candidates might be bad enough so that we can eliminate them already at this 
step).

>  
> I don’t know what this kind of trait is called, this oversensitivity, this 
> ability to suddenly shift from condition One to Condition Two with no smooth 
> transition points in between – but I think these kinds of systems will suffer 
> from problems like these.
>  
> Now, for all I know ALL voting systems have this kind of issue – we’ll see.

I think out of the discussed methods at least Range does not really have this 
kind of randomness / fractal behaviour / oversensitivity / stepwise guesses 
based problems. It simply measures the quality of the candidates (=sum of 
utilities) and picks the best candidate as the winner. Range has other 
strategic problems in competitive environments, but that is due to strategic 
voting, not due to an oversensitive algorithm. Also FPTP is quite ok, if one 
assumes that all voters vote sincerely and we are supposed to elect the 
candidate that has highest first preference support.

According to my experience the most typical way to get an oversensitive method 
is to use some serial elimination based algorithm that makes serial (heuristic) 
guesses on which candidates are potential winners and which ones are not. Those 
methods can be good methods though, if the randomness caused by the algorithm 
causes less harm than the other properties of the method give us benefits.

If we want to avoid this kind of oversensitivity / randomness, one good 
approach is to simply define a (candidate quality) criterion that points out 
which one of the candiates is the best for our needs.

Juho


>  
> -Benn Grant
> eFix Computer Consulting
> b...@4efix.com
> 603.283.6601
>  
> 
> 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] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Benjamin Grant]

From: Jameson Quinn [mailto:jameson.qu...@gmail.com] 
Sent: Monday, June 17, 2013 3:14 PM
Subject: Re: Participation Criteria and Bucklin - perhaps they *can* work
together after all?

 

Unfortunately, Bucklin systems fail that one too.

 

Hold on a sec. Let me think this through.  If we are using a Bucklin system,
perhaps a strictly ranked one, and X is currently winning.  Adding a single
ballot that has X ranked as the highest does two things: it changes the
threshold, and it awards one more vote to X.  The only way it can hurt X -
ie, cause X not to win, is if the harm in changing the threshold is greater
than the benefit of getting another first place vote. 

 

That's the key to why Buckley keep failing Participation!!  I think I
finally grasped the essential Participation flaw with Buckley!!

 

Each added ballot changes the threshold. Changing the threshold will either
have NO effect, or it will change how "deep" we have to go to find a winner.

 

In this case, even if we know ALL the ballot we are adding have X at the
top, adding even a single on if it changes the threshold enough will
suddenly bring into your totals all the next place rankings for the existing
ballots.  In other words, Buckley fails Participation because it is not a
"smooth" curve, it is a fragile one that can leap and lurch, if you see what
I am saying.

 

In its own way, Buckley is as unpredictable as IRV.  Both have fractal
moments where a very small change can completely swamp the system and
produce a very different result.  Any system as - what's the right word,
jagged? sensitive? fragile? is going to have one or more issues with
appealing to our common sense, because each has a point in which a tiny
change can cause a system wide shift.

 

Am I right?

 

I don't know what this kind of trait is called, this oversensitivity, this
ability to suddenly shift from condition One to Condition Two with no smooth
transition points in between - but I think these kinds of systems will
suffer from problems like these.

 

Now, for all I know ALL voting systems have this kind of issue - we'll see.

 

-Benn Grant

eFix Computer Consulting

  b...@4efix.com

603.283.6601

 


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

[EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Chris Benham]

Benjamin,

The criterion ("criteria" is the plural) you suggest is not new. It is called 
Mono-add-Top, and comes from Douglas Woodall.

It is met by IRV and MinMax(Margins) but is failed by Bucklin. In my opinion 
IRV is the best of the methods that meet it.
 
26: A>Y>X
25: B>Y>X
17: C>D>X
17: E>F>X
17: G>H>X
 
The majority threshold is 51 and X wins in the third round. But if we add 
anywhere between 3 and 100 
X>Y ballots then Y wins in the second round.
 
You'll find some interesting stuff on Kevin Venzke's old page:
http://nodesiege.tripod.com/elections/
 
Notice that your version (in an earlier post) of the Plurality criterion is 
wrong.
 
Chris Benham
 
Benjamin Grant wrote (17 June 2013):
OK, let's assume that as defined, Bucklin fails Participation. 



Let me specify a new criteria, which already either has its own name that I do 
not know, or which I can call Prime Participation:



"Adding one or more ballots that vote X as a highest preference should never
change the winner from X to Y"



In other words, expressing a first place/greatest magnitude preference for
X, if X was already winning, cannot make X not win.



This may be another one so basic that few or maybe no real voting systems
fail it?



-Benn Grant

eFix Computer Consulting

 benn at 4efix.com

603.283.6601

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

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Jameson Quinn]

2013/6/17 Abd ul-Rahman Lomax 

> At 01:23 PM 6/17/2013, Jameson Quinn wrote:
>
>  2013/6/17 Benjamin Grant 
> <benn@**4efix.com
>> >
>>
>>
>> Is *this* an example of Bucklin failing Participation?
>>
>> 5: A>B>C
>>
>> 4: B>C>A
>>
>> A wins
>>
>> Right
>>
>> But add these in:
>>
>> 2: C>A>B
>>
>>  B wins.
>>
>>
>> Yes, with your "tiebreaker".
>>
>
> This is not participation failure. Adding ballots ranking C highest did
> not cause C to lose.
>

Abd, you're wrong. Adding B>A ballots caused A to lose; that is a
participation failure.


>
> By the way, an oddity about this example. Bucklin is ranked approval. Did
> all the voters approve all candidates?
>

You would prefer it if he had left the third candidate off for each voter
group. A less obtuse way to say that would be to say "I would have written
this scenario as ... because ...".

>
> Round 1. Majority is 5
>
> A wins in round 1.
>
> Adding the2 voters, majority is now 6.
>
> First round:
> A: 5
> B: 4
> C: 2
>
> no majority, go to next round.
>
> Second round:
> A: 7
> B: 4
> C: 6
>

No. B:9. If you are going to claim that 2 others are wrong, please check
your work before sending it out.

>
> A still wins. B does *not* win. Bucklin terminates when a majority is
> found.
>
> Participation criterion from previous post: "Adding one or more ballots
> that vote X over Y should never change the winner from X to Y"
>
> Showing the third preferences is confusing and irrelevant. I do not know
> why Jameson approved "B wins." But even if B had won, it would not have
> shown participation failure. The vote must change the result away from C to
> another winner.
>
> One fact that should be understood about Bucklin: first of all, Bucklin
> votes are *approvals*. Every explicit Bucklin vote is voting *for* the
> candidate under the condition that the rank has been reached in the
> amalgamation process.
>
> Secondly, a Bucklin ballot is a *Range* ballot, covering the approved
> range only. So ranks may be left empty. Bucklin is *not* a pure ranked
> system. So if a voter has A>B>C, the voter will *not* vote for all three,
> unless there is some other worse candidates, or the voter really does want
> to completely stand aside from the election. And that doesn't work with
> respect to write-in candidates
>
> So if the voter has preferences A>B>C, the voter may vote, in the form of
> Bucklin we generally are working with, called Bucklin-ER (equal ranking),
> these votes, and all could be sincere:
>
> A
> A>B
> A>.>B (blank second rank)
> A=B
>
> This *assumes* that there is a third candidate, C, that is least
> preferred. If there are four candidates (or more), the voter can have *many
> more sincere voting patterns*.
>
> Each pattern has implications about *preference strength*. That is part of
> why I say that Bucklin uses a Range ballot.
>
> Suppose that the voter *really prefers* a candidate not on the ballot, and
> wants to vote for that candidate, we'll call W.
>
> W
> W>A
> W>A>B
> W>A=B
> W>.>A
> W>.>A=B
> W=A>B
> W=A>.>B
> W=A=B
>
> Just to make this clear.
>

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

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Abd ul-Rahman Lomax]

At 01:23 PM 6/17/2013, Jameson Quinn wrote:


2013/6/17 Benjamin Grant <b...@4efix.com>

Is *this* an example of Bucklin failing Participation?

5: A>B>C

4: B>C>A

A wins

Right

But add these in:

2: C>A>B

 B wins.


Yes, with your "tiebreaker".


This is not participation failure. Adding ballots ranking C highest 
did not cause C to lose.


By the way, an oddity about this example. Bucklin is ranked approval. 
Did all the voters approve all candidates?


Round 1. Majority is 5

A wins in round 1.

Adding the2 voters, majority is now 6.

First round:
A: 5
B: 4
C: 2

no majority, go to next round.

Second round:
A: 7
B: 4
C: 6

A still wins. B does *not* win. Bucklin terminates when a majority is found.

Participation criterion from previous post: "Adding one or more 
ballots that vote X over Y should never change the winner from X to Y"


Showing the third preferences is confusing and irrelevant. I do not 
know why Jameson approved "B wins." But even if B had won, it would 
not have shown participation failure. The vote must change the result 
away from C to another winner.


One fact that should be understood about Bucklin: first of all, 
Bucklin votes are *approvals*. Every explicit Bucklin vote is voting 
*for* the candidate under the condition that the rank has been 
reached in the amalgamation process.


Secondly, a Bucklin ballot is a *Range* ballot, covering the approved 
range only. So ranks may be left empty. Bucklin is *not* a pure 
ranked system. So if a voter has A>B>C, the voter will *not* vote for 
all three, unless there is some other worse candidates, or the voter 
really does want to completely stand aside from the election. And 
that doesn't work with respect to write-in candidates


So if the voter has preferences A>B>C, the voter may vote, in the 
form of Bucklin we generally are working with, called Bucklin-ER 
(equal ranking), these votes, and all could be sincere:


A
A>B
A>.>B (blank second rank)
A=B

This *assumes* that there is a third candidate, C, that is least 
preferred. If there are four candidates (or more), the voter can have 
*many more sincere voting patterns*.


Each pattern has implications about *preference strength*. That is 
part of why I say that Bucklin uses a Range ballot.


Suppose that the voter *really prefers* a candidate not on the 
ballot, and wants to vote for that candidate, we'll call W.


W
W>A
W>A>B
W>A=B
W>.>A
W>.>A=B
W=A>B
W=A>.>B
W=A=B

Just to make this clear. 



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

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Jameson Quinn]

Unfortunately, Bucklin systems fail that one too.

However, it passes "Adding one more ballot that votes X as highest
preference, and a ballot (either the same one or a second one) that votes Y
as lowest preference, should never change the winner from X to Y". You can
change "highest" to "above the winning median" and "lowest" to "below the
second-place median" and this passage still holds, although then the
criterion is meaningless for a non-median system.

Basically, Bucklin systems can fail participation if the added ballot(s)
rate both X and Y above, or both below, the winning median; it cannot fail
if the added ballot(s) span the median with X and Y. Thus if voters know
beforehand the winning median and the two frontrunners, they can make sure
that their ballot will not violate participation. And in a partisan
environment with two clear frontrunners, most people's ballots will
honestly meet that criterion without even a need for strategy.

Jameson

2013/6/17 Benjamin Grant 

> OK, let’s assume that as defined, Bucklin fails Participation. 
>
> ** **
>
> Let me specify a new criteria, which already either has its own name that
> I do not know, or which I can call Prime Participation:
>
> ** **
>
> “*Adding one or more ballots that vote X as a highest preference should
> never change the winner from X to Y*”
>
> ** **
>
> In other words, expressing a first place/greatest magnitude preference for
> X, if X was already winning, cannot make X not win.
>
> ** **
>
> This may be another one so basic that few or maybe no real voting systems
> fail it?
>
> ** **
>
> -Benn Grant
>
> eFix Computer Consulting
>
> b...@4efix.com
>
> 603.283.6601
>
> ** **
>

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

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Benjamin Grant]

OK, let's assume that as defined, Bucklin fails Participation. 

 

Let me specify a new criteria, which already either has its own name that I
do not know, or which I can call Prime Participation:

 

"Adding one or more ballots that vote X as a highest preference should never
change the winner from X to Y"

 

In other words, expressing a first place/greatest magnitude preference for
X, if X was already winning, cannot make X not win.

 

This may be another one so basic that few or maybe no real voting systems
fail it?

 

-Benn Grant

eFix Computer Consulting

  b...@4efix.com

603.283.6601

 


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

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Jameson Quinn]

2013/6/17 Benjamin Grant 

> Is **this** an example of Bucklin failing Participation?
>
> ** **
>
> 5: A>B>C
>
> 4: B>C>A
>
> ** **
>
> A wins
>

Right

> 
>
> ** **
>
> But add these in:
>
> 2: C>A>B
>
> ** **
>
> B wins.
>

Yes, with your "tiebreaker". Good job. But for other Bucklin "tiebreakers",
you might have to change this scenario some. For instance, in ranked ¿DAT?,
this example doesn't work, as A still wins after the added votes. However,
ranked ¿DAT? still fails participation in the more-complex scenario I gave
earlier.

Jameson

> 
>
> ** **
>
> If I didn’t make any mistakes, is this the failing of strictly ranked
> Bucklin versus Participation?
>
> ** **
>
> -Benn Grant
>
> eFix Computer Consulting
>
> b...@4efix.com
>
> 603.283.6601
>
> ** **
>

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

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Benjamin Grant]

Is *this* an example of Bucklin failing Participation?

 

5: A>B>C

4: B>C>A

 

A wins

 

But add these in:

2: C>A>B

 

B wins.

 

If I didn't make any mistakes, is this the failing of strictly ranked
Bucklin versus Participation?

 

-Benn Grant

eFix Computer Consulting

  b...@4efix.com

603.283.6601

 


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

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Jameson Quinn]

2013/6/17 Benjamin Grant 

> *From:* Jameson Quinn [mailto:jameson.qu...@gmail.com]
> *Sent:* Monday, June 17, 2013 1:25 PM
>
> *Subject:* Re: Participation Criteria and Bucklin - perhaps they *can*
> work together after all?
>
> ** **
>
> So to make a ranked example:
>
> ** **
>
> 49: XpqYrstuabcdef
>
> 49: XutYsrpqfedcba
>
> 50: abcYXdefpqrstu
>
> 50: fedYXcbautsrpq
>
> ** **
>
> OK, Y wins this one.
>
> ** **
>
> Add 4 votes:
>
> 4: aXYbcdefpqrstu
>
> ** **
>
> And now X wins this one.  
>
> ** **
>
> BUT I’m am still confused, Participation Criterion says: “*Adding one or
> more ballots that vote X over Y should never change the winner from X to Y
> *”  In this case the winner was NOT changed from X to Y, but from Y to X,
> so this is NOT an example of failing the Participation Criteria, is it?***
> *
>
> ** **
>
> Am I missing something here?
>
> **
>

Oops, typo on my part. The additional 4 votes should be aYXbcdefpqrstu.

Jameson

>  **
>
> -Benn Grant
>
> eFix Computer Consulting
>
> b...@4efix.com
>
> 603.283.6601
>

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

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Benjamin Grant]

From: Jameson Quinn [mailto:jameson.qu...@gmail.com] 
Sent: Monday, June 17, 2013 1:25 PM
Subject: Re: Participation Criteria and Bucklin - perhaps they *can* work
together after all?

 

So to make a ranked example:

 

49: XpqYrstuabcdef

49: XutYsrpqfedcba

50: abcYXdefpqrstu

50: fedYXcbautsrpq

 

OK, Y wins this one.

 

Add 4 votes:

4: aXYbcdefpqrstu

 

And now X wins this one.  

 

BUT I'm am still confused, Participation Criterion says: "Adding one or more
ballots that vote X over Y should never change the winner from X to Y"  In
this case the winner was NOT changed from X to Y, but from Y to X, so this
is NOT an example of failing the Participation Criteria, is it?

 

Am I missing something here?

 

-Benn Grant

eFix Computer Consulting

  b...@4efix.com

603.283.6601


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

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Benjamin Grant]

Wrapping my brain around it now, sorry if I am slow on the uptake, will post
later. :)

 

-Benn Grant

eFix Computer Consulting

  b...@4efix.com

603.283.6601

 

From: Jameson Quinn [mailto:jameson.qu...@gmail.com] 
Sent: Monday, June 17, 2013 1:25 PM
To: Benjamin Grant
Cc: EM
Subject: Re: Participation Criteria and Bucklin - perhaps they *can* work
together after all?

 

Previously we had:
 

49: X:1st   Y:4th

50: X:5th   Y:4th

Y wins.

 

Now we add two votes:

2: X:3rd   Y:2nd

X wins.

 

So to make a ranked example:

 

49: XpqYrstuabcdef

49: XutYsrpqfedcba

50: abcYXdefpqrstu

50: fedYXcbautsrpq

 

Add 4 votes:

4: aXYbcdefpqrstu

 

Now I added 12 candidates there, but I'm sure with a little work I could get
it down to somewhere in the range of just 4-8 extra candidates. But the
point is made.

 

Jameson

 

2013/6/17 Benjamin Grant mailto:b...@4efix.com> >

 

From: Jameson Quinn [mailto:jameson.qu...@gmail.com
 ] 
Sent: Monday, June 17, 2013 12:15 PM
Subject: Re: Participation Criteria and Bucklin - perhaps they *can* work
together after all?

 

2013/6/17 Benjamin Grant mailto:b...@4efix.com> >

is because we are letting people skip grades/places.  Or to put another way,
if we asked the voters under Bucklin to fill out each ballot more strictly,
ranking 1st through Nth where there are N candidates - I know that several
do not like this approach, *but* my question is this - does *strictly
ranked* Bucklin fail Participation??

 

Yes. Just add 500 other candidates, and fill in the gaps with
randomly-selected candidates from the 500. Obviously, you could probably get
by with a lot less than 500 - at a rough guess, I'd expect that 8 would be
plenty without changing the numbers here, and probably around 4-6 would be
enough to make a similar example with smaller gaps work, but my point is
that with enough extra candidates who cluster at the bottom of most ballots,
you can turn any rated scenario into a ranked scenario.

 

You are being tempted by a mirage here. The first lesson of "voting school
kindergarten" is that most problems don't have a perfect solution. That
doesn't mean you stop looking for ways to improve things, but it does mean
that when you imagine a "fix", you do your best to shoot holes in your own
idea. 95% of the time you'll succeed, but the other 5% still makes it worth
it.

 

Jameson

 

Oh.  That's disappointing.  I have to see it with my own eyes, although I am
sure you know what you are talking about, my brain won't let me move on
until I see the disproof.  So I will try to create one - a situation where
in using strictly ranked Bucklin, adding a new ballot in which A is ranked
higher than B, this new ballot somehow switches the winner from A to B.

 

The challenge is that its intuitively seems like such an impossible task, I
am worried that should such an example be possible (and you say it is, and I
believe you) I might never find it in my blind spot!

 

So if anyone *has* a handy example of this, I would be grateful for it being
brought to my attention, otherwise, I am going to have to try to create it
on my own in my own blind spot.

 

Thanks. :)

 

-Benn Grant

eFix Computer Consulting

  b...@4efix.com

603.283.6601

 

 


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

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Jameson Quinn]

Previously we had:
 **

49: X:1st   Y:4th

50: X:5th   Y:4th

Y wins.

** **

Now we add two votes:

2: X:3rd   Y:2nd

X wins.


So to make a ranked example:

49: XpqYrstuabcdef
49: XutYsrpqfedcba
50: abcYXdefpqrstu
50: fedYXcbautsrpq

Add 4 votes:
4: aXYbcdefpqrstu

Now I added 12 candidates there, but I'm sure with a little work I could
get it down to somewhere in the range of just 4-8 extra candidates. But the
point is made.

Jameson

2013/6/17 Benjamin Grant 

> ** **
>
> *From:* Jameson Quinn [mailto:jameson.qu...@gmail.com]
> *Sent:* Monday, June 17, 2013 12:15 PM
> *Subject:* Re: Participation Criteria and Bucklin - perhaps they *can*
> work together after all?
>
> ** **
>
> 2013/6/17 Benjamin Grant 
>
> is because we are letting people skip grades/places.  Or to put another
> way, if we asked the voters under Bucklin to fill out each ballot more
> strictly, ranking 1st through Nth where there are N candidates – I know
> that several do not like this approach, **but** my question is this –
> does **strictly ranked** Bucklin fail Participation??
>
> ** **
>
> Yes. Just add 500 other candidates, and fill in the gaps with
> randomly-selected candidates from the 500. Obviously, you could probably
> get by with a lot less than 500 — at a rough guess, I'd expect that 8 would
> be plenty without changing the numbers here, and probably around 4-6 would
> be enough to make a similar example with smaller gaps work, but my point is
> that with enough extra candidates who cluster at the bottom of most
> ballots, you can turn any rated scenario into a ranked scenario.
>
> ** **
>
> You are being tempted by a mirage here. The first lesson of "voting school
> kindergarten" is that most problems don't have a perfect solution. That
> doesn't mean you stop looking for ways to improve things, but it does mean
> that when you imagine a "fix", you do your best to shoot holes in your own
> idea. 95% of the time you'll succeed, but the other 5% still makes it worth
> it.
>
> ** **
>
> Jameson
>
> ** **
>
> Oh.  That’s disappointing.  I have to see it with my own eyes, although I
> am sure you know what you are talking about, my brain won’t let me move on
> until I see the disproof.  So I will try to create one – a situation where
> in using strictly ranked Bucklin, adding a new ballot in which A is ranked
> higher than B, this new ballot somehow switches the winner from A to B.***
> *
>
> ** **
>
> The challenge is that its intuitively seems like such an impossible task,
> I am worried that should such an example be possible (and you say it is,
> and I believe you) I might never find it in my blind spot!
>
> ** **
>
> So if anyone **has** a handy example of this, I would be grateful for it
> being brought to my attention, otherwise, I am going to have to try to
> create it on my own in my own blind spot.
>
> ** **
>
> Thanks. J
>
> ** **
>
> -Benn Grant
>
> eFix Computer Consulting
>
> b...@4efix.com
>
> 603.283.6601
>
> ** **
>

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

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Benjamin Grant]

 

From: Jameson Quinn [mailto:jameson.qu...@gmail.com] 
Sent: Monday, June 17, 2013 12:15 PM
Subject: Re: Participation Criteria and Bucklin - perhaps they *can* work
together after all?

 

2013/6/17 Benjamin Grant mailto:b...@4efix.com> >

is because we are letting people skip grades/places.  Or to put another way,
if we asked the voters under Bucklin to fill out each ballot more strictly,
ranking 1st through Nth where there are N candidates - I know that several
do not like this approach, *but* my question is this - does *strictly
ranked* Bucklin fail Participation??

 

Yes. Just add 500 other candidates, and fill in the gaps with
randomly-selected candidates from the 500. Obviously, you could probably get
by with a lot less than 500 - at a rough guess, I'd expect that 8 would be
plenty without changing the numbers here, and probably around 4-6 would be
enough to make a similar example with smaller gaps work, but my point is
that with enough extra candidates who cluster at the bottom of most ballots,
you can turn any rated scenario into a ranked scenario.

 

You are being tempted by a mirage here. The first lesson of "voting school
kindergarten" is that most problems don't have a perfect solution. That
doesn't mean you stop looking for ways to improve things, but it does mean
that when you imagine a "fix", you do your best to shoot holes in your own
idea. 95% of the time you'll succeed, but the other 5% still makes it worth
it.

 

Jameson

 

Oh.  That's disappointing.  I have to see it with my own eyes, although I am
sure you know what you are talking about, my brain won't let me move on
until I see the disproof.  So I will try to create one - a situation where
in using strictly ranked Bucklin, adding a new ballot in which A is ranked
higher than B, this new ballot somehow switches the winner from A to B.

 

The challenge is that its intuitively seems like such an impossible task, I
am worried that should such an example be possible (and you say it is, and I
believe you) I might never find it in my blind spot!

 

So if anyone *has* a handy example of this, I would be grateful for it being
brought to my attention, otherwise, I am going to have to try to create it
on my own in my own blind spot.

 

Thanks. :)

 

-Benn Grant

eFix Computer Consulting

  b...@4efix.com

603.283.6601

 


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

Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Jameson Quinn]

2013/6/17 Benjamin Grant 

> It occurred to me that the reason we are failing the Participation
> Criteria with Bucklin in the below example:
>
> ** **
>
> 49: X:1st   Y:4th
>
> 50: X:5th   Y:4th
>
> Y wins.
>
> ** **
>
> Now we add two votes:
>
> 2: X:3rd   Y:2nd
>
> X wins.
>
> ** **
>
> is because we are letting people skip grades/places.  Or to put another
> way, if we asked the voters under Bucklin to fill out each ballot more
> strictly, ranking 1st through Nth where there are N candidates – I know
> that several do not like this approach, **but** my question is this –
> does **strictly ranked** Bucklin fail Participation??
>

Yes. Just add 500 other candidates, and fill in the gaps with
randomly-selected candidates from the 500. Obviously, you could probably
get by with a lot less than 500 — at a rough guess, I'd expect that 8 would
be plenty without changing the numbers here, and probably around 4-6 would
be enough to make a similar example with smaller gaps work, but my point is
that with enough extra candidates who cluster at the bottom of most
ballots, you can turn any rated scenario into a ranked scenario.

You are being tempted by a mirage here. The first lesson of "voting school
kindergarten" is that most problems don't have a perfect solution. That
doesn't mean you stop looking for ways to improve things, but it does mean
that when you imagine a "fix", you do your best to shoot holes in your own
idea. 95% of the time you'll succeed, but the other 5% still makes it worth
it.

Jameson

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

[EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?

[Benjamin Grant]

It occurred to me that the reason we are failing the Participation Criteria
with Bucklin in the below example:

 

49: X:1st   Y:4th

50: X:5th   Y:4th

Y wins.

 

Now we add two votes:

2: X:3rd   Y:2nd

X wins.

 

is because we are letting people skip grades/places.  Or to put another way,
if we asked the voters under Bucklin to fill out each ballot more strictly,
ranking 1st through Nth where there are N candidates - I know that several
do not like this approach, *but* my question is this - does *strictly
ranked* Bucklin fail Participation??

 

49: X:1st   Y:2nd

50: X:2nd   Y:1st

Y wins on 1st round.

 

Now we add two votes:

2: X:2nd   Y:1st

Y still wins on first round.

 

In other words, I *think* what's bringing in the issues with Participation
is the gaps in the ranking the first approach permits.

 

Is it?

 

If so, it may be that Bucklin can be quite Participation compliant, so long
as you take certain steps like mandating a ranked order among your choices
on the ballot.

 

-Benn Grant

eFix Computer Consulting

  b...@4efix.com

603.283.6601


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

Re: [EM] Participation

[Kevin Venzke]

Hi Abd,

--- En date de : Dim 25.4.10, Abd ul-Rahman Lomax  a 
écrit :
> > I don't understand your terminology. Does "maximize
> utility" mean pick
> > the best winner every time, or does it just mean the
> method that comes
> > closest to doing this on average?
> 
> Fair enough, I'll need to express some definitions, and I'm
> going to keep it simple, and define a UM criterion,
> Utility-Maximizing. The UM ballot allows the expression, for
> each candidate, of some fraction of a full vote, i.e., each
> candidate receives a vote in the range of 0-1 vote. A
> "sincere UM ballot" is one in which every preference
> expressed is real, i.e., if the vote for one candidate is
> greater than a vote for a second candidate, then the voter
> actually prefers the first candidate to the second. However,
> the reverse is not necessarily true. If a voter prefers a
> candidate to another, it is possible that the voter chooses
> to vote the same fraction for them. I will assume, however,
> that the ballot allows the voter to express all preferences
> if the voter so chooses. (So it is, at a minimum, a Borda
> ballot).
> 
> A "UM ballot equivalent" is a ballot from another system
> translated to a UM ballot without violating the assumptions
> of the UM ballot and without creating discriminatory
> information not present on the other system's ballot.
> Example would be:
> 
> Plurality: One candidate, 1 full vote, all other candidates
> 0 vote.
> Borda: For N candidates, ranked, a vote of 0 for the lowest
> ranked candidate, 1 for the highest, and fractions of 1(N-1)
> stepwise for each in order of preference. (Unaddressed: what
> if the voter does not rank all candidates?)
> Range is a UM ballot intrinsically. (This includes
> Approval)
> Ranked methods without approval cutoff: Borda equivalent.
> Ranked methods with approval cutoff: ranks assigned are
> distributed equally across the range of 1/2 vote to 1 full
> vote for candidates approved, and across the range of 0 to
> 1/2 vote for candidates disapproved, but not 1/2 vote.
> (i.e., if there are two disapproved candidates, and if a
> preference is expressed, the most disapproved would be
> assigned 0 vote and the preferred one would be assigned 1/4
> vote. If three, the votes assigned would be 0, 1/6, 2/6,
> etc. (unranked candidates are assigned 0 vote, note that
> this, however, is "equal ranking." Which is frequently
> allowed in methods that supposedly don't allow equal
> ranking.)
> 
> A voting system satisfies the UM Criterion if it never
> chooses a candidate with a sum of votes on a UM ballot
> equivalent to the ballot used by the voting system, who has
> a lower sum of votes than the maximum among the candidates.
> 
> Plurality satisfies the UM Criterion because it does not
> allow the expression of other preferences, and, note, it
> must be this way because Range can be voted this way, if the
> voter has a preferred candidate. I.e., the equivalent of a
> Plurality ballot can be cast in Range, and if all voters do
> this, Range will provide a Plurality result.
> 
> >  Either way isn't it just *one* method?
> > I could believe that that method doesn't satisfy
> LNHarm, but it would be
> > hard to demonstrate that that method was the big
> winner.
> 
> "Method" the "big winner"? For the Later No Harm thing,
> it's quite enough that no ranked method satisfying Later No
> Harm -- which only applies to ranked methods or other
> methods allowing voting for multiple candidates while
> expressing a favorite -- cannot satisfy the Condorcet
> Criterion, not to mention the UM Criterion.

What do you say about the fact that Condorcet is almost certainly not
compatible with "UMC"? The CW has an above-average Borda score but of
course not always the highest. (At least, that is true with complete
rankings.)

Also, since the UM Criterion is based on positional assumptions
(when applied to a rank ballot) rather than actual utility, it's 
unclear that the best method possible (in terms of utility) satisfies 
UMC.

> > > And no method that maximizes social utility,
> overall
> > > satisfaction, can satisfy the majority or
> condorcet
> > > criteria, as fundamental as they seem, when only
> a single
> > > ballot is used. They can by using a second ballot
> to ratify
> > > (or reverse) an original election that finds the
> utility
> > > maximizer.
> > 
> > When we analyze methods we will usually assume that
> voters don't change
> > their positions between rounds, and the same voters
> vote in both rounds.
> 
> Which was, certainly, a simplifying assumption which
> completely neglects the reality of voting in multiple
> ballots.
> 
> (1) It's a different set of voters, usually.
> (2) They change their minds, based either on the first
> results, or on new information, or both.
> 
> By making this assumption, the analyst is tossing aside the
> reasons given in Robert's Rules of Order for holding
> repeated balloting instead of election by plurality or
> deterministic preferential voti

Re: [EM] Participation

[Abd ul-Rahman Lomax]

At 08:07 AM 4/26/2010, Kristofer Munsterhjelm wrote:

Abd ul-Rahman Lomax wrote:

At 11:57 PM 4/24/2010, Kevin Venzke wrote:

Hi Abd,

--- En date de : Sam 24.4.10, Abd ul-Rahman 
Lomax  a écrit :

> This is what is common with the
> use of voting systems criteria to study methods. Scenarios
> are created, sometimes cleverly, to cause a failure of a
> criterion. Does it matter if those conditions never exist?
> It should.

For the simple question of whether the criterion is satisfied or failed,
no it doesn't. Of course people then do go on to disagree about whether
certain criteria are important, and why. There is nobody who thinks every
single criterion is important.
That's right. But until utility analysis 
started to be done, the arguments had 
practically no foundation, they were just ideas 
about what democracy should look like, 
sometimes intuitions, and sometimes quite 
deceptive. Some criteria may be positively 
harmful, and Later No Harm is one of those. No 
method that maximizes utility can satisfy Later 
No Harm, no method that finds the best compromise winner can satisfy it.
And no method that maximizes social utility, 
overall satisfaction, can satisfy the majority 
or condorcet criteria, as fundamental as they 
seem, when only a single ballot is used. They 
can by using a second ballot to ratify (or 
reverse) an original election that finds the utility maximizer.


To me it seems that wouldn't be the case either. 
Consider the case of a top-two runoff (with 
Range as the first round) where the two winners 
are both supported by a minority. Then no matter 
who wins the runoff, the method as a whole has 
failed the Majority (and Condorcet) criterion.


The criteria are not designed to apply to 
multi-round elections. You can't even tell from 
the information given. What if more voters vote 
in the runoff? It happens, you know. A runoff is 
a separate election, that's very important to 
understand. If write-ins are allowed, or if the 
plurality preference is clearly in the runoff, as 
two examples, the Condorcet and Majority criteria 
are satisfied, assuming that the runoff method 
satisfies them. Bucklin doesn't satisfy 
Condorcet, technically, but in practice it does, 
I'm pretty sure. It does satisfy the Majority criterion, clearly.


Unlikely? Perhaps, but one failure is enough. Of 
course, you could then argue on basis of social 
utility (as you have), but you can't say the method passes the criteria.


You had two elections. The first one failed. The 
votes in it may determine ballot position, but 
they do not have any effect on the winner. They 
are then like any nomination rules, for example 
petition signatures or party endorsements. We 
don't claim that a method fails Condorcet because 
the nomination processes don't allow a condorcet 
winner to appear on the ballot!


One could also formulate criteria based on 
score, for instance: "if a candidate X is given 
more than half the points given by voters in 
that election in total, he should win" - a score/Range version of Majority.


I'm actually proposing using a Range ballot for a 
Bucklin method as primary, then examining the 
ballot, if there is majority failure, for various 
kinds of winners, and then including the 
important ones on the runoff ballot. I do 
advocate allowing write-ins on the runoff ballot, 
so there are actually *no* eliminations, just a 
kind of suggestion. It's rare, but write-ins do 
win elections, sometimes. A situation where a 
Condorcet winner, by some quirk, got eliminated 
is a case where it quite well might happen; in 
this case, there would be good data from the primary.


Because I'd use Bucklin for the runoff as well, 
it's conceivable that a Cndorcet winner could 
fail there, but this can only happen when there 
are excessive approvals by the supporters of the 
Condorcet winner. Essentially, it's either bad 
strategy -- and it's bad strategy when there is 
no excuse, the Condorcet winners supporters 
should know that this is, indeed, a Condorcet 
winner in the primary -- or it is a case of small 
preference strength in the votes for the 
Condorcet winner, compared to large preference 
strength in the votes for the actual winner of 
the election. In other words, this is a case 
where the Condoret winner was not ideal.


That's rare, but if we somehow had the magic 
perfect voting system, it would find this 
situation and would thus fail the Condorcet 
criterion. The question I ask: is, then, 
Condorcet failure of this kind a Bad Thing, to be avoided?


But ordinarily the Condorcet Criterion is quite 
important. That's why I'd like to make sure tha 
this winner, if there is majority failure, ends 
up on the runoff ballot. It allows those 
supporters to make a real, informed choice. For 
the Condorcet winner to fail, they must accept 
it, they must, at least, stand aside and not 
insist. If they persist, and if the Condorcet 
winner remains such through the expression of 
exclusive preferences, which req

Re: [EM] Participation

[Kristofer Munsterhjelm]

Abd ul-Rahman Lomax wrote:

At 11:57 PM 4/24/2010, Kevin Venzke wrote:

Hi Abd,

--- En date de : Sam 24.4.10, Abd ul-Rahman Lomax 
 a écrit :

> This is what is common with the
> use of voting systems criteria to study methods. Scenarios
> are created, sometimes cleverly, to cause a failure of a
> criterion. Does it matter if those conditions never exist?
> It should.

For the simple question of whether the criterion is satisfied or failed,
no it doesn't. Of course people then do go on to disagree about whether
certain criteria are important, and why. There is nobody who thinks every
single criterion is important.


That's right. But until utility analysis started to be done, the 
arguments had practically no foundation, they were just ideas about what 
democracy should look like, sometimes intuitions, and sometimes quite 
deceptive. Some criteria may be positively harmful, and Later No Harm is 
one of those. No method that maximizes utility can satisfy Later No 
Harm, no method that finds the best compromise winner can satisfy it.


And no method that maximizes social utility, overall satisfaction, can 
satisfy the majority or condorcet criteria, as fundamental as they seem, 
when only a single ballot is used. They can by using a second ballot to 
ratify (or reverse) an original election that finds the utility maximizer.


To me it seems that wouldn't be the case either. Consider the case of a 
top-two runoff (with Range as the first round) where the two winners are 
both supported by a minority. Then no matter who wins the runoff, the 
method as a whole has failed the Majority (and Condorcet) criterion.


Unlikely? Perhaps, but one failure is enough. Of course, you could then 
argue on basis of social utility (as you have), but you can't say the 
method passes the criteria.


One could also formulate criteria based on score, for instance: "if a 
candidate X is given more than half the points given by voters in that 
election in total, he should win" - a score/Range version of Majority.


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

Re: [EM] Participation

[Abd ul-Rahman Lomax]

At 01:24 PM 4/25/2010, Kevin Venzke wrote:

Hi Abd,

--- En date de : Dim 25.4.10, Abd ul-Rahman 
Lomax  a écrit :

> That's right. But until utility analysis started to be
> done, the arguments had practically no foundation, they were
> just ideas about what democracy should look like, sometimes
> intuitions, and sometimes quite deceptive. Some criteria may
> be positively harmful, and Later No Harm is one of those. No
> method that maximizes utility can satisfy Later No Harm, no
> method that finds the best compromise winner can satisfy
> it.

I don't understand your terminology. Does "maximize utility" mean pick
the best winner every time, or does it just mean the method that comes
closest to doing this on average?


Fair enough, I'll need to express some 
definitions, and I'm going to keep it simple, and 
define a UM criterion, Utility-Maximizing. The UM 
ballot allows the expression, for each candidate, 
of some fraction of a full vote, i.e., each 
candidate receives a vote in the range of 0-1 
vote. A "sincere UM ballot" is one in which every 
preference expressed is real, i.e., if the vote 
for one candidate is greater than a vote for a 
second candidate, then the voter actually prefers 
the first candidate to the second. However, the 
reverse is not necessarily true. If a voter 
prefers a candidate to another, it is possible 
that the voter chooses to vote the same fraction 
for them. I will assume, however, that the ballot 
allows the voter to express all preferences if 
the voter so chooses. (So it is, at a minimum, a Borda ballot).


A "UM ballot equivalent" is a ballot from another 
system translated to a UM ballot without 
violating the assumptions of the UM ballot and 
without creating discriminatory information not 
present on the other system's ballot. Example would be:


Plurality: One candidate, 1 full vote, all other candidates 0 vote.
Borda: For N candidates, ranked, a vote of 0 for 
the lowest ranked candidate, 1 for the highest, 
and fractions of 1(N-1) stepwise for each in 
order of preference. (Unaddressed: what if the 
voter does not rank all candidates?)

Range is a UM ballot intrinsically. (This includes Approval)
Ranked methods without approval cutoff: Borda equivalent.
Ranked methods with approval cutoff: ranks 
assigned are distributed equally across the range 
of 1/2 vote to 1 full vote for candidates 
approved, and across the range of 0 to 1/2 vote 
for candidates disapproved, but not 1/2 vote. 
(i.e., if there are two disapproved candidates, 
and if a preference is expressed, the most 
disapproved would be assigned 0 vote and the 
preferred one would be assigned 1/4 vote. If 
three, the votes assigned would be 0, 1/6, 2/6, 
etc. (unranked candidates are assigned 0 vote, 
note that this, however, is "equal ranking." 
Which is frequently allowed in methods that 
supposedly don't allow equal ranking.)


A voting system satisfies the UM Criterion if it 
never chooses a candidate with a sum of votes on 
a UM ballot equivalent to the ballot used by the 
voting system, who has a lower sum of votes than 
the maximum among the candidates.


Plurality satisfies the UM Criterion because it 
does not allow the expression of other 
preferences, and, note, it must be this way 
because Range can be voted this way, if the voter 
has a preferred candidate. I.e., the equivalent 
of a Plurality ballot can be cast in Range, and 
if all voters do this, Range will provide a Plurality result.




 Either way isn't it just *one* method?
I could believe that that method doesn't satisfy LNHarm, but it would be
hard to demonstrate that that method was the big winner.


"Method" the "big winner"? For the Later No Harm 
thing, it's quite enough that no ranked method 
satisfying Later No Harm -- which only applies to 
ranked methods or other methods allowing voting 
for multiple candidates while expressing a 
favorite -- cannot satisfy the Condorcet 
Criterion, not to mention the UM Criterion.



> And no method that maximizes social utility, overall
> satisfaction, can satisfy the majority or condorcet
> criteria, as fundamental as they seem, when only a single
> ballot is used. They can by using a second ballot to ratify
> (or reverse) an original election that finds the utility
> maximizer.

When we analyze methods we will usually assume that voters don't change
their positions between rounds, and the same voters vote in both rounds.


Which was, certainly, a simplifying assumption 
which completely neglects the reality of voting in multiple ballots.


(1) It's a different set of voters, usually.
(2) They change their minds, based either on the 
first results, or on new information, or both.


By making this assumption, the analyst is tossing 
aside the reasons given in Robert's Rules of 
Order for holding repeated balloting instead of 
election by plurality or deterministic preferential voting.



It's hard for me to imagine what approach could be used to show the
utility advantage of multiple roun

Re: [EM] Participation

[Kevin Venzke]

Hi Abd,

--- En date de : Dim 25.4.10, Abd ul-Rahman Lomax  a 
écrit :
> > --- En date de : Sam 24.4.10, Abd ul-Rahman Lomax
> 
> a écrit :
> > > This is what is common with the
> > > use of voting systems criteria to study methods.
> Scenarios
> > > are created, sometimes cleverly, to cause a
> failure of a
> > > criterion. Does it matter if those conditions
> never exist?
> > > It should.
> > 
> > For the simple question of whether the criterion is
> satisfied or failed,
> > no it doesn't. Of course people then do go on to
> disagree about whether
> > certain criteria are important, and why. There is
> nobody who thinks every
> > single criterion is important.
> 
> That's right. But until utility analysis started to be
> done, the arguments had practically no foundation, they were
> just ideas about what democracy should look like, sometimes
> intuitions, and sometimes quite deceptive. Some criteria may
> be positively harmful, and Later No Harm is one of those. No
> method that maximizes utility can satisfy Later No Harm, no
> method that finds the best compromise winner can satisfy
> it.

I don't understand your terminology. Does "maximize utility" mean pick
the best winner every time, or does it just mean the method that comes
closest to doing this on average? Either way isn't it just *one* method?
I could believe that that method doesn't satisfy LNHarm, but it would be
hard to demonstrate that that method was the big winner.

> And no method that maximizes social utility, overall
> satisfaction, can satisfy the majority or condorcet
> criteria, as fundamental as they seem, when only a single
> ballot is used. They can by using a second ballot to ratify
> (or reverse) an original election that finds the utility
> maximizer.

When we analyze methods we will usually assume that voters don't change
their positions between rounds, and the same voters vote in both rounds.
It's hard for me to imagine what approach could be used to show the
utility advantage of multiple rounds.

> > I don't think mono-add-top is very important. Markus
> probably doesn't
> > either.
> 
> The design of the criterion neglects, like almost all
> criteria, preference strength.

I don't consider mono-add-top important because I don't think it would
deter voting, or could be abused, or would be politically inexcusable
if failed.

> > > And now we come to my objection to Woodall's
> "harm"
> > > criteria. The consideration is whether a vote
> "harms a
> > > candidate," not whether or not it harms the
> *election,*
> > > i.e., the *electorate.*
> > 
> > If it does harm a candidate then it also harms the
> voter who added the
> > preference.
> 
> Not necessarily. Suppose I have a favorite I rate at 10.
> But there is another candidate who is really almost as good,
> and, in fact, this candidate I rate at 9 is better than I've
> every experienced being elected. Am I harmed if my lower
> ranked vote for the 9 causes the election to complete for
> this candidate, whereas without my vote perhaps it was a tie
> and it went to a runoff between the 9 and the 10? And did my
> adding that other vote actually "harm" my candidate, or did
> it merely reduce my support for the candidate?

Unless you want to invent new terminology, then yes, you are "harmed"
when your 9 vote moves the win from the 10 candidate to the 9 candidate.
I don't know what the practical difference is between "harming" your
10 candidate and "reducing your support thereby making him lose."

The reason we expect that to be bad is that if next time you choose
not to rank the 9 candidate, you could let your 0 candidate win, which
isn't what we want because we (the scenario designers) know that you
actually did have a compromise choice.

I guess your response would be "maybe the 9 candidate sucked." Maybe,
but we don't know, and I tend to think that in general, compromise
choices provide better utility than flank candidates.

> The goal of voting systems is to find a social compromise,
> and to fulfill that goal the favorites of many voters,
> sometimes even a majority of voters, must be "harmed," if we
> think not being elected is a harm Compromise is
> essential to community decision-making, and it always
> involves this kind of "harm." What a Later-No-Harm method
> does is to protect the voter from "harming" a candidate by
> taking the candidate out in back and shooting him. And then
> the method comes back to the voter and says, "Now that it
> won't harm your candidate, may he rest in peace, who else
> would you like to vote for?"

That's IRV. Most of the LNHarm methods don't eliminate candidates, the
particularly interesting ones being DSC and MMPO. (DSC gradually "rules
out" candidates but this isn't a prerequisite for counting lower prefs.)

> However, sauce for the good is
> sauce for the gander. If the method hadn't taken my favorite
> out back, if my favorite remained in the race, the method
> can still come to me and say, "is there anyone else
> acceptable to you?"

Re: [EM] Participation

[Abd ul-Rahman Lomax]

At 11:57 PM 4/24/2010, Kevin Venzke wrote:

Hi Abd,

--- En date de : Sam 24.4.10, Abd ul-Rahman 
Lomax  a écrit :

> This is what is common with the
> use of voting systems criteria to study methods. Scenarios
> are created, sometimes cleverly, to cause a failure of a
> criterion. Does it matter if those conditions never exist?
> It should.

For the simple question of whether the criterion is satisfied or failed,
no it doesn't. Of course people then do go on to disagree about whether
certain criteria are important, and why. There is nobody who thinks every
single criterion is important.


That's right. But until utility analysis started 
to be done, the arguments had practically no 
foundation, they were just ideas about what 
democracy should look like, sometimes intuitions, 
and sometimes quite deceptive. Some criteria may 
be positively harmful, and Later No Harm is one 
of those. No method that maximizes utility can 
satisfy Later No Harm, no method that finds the 
best compromise winner can satisfy it.


And no method that maximizes social utility, 
overall satisfaction, can satisfy the majority or 
condorcet criteria, as fundamental as they seem, 
when only a single ballot is used. They can by 
using a second ballot to ratify (or reverse) an 
original election that finds the utility maximizer.



I don't think mono-add-top is very important. Markus probably doesn't
either.


The design of the criterion neglects, like almost 
all criteria, preference strength.



> And now we come to my objection to Woodall's "harm"
> criteria. The consideration is whether a vote "harms a
> candidate," not whether or not it harms the *election,*
> i.e., the *electorate.*

If it does harm a candidate then it also harms the voter who added the
preference.


Not necessarily. Suppose I have a favorite I rate 
at 10. But there is another candidate who is 
really almost as good, and, in fact, this 
candidate I rate at 9 is better than I've every 
experienced being elected. Am I harmed if my 
lower ranked vote for the 9 causes the election 
to complete for this candidate, whereas without 
my vote perhaps it was a tie and it went to a 
runoff between the 9 and the 10? And did my 
adding that other vote actually "harm" my 
candidate, or did it merely reduce my support for the candidate?


The goal of voting systems is to find a social 
compromise, and to fulfill that goal the 
favorites of many voters, sometimes even a 
majority of voters, must be "harmed," if we think 
not being elected is a harm Compromise is 
essential to community decision-making, and it 
always involves this kind of "harm." What a 
Later-No-Harm method does is to protect the voter 
from "harming" a candidate by taking the 
candidate out in back and shooting him. And then 
the method comes back to the voter and says, "Now 
that it won't harm your candidate, may he rest in 
peace, who else would you like to vote for?" 
However, sauce for the good is sauce for the 
gander. If the method hadn't taken my favorite 
out back, if my favorite remained in the race, 
the method can still come to me and say, "is 
there anyone else acceptable to you?" And while 
my answer might "hurt" my favorite, on the other 
hand, the answers of others might "help" my 
favorite. My answer only has the possibility of 
"hurting" if my candidate wasn't going to win without additional votes.


Absolutely, if I answer "yes," this might result 
in some other choice than my favorite. But what 
would neighbors do, faced with a need to make 
some collective decision. Stick to their favorite 
until they absolutely know that, no matter what, 
their favorite isn't going to win? Let's say that 
I prefer not to have neighbors like that, and I'd 
prefer not to be a neighbor like that, and I'm 
unimpressed by a voting system that thinks this 
is something good it can offer to me.



 He could (depending on many factors, reasonably or
unreasonably) withhold lower preferences as a result, which means less
sincere voting.


No. This is a very common error. One withholds 
lower preferences because the preference strength 
is high. Truncation is not insincere, quite 
likely. A good voting system solicits and rewards 
sincere votes, and what we have done is to assume 
that voters aren't sincere when they say, "I 
prefer my favorite enough that I don't want to 
take a chance of electing someone else, I'm 
willing to take the risk that my vote becomes moot."



 Usually sincere voting produces a better outcome, in
this case due to a greater amount of information provided. So ultimately
the good of the electorate is the consideration.


"Sincere voting" is unfortunately not well 
defined, and so the statement that "sincere 
voting" is better is problematic. I agree that 
more information is better, but what kind of 
information? If incommensurable statistics are 
amalgamated, the result is noisy.


I've been working pretty intensively on Bucklin, 
and I believe that a strategically optimal 
Bucklin b

Re: [EM] Participation

[Kevin Venzke]

Hi Abd,

--- En date de : Sam 24.4.10, Abd ul-Rahman Lomax  a 
écrit :
> This is what is common with the
> use of voting systems criteria to study methods. Scenarios
> are created, sometimes cleverly, to cause a failure of a
> criterion. Does it matter if those conditions never exist?
> It should.

For the simple question of whether the criterion is satisfied or failed,
no it doesn't. Of course people then do go on to disagree about whether
certain criteria are important, and why. There is nobody who thinks every
single criterion is important.

I don't think mono-add-top is very important. Markus probably doesn't
either.

> And now we come to my objection to Woodall's "harm"
> criteria. The consideration is whether a vote "harms a
> candidate," not whether or not it harms the *election,*
> i.e., the *electorate.*

If it does harm a candidate then it also harms the voter who added the
preference. He could (depending on many factors, reasonably or 
unreasonably) withhold lower preferences as a result, which means less
sincere voting. Usually sincere voting produces a better outcome, in
this case due to a greater amount of information provided. So ultimately
the good of the electorate is the consideration.

Honestly I don't know how one could advocate a criterion which provides
a guarantee arbitrarily to candidates or voters without any greater
purpose. You have to be able to say that "people in general" receive a
benefit from this criterion (all things being equal, of course).

Kevin Venzke



  

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

Re: [EM] Participation

[Abd ul-Rahman Lomax]

At 03:06 PM 4/24/2010, fsimm...@pcc.edu wrote:

Markus pointed out that Bucklin fails mono add top.  Now I see why.  If x is
ranked second on all of the ballots except the new one, and some 
other candidate

y has exactly 50% first place support, then one ballot of the form x>y will
change the Bucklin winner from x to y, because now the collapse to second rank
is unnecessary..


What is meant here? I don't think it's correct as stated. Let's see:

50: y > x
50: z > x, x wins in second round.

add
1:  x>y, x still wins.

I think this is meant:

50: y >   > x
50: z >   > x (this was a legal Bucklin vote, ranks could be left 
blank. That's part of why I claim that a Bucklin ballot is a range ballot)

x wins in the third round, with 100% of the vote.

add
01: x > y

Still doesn't work Forest what do you have in mind? If the 
collapse to second rank is made unnecessary by the casting of an x>y 
vote, that means that the y vote is not counted, only the vote for x, 
so if this terminates the election, it must be for x. Not for y as you stated.




So we let's state a special version of participation that Bucklin satisfies:

If x wins Bucklin by collapse to level k, then adding a new ballot 
cannot switch

the winner from x to y unless y is ranked above level k or x is ranked below
level k.

In other words, the new winner has to be ranked relatively high to k or else x
has to be ranked relatively low to k in order to change the winner.

This seems like a reasonable Participation criterion.  It should be enough to
overcome the No Show phobia.


I don't think that bizarre election criteria failures, even if 
possible, will deter voting at all. Absolutely, voters in Bucklin 
will truncate when they prefer their favorite with sufficient 
strength. That's why the ballots work as range ballots! (I.e., they 
are strategically optimal, in ordinary circumstances, if voted 
according to sincere utility differences.) 



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

Re: [EM] Participation

[Abd ul-Rahman Lomax]

At 02:28 PM 4/24/2010, Markus Schulze wrote:

Hallo,

Bucklin violates mono-add-top. See:

http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012752.html


The criteria failures of Bucklin don't apply to all Bucklin methods.

Woodall's definition of mono-add-top:


Monotonicity. A candidate x should not be harmed if:
   * (mono-add-top) further ballots are added that have x top (and 
are otherwise arbitrary);
The example given showing mono-add-top failure for Bucklin used deep 
(full) ranking for six candidates, with no equal ranking allowed. 
Bucklin in original usage was a three-rank system, with equal ranking 
allowed in third rank. (Duluth Bucklin.) It's an Approval voting 
system, except that it phases in approvals according to ranks, and it 
is clearly improved by allowing equal ranking in all ranks, I 
wouldn't even consider tossing overvoted ballots (i.e, that rank more 
than one candidate in first or second rank.)


I'd like to look at this example, because it shows how preposterous 
assumptions about voting systems can lead to noise about how they perform.



12: A>B>C>D>E>F
11: C>A>B>D>E>F
10: B>C>A>D>E>F
27: D>E>F

This doesn't resemble real elections with Bucklin at all, but let's 
set that aside. This is what is common with the use of voting systems 
criteria to study methods. Scenarios are created, sometimes cleverly, 
to cause a failure of a criterion. Does it matter if those conditions 
never exist? It should. The only way to really study this is through 
simulations that could give some measure of how often a criterion 
failure might happen. And without utility information that would 
explain the preference profiles given, we have no idea of the damage 
done by criterion failure. It is entirely possible that, from a 
utility point of view, the election was improved by criterion failure!

I'll arrange this as Bucklin was usually reported:

60 Ballots, majority is 31.

A: 12 + 11 = 23, + 10 = 33
B: 10 + 12 = 22, + 11 = 33
C: 11 + 10 = 21, + 12 = 33
D: 27
E: 00 + 27
F: 00 + 00 + 27


A, B, and C are tied. They resolve the tie by looking back to the 
previous round and A is stronger. Maybe. Not sure I like that. What 
would range analysis say? Bucklin ballots, I've been claiming, are 
Range 4 ballots, with rating of 1 missing.


12: A = 4: total 48; B = 3: total 36; C = 2: total 24
11: A = 3: total 36; B = 2: total 24; C = 4: total 48
10: A = 2: total 20; B = 4: total 40; C = 3: total 30
27:D = 4: total 108
(E and F have
total scores A: 104   B: 100; C:  102   D:  108

I want to point this out: this is a very unusually close election. 
It's really close to a six-way tie. Note that with FPTP, the ABC trio 
have no chance at all, not with top two runoff or IRV. But D wins 
this election by Range, assuming that the ballot is a Range 4 ballot 
with the rating of 1 missing.


Now, comes 6 more ballots:

12: A>B>C>D>E>F
06:A>D
11: C>A>B>D>E>F
10: B>C>A>D>E>F
27: D>E>F

The ballots are very strange. If we go to the fourth round, the A, B, 
and C voters are all approving of D. Certainly, what makes the 
difference here is that the counting can go into the fourth round.


And now we come to my objection to Woodall's "harm" criteria. The 
consideration is whether a vote "harms a candidate," not whether or 
not it harms the *election,* i.e., the *electorate.*


This really isn't a known Bucklin form any more, for had it been, and 
those A, B, and C voters would, if they approved of D, voted for D in 
the third rank (equally with their other third choice), we will 
assume that the ballot does have four ranks. We must *still* assume 
that these are all approvals. In Bucklin, by voting for a candidate, 
they are approving of the election of the candidate.


Just looking at A and D.

66 ballots, majority is 34

A: 18 + 11 = 29, + 10 = 39
D: 27 + 06 = 33, + 00 = 33

A has a majority, A still wins, contrary to what was said. But I bet 
you could figure out an arrangement that causes this to count into 
the fourth round. But try to find one that uses three-round 
Bucklin-ER, and that isn't some insane 6-way election where a 
butterfly running into a window in China couldn't knock the election 
in some different direction.


I trust this analysis not at all.

Note that in real elections, far more ballots are truncated, getting 
a majority is harder, and multiple majorities would be rare. In 
rank-order systems such as Condorcet methods, deep ranking makes 
sense. In Bucklin, ranking below the approval cutoff makes no sense 
if these votes are going to be used to determine a winner.


Buckling can be made to have more than three ranks, sure, and the 
analysis of the ballot can be more sophisticated than simply 
sequential approval with a lowering approval cutoff, but using 
Bucklin in a runoff system is probably where it will shine the most, 
for in that environment, there is a stop-loss for ranking at a ve

Re: [EM] Participation

[fsimmons]

I want to thank Markus for keeping me from going too far off track.  And the 
link he gave below to a great 
message of Chris Benham was valuable for more than showing us that Bucklin 
violates mono-add-top:  
Chris also pointed out that WMA (weighted median approval) does satisfy 
Participation. 

I never fully appreciated before what a good method WMA was.

We assume that equal rankings are possible and that we have the probabilities 
of some monotonic, clone 
independent lottery L, like random ballot, at our disposal.  The weighted 
median approval cutoff is the 
highest "level" R above which the ranked alternatives have more than half the 
total probability of the lottery L. 

All alternatives ranked above R are approved.  

Approval ties are broken by the lottery L.  

It may be that the "level" R is below the truncation level, i.e. on some 
ballots the untruncated candidates 
have barely half the probability or less.  If that is the case on all of the 
ballots, all of the candidates are tied, 
so the election is decided by the lottery L.

Note that by this method any alternative with maximum approval will have above 
average approval, and the 
average approval will represent more than half of the lottery probability, 
since on each ballot more than half 
the lottery probability is located above the cutoff R. 

This method satisfies monotonicity and a marginal version of clone 
independence:  If clone family members 
are ranked equal, then when a winner is cloned in this way, the new winner will 
be a member of the old 
winner's clone family, and if a loser is cloned in this way, no member of the 
loser family will advance to 
winner.  

In other words, this WMA version satisfies clone independence about the same 
way Range does.  In fact, 
the easiest way to implement it is probably through the use of Range style 
ballots.  Any clone families that 
are not adjacent to the approval cutoff R can relax and spread out a little.

This method makes use of a lottery to break ties (which should be rare) and 
makes use of lottery 
probabilities to determine approval cutoffs.  Since the lottery probabilities 
are not random variables once the 
ballots are ready to be counted, the method is as deterministic as any method 
that uses randomness to 
break ties.




- Original Message -
> 
> Hallo,
> 
> Bucklin violates mono-add-top. See:
> 
> http://lists.electorama.com/pipermail/election-methods-
> electorama.com/2004-April/012752.html
> 
> Markus Schulze
> 

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

Re: [EM] Participation

[fsimmons]

Markus pointed out that Bucklin fails mono add top.  Now I see why.  If x is
ranked second on all of the ballots except the new one, and some other candidate
y has exactly 50% first place support, then one ballot of the form x>y will
change the Bucklin winner from x to y, because now the collapse to second rank
is unnecessary..

So we let's state a special version of participation that Bucklin satisfies:

If x wins Bucklin by collapse to level k, then adding a new ballot cannot switch
the winner from x to y unless y is ranked above level k or x is ranked below
level k.

In other words, the new winner has to be ranked relatively high to k or else x
has to be ranked relatively low to k in order to change the winner.

This seems like a reasonable Participation criterion.  It should be enough to
overcome the No Show phobia.

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

Re: [EM] Participation

[fsimmons]

The other thing I wanted to mention about why Bucklin and MMPO might complement 
each other is that MMPO potentially makes more use of the information in the 
lower ranks than Bucklin (especially in a many level cardinal weighted pairwise 
version), while MMPO tends to encourage equal ranking at the top (in order to 
satisfy the FBC), which is a service that Bucklin can perform for MMPO by 
collapsing the top levels down to the median of the candidate ratings..- 
Original Message -From: Date: Saturday, April 24, 2010 11:17 amSubject: 
ParticipationTo: election-methods@lists.electorama.com,> If I am not mistaken, 
both Bucklin and MMPO satisfy Perez' weak > version of> Participation: if the 
winner changes when a ballot is added, > then the old winner> was not ranked 
top on the added ballot.> > I wonder if some kind of hybrid between these two 
methods might > be better than> either without losing this form of 
Participation.> > For one thing, the pairwise oppositions in MMPO would need to 
be > replaced with> some kind of weighted pairwise opposition to ensure clone > 
independence.  For> that we need two or more levels if not full blown cardinal 
> ratings.  > > What if the three levels are (1) anything from the top rank 
down > to the level of> collapse that would be needed if Bucklin were used, (2) 
other > ranked, and (3)> truncated?  Then if a ballot has x  in level 1, and y  
in level > 3, that ballot> contributes two to the opposition of x against y, 
whereas if x > is only one level> above y, the ballot contributes only one to 
the opposition.> > Any other thoughts on this?

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

Re: [EM] Participation

[Markus Schulze]

Hallo,

Bucklin violates mono-add-top. See:

http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012752.html

Markus Schulze



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

[EM] Participation

[fsimmons]

If I am not mistaken, both Bucklin and MMPO satisfy Perez' weak version of
Participation: if the winner changes when a ballot is added, then the old winner
was not ranked top on the added ballot.

I wonder if some kind of hybrid between these two methods might be better than
either without losing this form of Participation.

For one thing, the pairwise oppositions in MMPO would need to be replaced with
some kind of weighted pairwise opposition to ensure clone independence.  For
that we need two or more levels if not full blown cardinal ratings.  

What if the three levels are (1) anything from the top rank down to the level of
collapse that would be needed if Bucklin were used, (2) other ranked, and (3)
truncated?  Then if a ballot has x  in level 1, and y  in level 3, that ballot
contributes two to the opposition of x against y, whereas if x is only one level
above y, the ballot contributes only one to the opposition.

Any other thoughts on this?

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