Re: [EM] Best-Single Method-MJ

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Re: [EM] Best-Single Method-MJ

steve bosworth

Hi Toby,

I will respond below inline.

Steve
Message: 3
Date: Thu, 27 Jun 2019 14:31:17 +0000 (UTC)
From: Toby Pereira <[hidden email]>
To: EM List <[hidden email]>
Subject: [EM] What should an ideal single-winner method achieve?
Message-ID: <[hidden email]>
Content-Type: text/plain; charset="utf-8"

T:  With all the discussion of different single-winner methods and the criteria they pass and fail, I'm interested to know what you think the "ideal" method should hope to achieve. For example, some people might want to maximise utility summed across the voters.

S:  Please help me by defining what you mean by  *utility” and explain exactly how it should be *summed*.

T:  Others might want to find the candidate that is closest to the "median voter".

S:  By *median voter*, do you mean something other than MJ’s winner who has received at least 50% plus one of the grades from all the voters which are equal to or higher than the highest median-grade received by any of the candidates?

T:  For others it might be more about obeying some sort of majority criterion (e.g. Condorcet). Etc.

S: If you require the winner to be supported by the above *majority*, no Condorcet method guarantees that such a winner will be found.  Unlike any other method, MJ does guarantee this.


T: Personally, the measure that makes most sense to me is to maximise utility….

S:  This is what MJ seems to do by electing the candidate judge to be the candidate most fit for office, i.e. the  one most able and likely to help to maximise the utility of society.  This is indicated by the highest median-grade that that winner received from this electorate.

T:  …. But this doesn't automatically mean score voting (where a score could simply be seen as a utility rating of a candidate), at least in part because strategies that voters adopt might reduce its effectiveness.

S:  This is only one of the flaws inherent in score.

T:  Obviously, a voting method also needs to be simple enough to understand (in terms of voting and understanding how the winner is calculated), and it might be that different types of election suit different methods.

S:  MJ finds the winner simply by comparing the median-grades of each candidate.  Also, more clearly than its alternatives, MJ allows each voter most fully to express their judgment of each candidate (Excellent, Very Good, Good, Acceptable, Poor, or Reject),  These qualities seem to make MJ the method most suited to elect any single-winner.  What do you think?  Please explain any flaws you see in MJ.

Toby

Steve





Message: 3
Date: Thu, 27 Jun 2019 14:31:17 +0000 (UTC)
From: Toby Pereira <[hidden email]>
To: EM List <[hidden email]>
Subject: [EM] What should an ideal single-winner method achieve?
Message-ID: <[hidden email]>
Content-Type: text/plain; charset="utf-8"

With all the discussion of different single-winner methods and the criteria they pass and fail, I'm interested to know what you think the "ideal" method should hope to achieve. For example, some people might want to maximise utility summed across the voters. Others might want to find the candidate that is closest to the "median voter". For others it might be more about obeying some sort of majority criterion (e.g. Condorcet). Etc.
Personally, the measure that makes most sense to me is to maximise utility. But this doesn't automatically mean score voting (where a score could simply be seen as a utility rating of a candidate), at least in part because strategies that voters adopt might reduce its effectiveness. Obviously a voting method also needs to be simple enough to understand (in terms of voting and understanding how the winner is calculated), and it might be that different types of election suit different methods.
Toby
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Re: [EM] Best-Single Method-MJ

Juho Laatu-4
Yes, it is useful to discuss both strategic and sincere performance of different election methods. I tend to divide the targets of single winner methods from this point of view in two categories, cardinal and ordinal/ranked methods. The former typically aim at providing best sum of utilities. The latter ones are more majority oriented.

In the utility oriented category it is typical to aim at maximal sum of utilities, but it would be also possible to try to lift the lowest utilities as high as possible. In practice this would probably not mean making the absolutely lowest utility higher (to please the most unsatisfied voter) but to achieve a distribution of utilities that emphasises lifting the lower half of utilities among the voters.

In the majority oriented methods most people on this list like the Condorcet criterion. This approach can be characterised as seeking a good compromise. Other approaches, like that of IRV, put more emphasis on the number of first preferences in the votes. There is also a difference between trying to find the ideal winner vs trying to establish a total social order among the candidates. The results may be different, depending on how you define the ideal winner or the ideal social order.

When determining the ideal winner in ranked methods, one could concentrate on the number of other candidates that would beat the potential winner in a pairwise comparison, or the strengths of those defeats, or the worst defeat, or closeness of being an ideal winner, or maybe even chains of defeats to other candidates. The arguments here could be related to how well the chosen winner would be able to do his job in the competitive situation he finds himself in after he has been elected. I.e. how much and what kind of opposition there could be working against him.

It is good if the results can be easily understood. People tend to like natural looking things, like the elimination approach of IRV. People may also like the idea of forcing the cyclic group opinions to a more natural looking linear order of candidates. One should be careful about when one is talking about something that looks good vs something where the end result actually is good (according to the chosen criteria).

Different societies may have different needs in different elections. There is no ideal single winner method that would be best in all situations. Ideal winner can be defined in a different way e.g. in sports and in politics.

One could thus try to seek a winner that has the best sum of utilities, that is best for the median or average voter, most liked by those with strong opinions, most acceptable to majority, least hated by all, most efficient according to experts (this could mean indirect elections where elected experts elect the final winner). Most often we assume the one-man-one-vote principle, but that need not be the case always. We may plan the method for large or small elections, or large or small number of candidates. Sometimes easy and effortless voting is a key target, to guarantee high level of participation in the election, or to allow frequent and effortless voting. Easy understandability may mean also ability to see afterwards why the winner won, and what the opinions of different districts were, and how they summed up, or how close to victory the other candidates were. In political elections we typically like methods that can hide the opinions of individual voters.

In non-competitive elections we have lots of alternative approaches to select from. In competitive elections our choices are more limited since we need to take also the strategic vulnerabilities into account. The definition of ideal winner may actually already include some assumptions about what kind of a winner would be ideal in a competitive world (e.g. one that could work efficiently also when the opposition does not support his work).

Juho


From: Toby Pereira

With all the discussion of different single-winner methods and the criteria they pass and fail, I'm interested to know what you think the "ideal" method should hope to achieve. For example, some people might want to maximise utility summed across the voters. Others might want to find the candidate that is closest to the "median voter". For others it might be more about obeying some sort of majority criterion (e.g. Condorcet). Etc.
Personally, the measure that makes most sense to me is to maximise utility. But this doesn't automatically mean score voting (where a score could simply be seen as a utility rating of a candidate), at least in part because strategies that voters adopt might reduce its effectiveness. Obviously a voting method also needs to be simple enough to understand (in terms of voting and understanding how the winner is calculated), and it might be that different types of election suit different methods.
Toby


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Re: [EM] Best-Single Method-MJ

Toby Pereira
In reply to this post by steve bosworth
Steve

I'll reply all in one lump rather than line by line.

By "utility" I mean basically that every voter has a "happiness" score for each candidate. And these are added up for each candidate to find the utility winner.

By median voter, I mean that in the x dimensional "policy space" every voter will have a position along each axis and will sit as a point on a multi-dimensional graph. We take the median position of these points and find the candidate closest to this point. https://en.wikipedia.org/wiki/Geometric_median However, I'm not sure to what extent the assumption of these distinct axes with voters having a well-defined point on each axis actually mirrors reality. But you could in any case model this, and run simulations to find which voting methods (under certain strategical and other assumptions) would work best in practice for this principle.

I haven't replied previously to your posts on MJ, but I have read what some of the other posters have said. I do agree with Chris Benham that "irrelevant ballots" are a problem for MJ. Candidate A beats candidate B until a handful of voters that don't give a rating for either enter the election and then they swap round. They could even be blank ballots, or ballots that explicitly reject every candidate.

Arguably it's a problem that MJ is only concerned with the median (50th percentile) score for each candidate. It might be that candidate A beats candidate B at virtually every percentile apart from the 50th, but that's all MJ cares about. For example:

Candidate A: AAACCCC
Candidate B: BBBBFFFF

And in this case, a couple of new voters that reject both would shift the position of the median to favour A, when in reality nothing has really changed in terms of the electorate's view of these candidates relative to each other. Candidate B currently has a very fragile victory over candidate A, which strongly depends on where the median ends up landing. Results under MJ do seem to be very fragile, which is a bad thing.

There will also very often be ties under MJ, which means more than virtually any other conceivable method, it will be reliant on the its tiebreak procedure. Is MJ enough better than other methods and its tiebreak procedure good and robust enough to make MJ a better method overall than other methods that would rarely if ever have to resort to a tiebreak?

I probably won't have the time to trade 1000-word replies by the way!

Toby




On Friday, 28 June 2019, 05:58:24 BST, steve bosworth <[hidden email]> wrote:


Hi Toby,

I will respond below inline.

Steve
Message: 3
Date: Thu, 27 Jun 2019 14:31:17 +0000 (UTC)
From: Toby Pereira <[hidden email]>
To: EM List <[hidden email]>
Subject: [EM] What should an ideal single-winner method achieve?
Message-ID: <[hidden email]>
Content-Type: text/plain; charset="utf-8"

T:  With all the discussion of different single-winner methods and the criteria they pass and fail, I'm interested to know what you think the "ideal" method should hope to achieve. For example, some people might want to maximise utility summed across the voters.

S:  Please help me by defining what you mean by  *utility” and explain exactly how it should be *summed*.

T:  Others might want to find the candidate that is closest to the "median voter".

S:  By *median voter*, do you mean something other than MJ’s winner who has received at least 50% plus one of the grades from all the voters which are equal to or higher than the highest median-grade received by any of the candidates?

T:  For others it might be more about obeying some sort of majority criterion (e.g. Condorcet). Etc.

S: If you require the winner to be supported by the above *majority*, no Condorcet method guarantees that such a winner will be found.  Unlike any other method, MJ does guarantee this.


T: Personally, the measure that makes most sense to me is to maximise utility….

S:  This is what MJ seems to do by electing the candidate judge to be the candidate most fit for office, i.e. the  one most able and likely to help to maximise the utility of society.  This is indicated by the highest median-grade that that winner received from this electorate.

T:  …. But this doesn't automatically mean score voting (where a score could simply be seen as a utility rating of a candidate), at least in part because strategies that voters adopt might reduce its effectiveness.

S:  This is only one of the flaws inherent in score.

T:  Obviously, a voting method also needs to be simple enough to understand (in terms of voting and understanding how the winner is calculated), and it might be that different types of election suit different methods.

S:  MJ finds the winner simply by comparing the median-grades of each candidate.  Also, more clearly than its alternatives, MJ allows each voter most fully to express their judgment of each candidate (Excellent, Very Good, Good, Acceptable, Poor, or Reject),  These qualities seem to make MJ the method most suited to elect any single-winner.  What do you think?  Please explain any flaws you see in MJ.

Toby

Steve





Message: 3
Date: Thu, 27 Jun 2019 14:31:17 +0000 (UTC)
From: Toby Pereira <[hidden email]>
To: EM List <[hidden email]>
Subject: [EM] What should an ideal single-winner method achieve?
Message-ID: <[hidden email]>
Content-Type: text/plain; charset="utf-8"

With all the discussion of different single-winner methods and the criteria they pass and fail, I'm interested to know what you think the "ideal" method should hope to achieve. For example, some people might want to maximise utility summed across the voters. Others might want to find the candidate that is closest to the "median voter". For others it might be more about obeying some sort of majority criterion (e.g. Condorcet). Etc.
Personally, the measure that makes most sense to me is to maximise utility. But this doesn't automatically mean score voting (where a score could simply be seen as a utility rating of a candidate), at least in part because strategies that voters adopt might reduce its effectiveness. Obviously a voting method also needs to be simple enough to understand (in terms of voting and understanding how the winner is calculated), and it might be that different types of election suit different methods.
Toby
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Re: [EM] Steve's reply: Best-Single Method-MJ

steve bosworth
Hi Toby,
Thank you for your response.  Correctly you pose the following question:  *Is MJ enough better than other methods and its tiebreak procedure good and robust enough to make MJ a better method overall than other methods that would rarely if ever have to resort to a tiebreak?* When you continue to think about what your own answer to this question should be, perhaps you will again carefully weigh  the importance of
1) the fact that MJ's tie breaking procedure is both simple and not arbitrary (the winner is always the one who currently has the highest median grade), and
2) the  truth that each citizen's voter is treated equally only when the method guarantees that the winner will be supported by a majority of all the votes cast.  Only MJ does this.  MJ casted ballots are only those that explicitly grade at least one candidate as at least Acceptable.
I wish you well.
Steve



From: Toby Pereira <[hidden email]>
Sent: Friday, June 28, 2019 4:33 PM
To: [hidden email]; steve bosworth
Subject: Re: Best-Single Method-MJ
 
Steve

I'll reply all in one lump rather than line by line.

By "utility" I mean basically that every voter has a "happiness" score for each candidate. And these are added up for each candidate to find the utility winner.

By median voter, I mean that in the x dimensional "policy space" every voter will have a position along each axis and will sit as a point on a multi-dimensional graph. We take the median position of these points and find the candidate closest to this point. https://en.wikipedia.org/wiki/Geometric_median However, I'm not sure to what extent the assumption of these distinct axes with voters having a well-defined point on each axis actually mirrors reality. But you could in any case model this, and run simulations to find which voting methods (under certain strategical and other assumptions) would work best in practice for this principle.

I haven't replied previously to your posts on MJ, but I have read what some of the other posters have said. I do agree with Chris Benham that "irrelevant ballots" are a problem for MJ. Candidate A beats candidate B until a handful of voters that don't give a rating for either enter the election and then they swap round. They could even be blank ballots, or ballots that explicitly reject every candidate.

Arguably it's a problem that MJ is only concerned with the median (50th percentile) score for each candidate. It might be that candidate A beats candidate B at virtually every percentile apart from the 50th, but that's all MJ cares about. For example:

Candidate A: AAACCCC
Candidate B: BBBBFFFF

And in this case, a couple of new voters that reject both would shift the position of the median to favour A, when in reality nothing has really changed in terms of the electorate's view of these candidates relative to each other. Candidate B currently has a very fragile victory over candidate A, which strongly depends on where the median ends up landing. Results under MJ do seem to be very fragile, which is a bad thing.

There will also very often be ties under MJ, which means more than virtually any other conceivable method, it will be reliant on the its tiebreak procedure. Is MJ enough better than other methods and its tiebreak procedure good and robust enough to make MJ a better method overall than other methods that would rarely if ever have to resort to a tiebreak?

I probably won't have the time to trade 1000-word replies by the way!

Toby




On Friday, 28 June 2019, 05:58:24 BST, steve bosworth <[hidden email]> wrote:


Hi Toby,

I will respond below inline.

Steve
Message: 3
Date: Thu, 27 Jun 2019 14:31:17 +0000 (UTC)
From: Toby Pereira <[hidden email]>
To: EM List <[hidden email]>
Subject: [EM] What should an ideal single-winner method achieve?
Message-ID: <[hidden email]>
Content-Type: text/plain; charset="utf-8"

T:  With all the discussion of different single-winner methods and the criteria they pass and fail, I'm interested to know what you think the "ideal" method should hope to achieve. For example, some people might want to maximise utility summed across the voters.

S:  Please help me by defining what you mean by  *utility” and explain exactly how it should be *summed*.

T:  Others might want to find the candidate that is closest to the "median voter".

S:  By *median voter*, do you mean something other than MJ’s winner who has received at least 50% plus one of the grades from all the voters which are equal to or higher than the highest median-grade received by any of the candidates?

T:  For others it might be more about obeying some sort of majority criterion (e.g. Condorcet). Etc.

S: If you require the winner to be supported by the above *majority*, no Condorcet method guarantees that such a winner will be found.  Unlike any other method, MJ does guarantee this.


T: Personally, the measure that makes most sense to me is to maximise utility….

S:  This is what MJ seems to do by electing the candidate judge to be the candidate most fit for office, i.e. the  one most able and likely to help to maximise the utility of society.  This is indicated by the highest median-grade that that winner received from this electorate.

T:  …. But this doesn't automatically mean score voting (where a score could simply be seen as a utility rating of a candidate), at least in part because strategies that voters adopt might reduce its effectiveness.

S:  This is only one of the flaws inherent in score.

T:  Obviously, a voting method also needs to be simple enough to understand (in terms of voting and understanding how the winner is calculated), and it might be that different types of election suit different methods.

S:  MJ finds the winner simply by comparing the median-grades of each candidate.  Also, more clearly than its alternatives, MJ allows each voter most fully to express their judgment of each candidate (Excellent, Very Good, Good, Acceptable, Poor, or Reject),  These qualities seem to make MJ the method most suited to elect any single-winner.  What do you think?  Please explain any flaws you see in MJ.

Toby

Steve





Message: 3
Date: Thu, 27 Jun 2019 14:31:17 +0000 (UTC)
From: Toby Pereira <[hidden email]>
To: EM List <[hidden email]>
Subject: [EM] What should an ideal single-winner method achieve?
Message-ID: <[hidden email]>
Content-Type: text/plain; charset="utf-8"

With all the discussion of different single-winner methods and the criteria they pass and fail, I'm interested to know what you think the "ideal" method should hope to achieve. For example, some people might want to maximise utility summed across the voters. Others might want to find the candidate that is closest to the "median voter". For others it might be more about obeying some sort of majority criterion (e.g. Condorcet). Etc.
Personally, the measure that makes most sense to me is to maximise utility. But this doesn't automatically mean score voting (where a score could simply be seen as a utility rating of a candidate), at least in part because strategies that voters adopt might reduce its effectiveness. Obviously a voting method also needs to be simple enough to understand (in terms of voting and understanding how the winner is calculated), and it might be that different types of election suit different methods.
Toby
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Re: [EM] Best-Single Method-MJ

robert bristow-johnson
In reply to this post by Toby Pereira



---------------------------- Original Message ----------------------------
Subject: Re: [EM] Best-Single Method-MJ
From: "Toby Pereira" <[hidden email]>
Date: Fri, June 28, 2019 9:33 am
To: "[hidden email]" <[hidden email]>
"steve bosworth" <[hidden email]>
--------------------------------------------------------------------------

> By "utility" I mean basically that every voter has a "happiness" score for each candidate. And these are added up for each candidate to find the utility winner.

So, Toby, just to be clear.  If I really, really, really like my candidate and you just  sorta prefer your candidate, does my vote count for more than your vote?

 

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Re: [EM] Best-Single Method-MJ

Toby Pereira


On Friday, 28 June 2019, 20:30:33 BST, robert bristow-johnson <[hidden email]> wrote:




---------------------------- Original Message ----------------------------
Subject: Re: [EM] Best-Single Method-MJ
From: "Toby Pereira" <[hidden email]>
Date: Fri, June 28, 2019 9:33 am
To: "[hidden email]" <[hidden email]>
"steve bosworth" <[hidden email]>
--------------------------------------------------------------------------

>> By "utility" I mean basically that every voter has a "happiness" score for each candidate. And these are added up for each candidate to find the utility winner.

>So, Toby, just to be clear.  If I really, really, really like my candidate and you just  sorta prefer your candidate, does my vote count for more than your vote?

Well it partly depends on how you define a vote counting for more. But if these are the two frontrunners, then under a raw utility method, then yes, your vote would count for more. But there isn't a method that reads our minds to judge what we would consider to be our utility of each candidate. Under score voting, we would both have the choice of how to score these candidates. I can still maximise the difference if I want, but then I understand that you would counter that I am placed with a tactical burden while doing this.

I don't think the problems of score are as bad as you think they are, but I'm not wedded to it either. One could make a big thing about Condorcet methods (and probably virtually all methods discussed on here) failing participation. Never mind someone's vote counting for more than mine - my vote might count negative!

Toby

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Re: [EM] Best-Single Method-MJ

robert bristow-johnson



---------------------------- Original Message ----------------------------
Subject: Re: [EM] Best-Single Method-MJ
From: "Toby Pereira" <[hidden email]>
Date: Fri, June 28, 2019 1:33 pm
To: "robert bristow-johnson" <[hidden email]>
Cc: "[hidden email]" <[hidden email]>
"steve bosworth" <[hidden email]>
--------------------------------------------------------------------------

>
>
> On Friday, 28 June 2019, 20:30:33 BST, robert bristow-johnson <[hidden email]> wrote:
>
>
>
> ---------------------------- Original Message ----------------------------
> Subject: Re: [EM] Best-Single Method-MJ
>
From: "Toby Pereira" <[hidden email]>
> Date: Fri, June 28, 2019 9:33 am
> To: "[hidden email]" <[hidden email]>
> "steve bosworth" <[hidden email]>
> --------------------------------------------------------------------------
>
>>> By "utility" I mean basically that every voter has a "happiness" score for each candidate. And these are added up for each candidate to find the utility winner.
>>So, Toby, just to be clear.  If I really, really, really like my candidate and you just  sortaprefer your candidate, does my vote count for more than your vote?
> Well it partly depends on how you define a vote counting for more. But if these are the two frontrunners, then under a raw utility method, then yes, your vote would count for more. But there isn't a method that reads our minds to judge what we would consider to be our utility of each candidate. Under score voting, we would both have the choice of how to score these candidates. I can still maximise the difference if I want, but then I understand that you would counter that I am placed with a tactical burden while doing this.
> I don't think the problems of score are as bad as you think they are, but I'm not wedded to it either. One could make a big thing about Condorcet methods (and probably virtually all methods discussed on here) failing participation. Never mind someone's vote counting for more than mine - my vote might count negative!
 

but a situation that would cause non-monotonicity (where your political interests are better served by your not voting)  has to be a pretty strange situation similar to some of the thought experiments you guys cook up here.  i think it would be completely normal, in a partisan situation, that people will strategically pick the candidate having any hope of winning that is the least undesirable.  then they will "bullet-score" that candidate and Score Voting becomes essentially FPTP scaled by 5 or 10.  Or if Approval, they will "approve" only that candidate and no one else making this essentially FPTP.


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Re: [EM] Best-Single Method-MJ

Kristofer Munsterhjelm-3
On 29/06/2019 00.23, robert bristow-johnson wrote:

> but a situation that would cause non-monotonicity (where your political
> interests are better served by your not voting)  has to be a pretty
> strange situation similar to some of the thought experiments you guys
> cook up here.  i think it would be completely normal, in a partisan
> situation, that people will strategically pick the candidate having any
> hope of winning that is the least undesirable.  then they will
> "bullet-score" that candidate and Score Voting becomes essentially FPTP
> scaled by 5 or 10.  Or if Approval, they will "approve" only that
> candidate and no one else making this essentially FPTP.

I prefer Condorcet to Approval, but that isn't entirely true. In
Approval, it does you no harm to approve candidates who you prefer to
the least undesirable viable candidate; by doing so, you may show,
through the results, that someone everybody thought was unviable is
starting to become viable.

For instance, if you like the Green and Democratic parties, and prefer
the former to the latter, you may vote {G, D} or {G}. There's no reason
to vote only {D}.

The burden on the voter comes when G and D are roughly equal in support.
Do you vote G only and risk the Republicans winning instead, or do you
vote G and D and make it impossible for G to overtake D with your vote
alone? A ranked method, of course, has none of this: if you're a honest
voter, you can simply vote G>D>R. Only strategic voters are burdened.
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