Hi Toby,
You probably already know that Balinski suggests that we use Majority Judgment instead for single-winner elections. It asks each voter to grade the suitability for office of as many of the candidates as they might wish as either Excellent, Very Good,
Good, Acceptable, Poor, or Reject. The same grade can be given to more than one candidate. An candidate not explicitly marked is counted as "Reject". The candidate who immediately or eventually receives the highest median-grade is the winner. Thus,
in contrast to the median-grade of any of the other candidate, the winner is the own 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 .
Also note that using these grades removes altogether the ambiguity you correctly illustrated below in your post. Why not just abandon such ranking methods and their problems, and use MJ instead? MJ's grades are more discerning, meaningful and informative
than rankings. Ranking can be inferred from a list of grades but grades cannot be inferred from rankings. What do you think?
Steve
FMessage: 2
Date: Wed, 29 May 2019 13:07:55 +0000 (UTC)
From: Toby Pereira <[hidden email]> To: "[hidden email]" <[hidden email]>, "[hidden email]" <[hidden email]> Subject: Re: [EM] Losing Votes (equal-ranking whole) Message-ID: <[hidden email]> Content-Type: text/plain; charset="utf-8" I don't have a definite answer to the question of equally ranked ballots, and to me I suppose it's still an open question exactly what the best way forwards is, even if you make a good argument against margins. I don't have an example where the plurality criterion bars from winning the candidate that I think should have won. Looking at the definition on the Wikipedia: "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is given any preference, then A's probability of winning must be no less than B's.", it's more that I would disagree with the terminology "given any preference." If the definition was "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is ranked anything other than last or joint last (either explicitly or through implication on a truncated ballot), then A's probability of winning must be no less than B's." then I'd be less critical of it. I think the way it's worded implies an approval cut-off even if in practice it makes no difference. Toby ---- Election-Methods mailing list - see https://electorama.com/em for list info |
Well yes, MJ is an interesting method in its own right and you seem to be its salesman! But I don't think that precludes discussion of whether winning votes/margins/losing votes etc. is the best way to implement pairwise methods. From: steve bosworth <[hidden email]> To: "[hidden email]" <[hidden email]> Cc: EM list <[hidden email]> Sent: Friday, 31 May 2019, 23:19 Subject: Re: [EM] Losing Votes (equal-ranking whole) vs MJ
Hi Toby,
You probably already know that Balinski suggests that we use Majority Judgment instead for single-winner elections. It asks each voter to grade the suitability for office of as many of the candidates as they might wish as either Excellent, Very Good,
Good, Acceptable, Poor, or Reject. The same grade can be given to more than one candidate. An candidate not explicitly marked is counted as "Reject". The candidate who immediately or eventually receives the highest median-grade is the winner. Thus,
in contrast to the median-grade of any of the other candidate, the winner is the own 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 .
Also note that using these grades removes altogether the ambiguity you correctly illustrated below in your post. Why not just abandon such ranking methods and their problems, and use MJ instead? MJ's grades are more discerning, meaningful and informative
than rankings. Ranking can be inferred from a list of grades but grades cannot be inferred from rankings. What do you think?
Steve
FMessage: 2
Date: Wed, 29 May 2019 13:07:55 +0000 (UTC)
From: Toby Pereira <[hidden email]> To: "[hidden email]" <[hidden email]>, "[hidden email]" <[hidden email]> Subject: Re: [EM] Losing Votes (equal-ranking whole) Message-ID: <[hidden email]> Content-Type: text/plain; charset="utf-8" I don't have a definite answer to the question of equally ranked ballots, and to me I suppose it's still an open question exactly what the best way forwards is, even if you make a good argument against margins. I don't have an example where the plurality criterion bars from winning the candidate that I think should have won. Looking at the definition on the Wikipedia: "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is given any preference, then A's probability of winning must be no less than B's.", it's more that I would disagree with the terminology "given any preference." If the definition was "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is ranked anything other than last or joint last (either explicitly or through implication on a truncated ballot), then A's probability of winning must be no less than B's." then I'd be less critical of it. I think the way it's worded implies an approval cut-off even if in practice it makes no difference. Toby Election-Methods mailing list - see https://electorama.com/em for list info ---- Election-Methods mailing list - see https://electorama.com/em for list info |
Hi Toby,
Yes, it is mathematically and intellectually challenging to discuss such questions and I wish you well.
However, as far as I can see, none of the Condorcet methods, nor any of the other alternatives offer the clear benefits for practical use as most fully provided by MJ:
Its grades allow each citizen fully to express their judgments about the suitability of each candidate for office. All these expressions help to determine the median-grade of each candidate. Consequently, the winner is the one who has received at least
50% plus one of all the votes cast. The winning grades of the elected candidate are composed of grades equal to or higher than the highest median-grade received by any of the candidates. The results reveal how every voting citizen judged each candidate's
suitability. That the winner is determined only by the highest median-grade reduces the incentives and opportunities for successful tactical voting by about "half". Thus, all the grades given to each candidate are most likely to be honest, as well as discerning
and informative from the electorates' point of view. A voter is guaranteed that all of their judgments will be so counted even if they explicitly grade only one candidate as at least Acceptable.
What do you think? Do you see any method better for practical use as a support for democracy?
From: Toby Pereira <[hidden email]>
Sent: Sunday, June 2, 2019 4:30 PM To: steve bosworth; [hidden email] Cc: EM list Subject: Re: [EM] Losing Votes (equal-ranking whole) vs MJ Well yes, MJ is an interesting method in its own right and you seem to be its salesman! But I don't think that precludes discussion of whether winning votes/margins/losing
votes etc. is the best way to implement pairwise methods.
From: steve bosworth <[hidden email]> To: "[hidden email]" <[hidden email]> Cc: EM list <[hidden email]> Sent: Friday, 31 May 2019, 23:19 Subject: Re: [EM] Losing Votes (equal-ranking whole) vs MJ
Hi Toby,
You probably already know that Balinski suggests that we use Majority Judgment instead for single-winner elections. It asks each voter to grade the suitability for office of as many of the candidates as they
might wish as either Excellent, Very Good, Good, Acceptable, Poor, or Reject. The same grade can be given to more than one candidate. An candidate not explicitly marked is counted as "Reject". The candidate who immediately or eventually receives the highest
median-grade is the winner. Thus,
in contrast to the median-grade of any of the other candidate, the winner is the own 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 .
Also note that using these grades removes altogether the ambiguity you correctly illustrated below in your post. Why not just abandon such ranking methods and their problems, and use MJ instead? MJ's grades are more discerning, meaningful and informative
than rankings. Ranking can be inferred from a list of grades but grades cannot be inferred from rankings. What do you think?
Steve
FMessage: 2
Date: Wed, 29 May 2019 13:07:55 +0000 (UTC)
From: Toby Pereira <[hidden email]> To: "[hidden email]" <[hidden email]>, "[hidden email]" <[hidden email]> Subject: Re: [EM] Losing Votes (equal-ranking whole) Message-ID: <[hidden email]> Content-Type: text/plain; charset="utf-8" I don't have a definite answer to the question of equally ranked ballots, and to me I suppose it's still an open question exactly what the best way forwards is, even if you make a good argument against margins. I don't have an example where the plurality criterion bars from winning the candidate that I think should have won. Looking at the definition on the Wikipedia: "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is given any preference, then A's probability of winning must be no less than B's.", it's more that I would disagree with the terminology "given any preference." If the definition was "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is ranked anything other than last or joint last (either explicitly or through implication on a truncated ballot), then A's probability of winning must be no less than B's." then I'd be less critical of it. I think the way it's worded implies an approval cut-off even if in practice it makes no difference. Toby Election-Methods mailing list - see https://electorama.com/em for list info ---- Election-Methods mailing list - see https://electorama.com/em for list info |
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