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Two mathematicians propose new voting method, Majority Judgment

RS
Ralph Suter
Thu, May 12, 2016 2:31 PM

Two French mathematicians, who say they have spent the last dozen years
studying voting systems, have proposed a new method they call Majority
Judgment. In a US presidential election, it would ask voters to judge
how good or bad a president they believe each candidate would be if
elected. There would be 6 options:

Great President
Good President
Average President
Poor President
Terrible President
Never Heard of Candidate

Their proposal was posted May 9, 2016 at The Conversation and May 11 at
Salon.com:

https://theconversation.com/trump-and-clinton-victorious-proof-that-us-voting-system-doesnt-work-58752
http://www.salon.com/2016/05/11/two_faces_of_a_rotting_system_partner/

The authors make the following claim, among others:

"Majority judgment
<https://mitpress.mit.edu/books/majority-judgment> resolves the
conundrum of Arrow’s theorem: neither the Condorcet nor the Arrow
paradox can occur.

I'd appreciate any thoughts about their proposal and about how Majority
Judgment compares to other voting methods, particularly Range Voting.

Thanks,
Ralph Suter

Two French mathematicians, who say they have spent the last dozen years studying voting systems, have proposed a new method they call Majority Judgment. In a US presidential election, it would ask voters to judge how good or bad a president they believe each candidate would be if elected. There would be 6 options: Great President Good President Average President Poor President Terrible President Never Heard of Candidate Their proposal was posted May 9, 2016 at The Conversation and May 11 at Salon.com: https://theconversation.com/trump-and-clinton-victorious-proof-that-us-voting-system-doesnt-work-58752 http://www.salon.com/2016/05/11/two_faces_of_a_rotting_system_partner/ The authors make the following claim, among others: "Majority judgment <https://mitpress.mit.edu/books/majority-judgment> resolves the conundrum of Arrow’s theorem: neither the Condorcet nor the Arrow paradox can occur. I'd appreciate any thoughts about their proposal and about how Majority Judgment compares to other voting methods, particularly Range Voting. Thanks, Ralph Suter
SR
Stéphane Rouillon
Thu, May 12, 2016 4:16 PM

Majority Judgment seems some discrete version of median voting, a subject these professors already treated. Obviously, like range voting, it solves Condorcet paradox which is based on preferences. It may have some other problems, linked to their gauge value definition. Is +33 vs -32 really better than +30 vs -1 ?

Envoyé de mon iPhone

Le 12 mai 2016 à 10:31, Ralph Suter RLSuter@aol.com a écrit :

Two French mathematicians, who say they have spent the last dozen years studying voting systems, have proposed a new method they call Majority Judgment. In a US presidential election, it would ask voters to judge how good or bad a president they believe each candidate would be if elected. There would be 6 options:

Great President
Good President
Average President
Poor President
Terrible President
Never Heard of Candidate

Their proposal was posted May 9, 2016 at The Conversation and May 11 at Salon.com:
https://theconversation.com/trump-and-clinton-victorious-proof-that-us-voting-system-doesnt-work-58752
http://www.salon.com/2016/05/11/two_faces_of_a_rotting_system_partner/
The authors make the following claim, among others:
"Majority judgment resolves the conundrum of Arrow’s theorem: neither the Condorcet nor the Arrow paradox can occur.
I'd appreciate any thoughts about their proposal and about how Majority Judgment compares to other voting methods, particularly Range Voting.

Thanks,
Ralph Suter

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

Majority Judgment seems some discrete version of median voting, a subject these professors already treated. Obviously, like range voting, it solves Condorcet paradox which is based on preferences. It may have some other problems, linked to their gauge value definition. Is +33 vs -32 really better than +30 vs -1 ? Envoyé de mon iPhone > Le 12 mai 2016 à 10:31, Ralph Suter <RLSuter@aol.com> a écrit : > > Two French mathematicians, who say they have spent the last dozen years studying voting systems, have proposed a new method they call Majority Judgment. In a US presidential election, it would ask voters to judge how good or bad a president they believe each candidate would be if elected. There would be 6 options: > > Great President > Good President > Average President > Poor President > Terrible President > Never Heard of Candidate > > Their proposal was posted May 9, 2016 at The Conversation and May 11 at Salon.com: > https://theconversation.com/trump-and-clinton-victorious-proof-that-us-voting-system-doesnt-work-58752 > http://www.salon.com/2016/05/11/two_faces_of_a_rotting_system_partner/ > The authors make the following claim, among others: > "Majority judgment resolves the conundrum of Arrow’s theorem: neither the Condorcet nor the Arrow paradox can occur. > I'd appreciate any thoughts about their proposal and about how Majority Judgment compares to other voting methods, particularly Range Voting. > > Thanks, > Ralph Suter > ---- > Election-Methods mailing list - see http://electorama.com/em for list info
KM
Kristofer Munsterhjelm
Thu, Jun 2, 2016 11:48 AM

On 05/12/2016 04:31 PM, Ralph Suter wrote:

The authors make the following claim, among others:

 "Majority judgment
 <https://mitpress.mit.edu/books/majority-judgment> resolves the
 conundrum of Arrow’s theorem: neither the Condorcet nor the Arrow
 paradox can occur.

I'd appreciate any thoughts about their proposal and about how Majority
Judgment compares to other voting methods, particularly Range Voting.

It's not a new system (in terms of this list). It consists of, very
roughly speaking:

Each voter gives each candidate a grade (e.g. A to F, but other names ae
also possible, like Great, Good, etc).
The system finds out, for each candidate, what the highest grade where a
majority grades the candidate at least that high. E.g. if some candidate
X had 20% A, 25% B, 10%C, and so on... then the 50% mark is at C because
more than 50% gave him a C or better.
The candidate with the highest majority grade / judgement wins.

There are some tiebreaks, but the above should give the gist of how it
works.

Two good things about this method are:

  • Unlike Range, it's relatively hard to manipulate. If X's grade is a C,
    you don't alter the outcome by changing your vote from a B to an A, or
    from a D to a C.

  • If everybody judges the candidates to a common standard, the method
    circumvents Arrow's paradox.

"Judging to a common standard" means that the voters ask themselves
"does candidate X deserve an A or a B? Does candidate Y deserve an A or
a B?" rather than going "I like X more than Y, so thus I'll give X a
higher grade than Y". The distinction is subtle, but judging to a common
standard means that if some candidate X is taken off the ballots, the
voters don't alter their votes for the other candidates, hence IIA
trivially follows.

Note that if the voters don't judge to a common standard, then the
method is subject to the Condorcet paradox. It doesn't pass Condorcet in
that case.

The French mathematicians then wrote this paper:

http://cmup.fc.up.pt/cmup/engmat/2012/seminario/artigos2012/bruno_neto/ElectionByMajorityJudgment%28ExperimentalEvidence%29Final.pdf

where they argued, IIRC, that:

  1. the evidence where MJ has been tried in exit polling shows that most
    people judge to a common standard,

  2. people don't judge to a common standard under Approval voting, so the
    same doesn't hold there,

and

  1. MJ agrees with Condorcet where Condorcet finds a strong consensus
    candidate, and disagrees with Condorcet where Condorcet finds a weak
    centrist, thus giving the best of both worlds.

Others disagree. In particular, I think Warren said the evidence looks
like that the voters didn't judge to a common standard even under MJ.

On 05/12/2016 04:31 PM, Ralph Suter wrote: > The authors make the following claim, among others: > > "Majority judgment > <https://mitpress.mit.edu/books/majority-judgment> resolves the > conundrum of Arrow’s theorem: neither the Condorcet nor the Arrow > paradox can occur. > > I'd appreciate any thoughts about their proposal and about how Majority > Judgment compares to other voting methods, particularly Range Voting. It's not a new system (in terms of this list). It consists of, very roughly speaking: Each voter gives each candidate a grade (e.g. A to F, but other names ae also possible, like Great, Good, etc). The system finds out, for each candidate, what the highest grade where a majority grades the candidate at least that high. E.g. if some candidate X had 20% A, 25% B, 10%C, and so on... then the 50% mark is at C because more than 50% gave him a C or better. The candidate with the highest majority grade / judgement wins. There are some tiebreaks, but the above should give the gist of how it works. Two good things about this method are: - Unlike Range, it's relatively hard to manipulate. If X's grade is a C, you don't alter the outcome by changing your vote from a B to an A, or from a D to a C. - If everybody judges the candidates to a common standard, the method circumvents Arrow's paradox. "Judging to a common standard" means that the voters ask themselves "does candidate X deserve an A or a B? Does candidate Y deserve an A or a B?" rather than going "I like X more than Y, so thus I'll give X a higher grade than Y". The distinction is subtle, but judging to a common standard means that if some candidate X is taken off the ballots, the voters don't alter their votes for the other candidates, hence IIA trivially follows. Note that if the voters don't judge to a common standard, then the method is subject to the Condorcet paradox. It doesn't pass Condorcet in that case. The French mathematicians then wrote this paper: http://cmup.fc.up.pt/cmup/engmat/2012/seminario/artigos2012/bruno_neto/ElectionByMajorityJudgment%28ExperimentalEvidence%29Final.pdf where they argued, IIRC, that: 1. the evidence where MJ has been tried in exit polling shows that most people judge to a common standard, 2. people don't judge to a common standard under Approval voting, so the same doesn't hold there, and 3. MJ agrees with Condorcet where Condorcet finds a strong consensus candidate, and disagrees with Condorcet where Condorcet finds a weak centrist, thus giving the best of both worlds. Others disagree. In particular, I think Warren said the evidence looks like that the voters didn't judge to a common standard even under MJ.