[EM] Two mathematicians propose new voting method, Majority Judgment

[Kristofer Munsterhjelm]

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.