# [EM] Best-Single Method-MJ

Toby Pereira tdp201b at yahoo.co.uk
Fri Jun 28 09:33:15 PDT 2019

``` 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: AAACCCCCandidate 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 <stevebosworth at hotmail.com> wrote:

Hi Toby,

I will respond below inline.

Steve
Message: 3
Date: Thu, 27 Jun 2019 14:31:17 +0000 (UTC)
From: Toby Pereira <tdp201b at yahoo.co.uk>
To: EM List <election-methods at electorama.com>
Subject: [EM] What should an ideal single-winner method achieve?
Message-ID: <2093644385.1380055.1561645877622 at mail.yahoo.com>
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 <tdp201b at yahoo.co.uk>
To: EM List <election-methods at electorama.com>
Subject: [EM] What should an ideal single-winner method achieve?
Message-ID: <2093644385.1380055.1561645877622 at mail.yahoo.com>
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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