[EM] Losing Votes (equal-ranking whole) vs MJ

[steve bosworth]

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 <tdp201b at yahoo.co.uk>
To: "cbenham at adam.com.au" <cbenham at adam.com.au>,
        "election-methods at lists.electorama.com"
        <election-methods at lists.electorama.com>
Subject: Re: [EM] Losing Votes (equal-ranking whole)
Message-ID: <734797744.12568595.1559135275607 at mail.yahoo.com>
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


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