[EM] Modified Overall Preferences / margins, Smith set

Fri Jul 12 23:50:07 PDT 2019

As I said, that example is a worst case scenario, not a typical outcome of an election. My example should indeed maybe avoid ties, and be written for three candidates, so we can avoid the problem of discussing what to do with ties, and which method to use. My default method is usually Minmax, but I of course should not assume others to have a similar approach. I tried to make the example visually more informative with multiple candidates on both sides, but I guess the rudimentary three candidate approach would work better and is clearer. With no tie possibilities and three candidates the example could be written 49: A, 48: B>C. 3: C>A. With these votes we can maybe better discuss the role of Margins, Winning Votes and also Losing Votes.

In this example there are two main groups, the A group and the BC group. Both groups tend to truncate candidates of the other group (48: B>C voters truncating A does however not have much influence, since there is only one candidate in the A group). Sincere opinions of the A supporters could be simply A>B=C, or alternatively more A>B>C oriented than A>C>B oriented (i.e. with no hidden strong support to C). Three C supporters are the special group that might make the results confusing.

My first question is, who should win if these votes are all sincere votes (including 49: A>B=C)? I tend to see A and B as the obvious strong candidates, and C as a weak candidate that probably should not win. Winning Votes seem to elect C. That can be interpreted as poor performance with sincere votes. Or if the sincere opinion of the C supporters was 3: C>B, then that can be interpreted as a serious vulnerability to burying.

Losing Votes don't seem to have that problem. It seems I used a non working calculator last time with Winning Votes. I have to find new better (bad) examples for it.

It is quite possible that in some elections both groups truncate heavily, but what if only a limited amount of them do so. Margins and Winning Votes get more similar when the number of voters that give full rankings increases, but there is still a difference. Votes 10: A>B>C, 10: A>C>B, 29: A, 40: B>C, 11:C>A, and votes 20: A>B>C, 29: A, 30: B>C, 21:C>A would yield similar results (assuming that my calculations are correct, please check).

When comparing strategies in Margins and Winning Votes, my basic understanding is that there is no easy way out. When one tries to patch one hole, one typically opens another hole somewhere else. It is typical that the very same examples, when read from different angles, give different viewpoints to what went wrong. Sometimes also performance with sincere votes and performance under strategic voting are fighting for the same space. My tendency to favour Margins is because of its natural behaviour with sincere votes (there are other closely related but a bit more complex alternatives too). I think most Condorcet elections would be quite sincere. But if need to defend against strategies arises, my favourite path might be to go somewhere in the direction of MOP-F2 / MOP. I think the most common problems of Margins can be alleviated also that way, without disturbing sincere voting (ability to collect sincere votes / voters' trust on being safe when doing so) and performance with sincere votes (picking a good winner) too much (or maybe not at all, leaving added complexity the main thing that would be negative in this approach).

Juho

> On 12 Jul 2019, at 01:31, C.Benham <cbenham at adam.com.au> wrote:
> 
> 
> On 10/07/2019 8:48 pm, Juho Laatu wrote:
> 
>> Concerning concrete examples with Losing Votes, similar examples seem to serve as bad examples also with Losing Votes and Pairwise Opposition (in addition to Winning Votes). I mean vote sets like 50: A>B, 50:C>D, 1:D>*, where * refers to either A or B.
> Juho, say * is A. Whereas my examples are simple and plausible yours are not.  Your example would be a bit more "realistic" if none of the pairwise
> scores were identical, none of the first-preference scores were identical, none of the pairwise contests were exact ties and every candidate got some support
> in every pairwise contest.
> 
> In your example three of the pairwise contests are 51-50 (A>C, D>A, D>B), A and C both have 50 first-preference votes, B and C tie 50-50 and B has no pairwise
> support against A. Nonetheless  in your example I don't see how all three of Margins, Winning Votes and Margins not elect C (say with Smith//MinMax).
> 
> Chris Benham
> 
>>> On 09 Jul 2019, at 00:55, Juho Laatu <juho.laatu at gmail.com <mailto:juho.laatu at gmail.com>> wrote:
>>> 
>>>> On 08 Jul 2019, at 22:05, C.Benham <cbenham at adam.com.au <mailto:cbenham at adam.com.au>> wrote:
>>>> 46: A>C
>>>> 10: B>A
>>>> 10: B>C
>>>> 34: C=B
>>>> 
>>>> B>A  54-46 (margin=8),   A>C 56-44 (margin=12),  C>B 46-20 (margin=26).
>>>> 
>>>> Here on more than half the ballots B is voted both above A and no lower than equal-top, and yet Margins elects A.
>>>> 
>>>> No other candidate is voted at least equal-top on more than half the ballots. Fans of Bucklin or any version of Median
>>>> Ratings would be particularly incensed.  
>>>> 
>>>> The version of Losing Votes that I advocate elects B because it has the 34C=B ballots give a whole vote to each of C and B 
>>>> in their pairwise comparison, so "C>B 46-20" becomes C>B 80-54, giving B a winning MM Losing Votes score of 54.  
>>> I don't like losing votes too much since they may give strange results already with sincere votes. I don't have any dramatic examples available, but I believe there are such examples. I gave one example on winning votes earlier (50: A>B>C, 50: D>E>F, 1: F>A). Sorry about basing my claim on losing votes on "feelings only".
>> 
>> P.S.
>> 
>> Concerning concrete examples with Losing Votes, similar examples seem to serve as bad examples also with Losing Votes and Pairwise Opposition (in addition to Winning Votes). I mean vote sets like 50: A>B, 50:C>D, 1:D>*, where * refers to either A or B.
>> 
>> Winning Votes, Losing Votes and Pairwise Opposition are quite artificial constructions when compared to margins and other such pairwise comparison functions that aim more at estimating the (society related) seriousness of each defeat. I discussed such more natural pairwise comparison functions (e.g. Relative Margins and Moderated Margins) a bit more in http://lists.electorama.com/pipermail/election-methods-electorama.com/2019-May/002126.html <http://lists.electorama.com/pipermail/election-methods-electorama.com/2019-May/002126.html>. If one wants to change the behaviour of Margins, one option is not to jump directly to Winning Votes etc but to make some less radical changes (that avoid the worst pathologies). Also the MOP track is interesting in the sense that the modification function can be used to tweak the original (Margins or other) strengths in a similar manner (e.g. based on indicated favourites as in MOP-F2).
>> 
>> 
>> 
>> 
>> 
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