<html><head><meta http-equiv="Content-Type" content="text/html charset=windows-1252"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">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.<div class=""><br class=""></div><div class="">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.</div><div class=""><br class=""></div><div class="">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.</div><div class=""><br class=""></div><div class="">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.</div><div class=""><br class=""></div><div class="">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).</div><div class=""><br class=""></div><div class="">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).</div><div class=""><br class=""></div><div class=""><div class=""><div>Juho</div><div><br class=""></div><div><br class=""></div><div><br class=""><blockquote type="cite" class=""><div class="">On 12 Jul 2019, at 01:31, C.Benham <<a href="mailto:cbenham@adam.com.au" class="">cbenham@adam.com.au</a>> wrote:</div><br class="Apple-interchange-newline"><div class="">
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<div class="moz-cite-prefix">On 10/07/2019 8:48 pm, Juho Laatu
wrote:<br class="">
<br class="">
<blockquote type="cite" class="">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.</blockquote>
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<br class="">
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<br class="">
in every pairwise contest.<br class="">
<br class="">
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<br class="">
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).<br class="">
<br class="">
Chris Benham<br class="">
<br class="">
</div>
<blockquote type="cite" cite="mid:9003E3CD-24E4-40CF-B1B0-38B1E6EB048F@gmail.com" class="">
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<div class="">On 09 Jul 2019, at 00:55, Juho Laatu <<a href="mailto:juho.laatu@gmail.com" class="" moz-do-not-send="true">juho.laatu@gmail.com</a>> wrote:</div>
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<blockquote type="cite" class="">
<div class="">On 08 Jul 2019, at 22:05, C.Benham <<a href="mailto:cbenham@adam.com.au" class="" moz-do-not-send="true">cbenham@adam.com.au</a>>
wrote:</div>
</blockquote>
</div>
</div>
</div>
</blockquote>
<blockquote type="cite" class="">
<div class="">
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<div class="">
<blockquote type="cite" class="">
<div class="">
<div text="#000000" bgcolor="#FFFFFF" class=""><p class="">46: A>C<br class="">
10: B>A<br class="">
10: B>C<br class="">
34: C=B<br class="">
<br class="">
B>A 54-46 (margin=8), A>C 56-44
(margin=12), C>B 46-20 (margin=26).<br class="">
<br class="">
Here on more than half the ballots B is voted
both above A and no lower than equal-top, and
yet Margins elects A.<br class="">
<br class="">
No other candidate is voted at least equal-top
on more than half the ballots. Fans of Bucklin
or any version of Median<br class="">
Ratings would be particularly incensed. <br class="">
<br class="">
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 <br class="">
in their pairwise comparison, so "C>B 46-20"
becomes C>B 80-54, giving B a winning MM
Losing Votes score of 54. <br class="">
</p>
</div>
</div>
</blockquote>
<div class="">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".</div>
</div>
</div>
</div>
</blockquote>
<div class=""><br class="">
</div>
<div class="">P.S.</div>
<div class=""><br class="">
</div>
<div class="">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.</div>
<div class=""><br class="">
</div>
<div class="">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 <a href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2019-May/002126.html" class="" moz-do-not-send="true">http://lists.electorama.com/pipermail/election-methods-electorama.com/2019-May/002126.html</a>.
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).</div>
<div class=""><br class="">
</div>
<div class=""><br class="">
</div>
<div class=""><br class="">
</div>
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