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<div class="moz-cite-prefix">On 10/07/2019 8:48 pm, Juho Laatu
wrote:<br>
<br>
<blockquote type="cite">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>
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>
in every pairwise contest.<br>
<br>
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>
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>
<br>
Chris Benham<br>
<br>
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<blockquote type="cite"
cite="mid:9003E3CD-24E4-40CF-B1B0-38B1E6EB048F@gmail.com">
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<blockquote type="cite" class="">
<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>
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<blockquote type="cite" class="">
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<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="">
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</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>
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<div><br class="">
</div>
<div>P.S.</div>
<div><br class="">
</div>
<div>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><br class="">
</div>
<div>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>
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