<html><head><meta http-equiv="Content-Type" content="text/html charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div><blockquote type="cite" class=""><div class="">On 09 Jul 2019, at 00:55, Juho Laatu <<a href="mailto:juho.laatu@gmail.com" class="">juho.laatu@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta http-equiv="Content-Type" content="text/html charset=us-ascii" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class=""><blockquote type="cite" class=""><div class="">On 08 Jul 2019, at 22:05, C.Benham <<a href="mailto:cbenham@adam.com.au" class="">cbenham@adam.com.au</a>> wrote:</div></blockquote></div></div></div></blockquote><blockquote type="cite" class=""><div class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><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><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="">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><br class=""></div><div><br class=""></div><div><br class=""></div></div></body></html>