<html><head></head><body><div style="color:#000; background-color:#fff; font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px"><div id="yui_3_16_0_ym19_1_1493121154794_9825"><span id="yui_3_16_0_ym19_1_1493121154794_12205"><font size="3" id="yui_3_16_0_ym19_1_1493121154794_12204">Yes, WV satisfies Plurality. In fact margins methods are among the only serious proposals that don't satisfy it. This property</font></span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825"><span><font size="3">says that e.g. A can't win </font></span><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_15357">in this </span><span style="font-size: medium;">scenario:</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825"><span style="font-size: medium;"><br></span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span id="yui_3_16_0_ym19_1_1493121154794_12981"><font size="3" id="yui_3_16_0_ym19_1_1493121154794_12980">7 A>B</font></span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><font size="3" id="yui_3_16_0_ym19_1_1493121154794_12979">5 B</font></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><font size="3">8 C</font></div><div id="yui_3_16_0_ym19_1_1493121154794_9825"><span><font size="3"><br></font></span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span id="yui_3_16_0_ym19_1_1493121154794_12321"><font size="3" id="yui_3_16_0_ym19_1_1493121154794_12320">Methods that have added Smith compliance to MinMax usually call for WV. </font></span><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13884">Schulze's paper </span><span id="yui_3_16_0_ym19_1_1493121154794_12325"><font size="3" id="yui_3_16_0_ym19_1_1493121154794_12324">describing the Schulze method</font></span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span id="yui_3_16_0_ym19_1_1493121154794_12993"><font size="3" id="yui_3_16_0_ym19_1_1493121154794_12992">used to say that there had been discussion concluding that </font></span><span id="yui_3_16_0_ym19_1_1493121154794_12413"><font size="3" id="yui_3_16_0_ym19_1_1493121154794_12412">margins wasn't recommended due to strategic </font></span><font size="3" id="yui_3_16_0_ym19_1_1493121154794_12840">reasons, </font><span id="yui_3_16_0_ym19_1_1493121154794_12491" style="font-size: medium;">though I</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;">can't find that </span><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13325">language there anymore. That being </span><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13324">said, </span><span id="yui_3_16_0_ym19_1_1493121154794_12492" style="font-size: medium;">I would be a bit surprised to learn that anyone using </span><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_12839">Schulze has </span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;">chosen </span><span style="font-size: medium;">a </span><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13327">margins version </span><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13326">of it.</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;"><br></span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13014">The issue is pretty controversial and becomes complicated when you get into the strategic implications. </span><span id="yui_3_16_0_ym19_1_1493121154794_13328" style="font-size: medium;">Arguments that </span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;">margins just </span><span id="yui_3_16_0_ym19_1_1493121154794_13237" style="font-size: medium;">"makes more sense" than WV are common, but I find them rather abstract in </span><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_14053">comparison to what I think voters</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;">would expect from a method.</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;"><br></span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13539">As an example of the latter, suppose there is only one pairwise contest A>B in which all of the voters expressed a strict</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13537">preference. Say it was very close, 51%-49%. The margins logic is that this contest is fair game to be discarded because of</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13538">how close a race it was. But I would say that this contest is probably the one that the voters view as the most important </span><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13888">one,</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13683">everyone having voted on it, and they would not expect its loser to be elected. They (at least the 51%) will likely view this</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13682">as a spoiler situation, as whatever other candidates were in the race (to cause this outcome) did not themselves win; they</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13827">simply threw the race to the candidate who (without their presence) would have lost.</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;"><br></span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_13885">The desire to say that a 35-0 win is stronger than a 51-49 win could make sense if a strong win in itself was of some value.</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_15361">But all that realistically matters is who wins the entire race. If the 35-0 winner is not in a position to get elected, there is </span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_15362">nothing to be gained in letting that contest affect the outcome. It doesn't aid him or his supporters, it is pure noise. It could</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1493121154794_15448">as well be treated as zero strength.</span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;"><br></span></div><div id="yui_3_16_0_ym19_1_1493121154794_9825" dir="ltr"><span style="font-size: medium;">Kevin</span></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1493121154794_9824"><br><br></div><div class="yahoo_quoted" id="yui_3_16_0_ym19_1_1493121154794_9718" style="display: block;"> <div style="font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px;" id="yui_3_16_0_ym19_1_1493121154794_9717"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;" id="yui_3_16_0_ym19_1_1493121154794_9716"> <div dir="ltr" id="yui_3_16_0_ym19_1_1493121154794_9822"> <font size="2" face="Arial" id="yui_3_16_0_ym19_1_1493121154794_9821"> <hr size="1" id="yui_3_16_0_ym19_1_1493121154794_9823"> <b><span style="font-weight:bold;">De :</span></b> Kristofer Munsterhjelm <km_elmet@t-online.de><br> <b><span style="font-weight: bold;">À :</span></b> Andrew Myers <andru@cs.cornell.edu>; Election Methods <election-methods@lists.electorama.com> <br> <b><span style="font-weight: bold;">Envoyé le :</span></b> Mardi 25 avril 2017 3h08<br> <b><span style="font-weight: bold;">Objet :</span></b> Re: [EM] Ordering defeats in Minimax<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_ym19_1_1493121154794_9715"><br><div dir="ltr" id="yui_3_16_0_ym19_1_1493121154794_9714">On 04/25/2017 05:36 AM, Andrew Myers wrote:<br clear="none">> Hi all,<br clear="none">> <br clear="none">> I recently added Minimax to the algorithms supported by CIVS, because it<br clear="none">> has some nice properties, especially regarding stability of the<br clear="none">> ordering. However, there's a bit of a challenge lurking. Minimax as<br clear="none">> classically defined assumes that all ballots are totally ordered. CIVS<br clear="none">> allows ties, however. So for any pair of alternatives there is a (W, L)<br clear="none">> pair where W is the number of people who prefer the first alternative<br clear="none">> and L is the number who prefer the second.<br clear="none">> <br clear="none">> Recall that Minimax chooses the alternative whose strongest defeat is<br clear="none">> the weakest. What is the right way to define the ordering on defeats?<br clear="none">> <br clear="none">> 1. WV: (W1, L1) > (W2, L2) if W1 > W2 or (W1=W2 and L2 > L1) <br clear="none">> [currently implemented]<br clear="none">> 2. Margins: (W1, L1) > (W2, L2) if W1 - L1 > W2 - L2<br clear="none">> 3. LV: (W1, L1) > (W2, L2) if L1 < L2 or (L1 = L2 and W1 > W2)<br clear="none">> <br clear="none">> I'm sure this has been discussed already at great length. Your advice is<br clear="none">> appreciated.<br clear="none"><br clear="none">It depends on what properties you want. The most obvious difference that<br clear="none">comes to mind: Minmax(wv) passes the Plurality criterion (if I recall<br clear="none">correctly) whereas Minmax(margins) passes Mono-add-top; but wv doesn't<br clear="none">pass MAT and margins doesn't pass Plurality.<br clear="none"><br clear="none">I'm usually a wv person, but I think Minmax is more classically<br clear="none">associated with margins. Or perhaps I think that because Juho is here<br clear="none">and he prefers margins :-)<br clear="none"><br clear="none">On a side note, Minmax can produce a lot of ties if there are few voters<br clear="none">involved, so sometimes I prefer to break ties by second strongest defeat<br clear="none">(and then third strongest, fourth strongest, etc). That isn't<br clear="none">*classical* Minmax, but it shouldn't break any of Minmax's criteria.<div class="yqt3738474438" id="yqtfd17837"><br clear="none">----<br clear="none">Election-Methods mailing list - see <a shape="rect" href="http://electorama.com/em" target="_blank">http://electorama.com/em </a>for list info<br clear="none"></div></div><br><br></div> </div> </div> </div></div></body></html>