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<div dir="auto">51 A>B>C>D
<div dir="auto">49 B>C>D>A</div>
<div dir="auto"><br>
</div>
<div dir="auto">Is A a better choice than B?</div>
<div dir="auto"><br>
</div>
<div dir="auto">1. Yes. Plurality demands it. Moreover, B beats C and D on all ballots, so C and D can be ignored and the pairwise race is all that's left.</div>
<div dir="auto"><br>
</div>
<div dir="auto">2. No. A is ranked bottom on 49% of ballots, B ranked at least second on 100%, top on almost half.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Are C and D Irrelevant Alternatives?</div>
<div dir="auto"><br>
</div>
<div dir="auto">Jim Faran</div>
</div>
<div class="gmail_extra"><br>
<div class="gmail_quote">On Jun 1, 2019 5:28 AM, "C.Benham" <cbenham@adam.com.au> wrote:<br type="attribution">
</div>
</div>
<div>
<p>Toby,<br>
<br>
I didn't coin the Plurality criterion, and I do somewhat prefer your suggested alternative wording. To take account of equal-top ranking being<br>
allowed, I would specify the fractional interpretation of "number of ballots ranking A as the first preference". The original coiner of the criterion<br>
was operating on the assumption that no equal-ranking would be allowed (except at the bottom implied by truncation which would be allowed)
<br>
and perhaps also that no-one would needlessly mark a candidate strictly bottom when they could just truncate.<br>
<br>
I think in part the criterion is tailor-made for voters accustomed to and content with plurality voting, and after some new election on ballots<br>
that allow voters to rank the candidates is used, they want to know why B won while their favourite candidate A was voted (alone) in first place<br>
on more ballots than B was voted above bottom. And I like the criterion because I agree that there can't be a good enough answer.
<br>
<br>
A standard (and possible criterion) I like says that if A both positionally dominates and pairwise beats B then B can't win. That implies Plurality.<br>
</p>
<div dir="ltr">35: A<br clear="none">
</div>
<div dir="ltr">10: A=B<br clear="none">
</div>
<div dir="ltr">30: B>C<br clear="none">
</div>
25: C<br>
<p>Here no ballots vote A or B below equal-top. A has more top (or first) place votes than B so positionally dominates and pairwise beats B.<br>
Do you think B is an acceptable winner?<br>
<br>
Chris Benham<br>
</p>
<p><br>
<br>
</p>
<div class="moz-cite-prefix">On 29/05/2019 10:37 pm, Toby Pereira wrote:<br>
</div>
<blockquote type="cite">
<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_1559134455557_8273" dir="ltr"><span id="yui_3_16_0_ym19_1_1559134455557_8307">I don't have a definite answer to the question of equally ranked ballots, and to me I suppose it's still an open question exactly what the best way forwards
is, even if you make a good argument against margins.</span></div>
<div id="yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr"><span><br>
</span></div>
<div id="yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr">I don't have an example where the plurality criterion bars from winning the candidate that I think should have won. Looking at the definition on the Wikipedia: "If the number of ballots ranking A as the
first preference is greater than the number of ballots on which another candidate B is given any preference, then A's probability of winning must be no less than B's.", it's more that I would disagree with the terminology "given any preference."</div>
<div id="yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr"><br>
</div>
<div id="yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr">If the definition was "If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is ranked anything other than last or joint last (either
explicitly or through implication on a truncated ballot), then A's probability of winning must be no less than B's." then I'd be less critical of it. I think the way it's worded implies an approval cut-off even if in practice it makes no difference.</div>
<div id="yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr"><br>
</div>
<div id="yui_3_16_0_ym19_1_1559134455557_8273" dir="ltr">Toby</div>
<div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1559134455557_8274"><br>
<br>
</div>
<div class="yahoo_quoted" id="yui_3_16_0_ym19_1_1559134455557_8278" style="display:block">
<div id="yui_3_16_0_ym19_1_1559134455557_8277" style="font-family:Helvetica Neue,Helvetica,Arial,Lucida Grande,sans-serif; font-size:13px">
<div id="yui_3_16_0_ym19_1_1559134455557_8276" style="font-family:HelveticaNeue,Helvetica Neue,Helvetica,Arial,Lucida Grande,Sans-Serif; font-size:16px">
<div dir="ltr" id="yui_3_16_0_ym19_1_1559134455557_8275"><font id="yui_3_16_0_ym19_1_1559134455557_8279" size="2" face="Arial">
<hr id="yui_3_16_0_ym19_1_1559134455557_8306" size="1">
<b><span style="font-weight:bold">From:</span></b> C.Benham <a class="moz-txt-link-rfc2396E" href="mailto:cbenham@adam.com.au">
<cbenham@adam.com.au></a><br>
<b><span style="font-weight:bold">To:</span></b> Toby Pereira <a class="moz-txt-link-rfc2396E" href="mailto:tdp201b@yahoo.co.uk">
<tdp201b@yahoo.co.uk></a>; <a class="moz-txt-link-rfc2396E" href="mailto:cbenham@adam.com.au">
"cbenham@adam.com.au"</a> <a class="moz-txt-link-rfc2396E" href="mailto:cbenham@adam.com.au">
<cbenham@adam.com.au></a>; <a class="moz-txt-link-rfc2396E" href="mailto:election-methods@lists.electorama.com">
"election-methods@lists.electorama.com"</a> <a class="moz-txt-link-rfc2396E" href="mailto:election-methods@lists.electorama.com">
<election-methods@lists.electorama.com></a> <br>
<b><span style="font-weight:bold">Sent:</span></b> Sunday, 26 May 2019, 20:19<br>
<b><span style="font-weight:bold">Subject:</span></b> Re: [EM] Losing Votes (equal-ranking whole)<br>
</font></div>
<div class="y_msg_container" id="yui_3_16_0_ym19_1_1559134455557_8383"><br>
<div id="yiv9431740989">
<div id="yui_3_16_0_ym19_1_1559134455557_8385">
<div id="yui_3_16_0_ym19_1_1559134455557_8384">Toby,<br clear="none">
<br clear="none">
If you try to give that calculator a truncated ballot it will just turn it into the sort of ballot you like.<br clear="none">
<br clear="none">
How do you think equally-ranked ballots should be counted in a pairwise comparison? A half-vote to<br clear="none">
each or zero to both?<br clear="none">
<br clear="none">
So you can't actually point to any election example where the Plurality criterion bars from winning the candidate
<br clear="none">
that you think should have won?<br clear="none">
</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884457758">46: A</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884462587">44: B>C</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884480116">10: C</div>
<div>Returning to this, are you happy with B winning? And if not, why not?<br clear="none">
<br clear="none">
Chris Benham<br clear="none">
<br clear="none">
</div>
<div class="yiv9431740989yqt2928960308" id="yiv9431740989yqt29538">
<div class="yiv9431740989moz-cite-prefix">On 27/05/2019 3:38 am, Toby Pereira wrote:<br clear="none">
</div>
<blockquote type="cite"></blockquote>
</div>
</div>
<div class="yiv9431740989yqt2928960308" id="yiv9431740989yqt91070">
<div>
<div style="color:#000; background-color:#fff; font-family:Helvetica
Neue,Helvetica,Arial,Lucida Grande,sans-serif; font-size:13px">
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4290">By unranked candidates, I meant the ones that had not had any sort of "vote" - the ones not explicitly listed by the voter. If there are
three candidates in an election, A, B, and C, I might like A but absolutely hate the others. My vote might simply be:</span></div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span>A</span></div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4394">On the other hand, while I might still absolutely hate B and C, I might still hate C more. So my vote might be:</span></div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span>A>B</span></div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div dir="ltr" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237">But just because I have ranked B on my ballot, this should not be taken as any sort of endorsement of B or a vote "for" B. <span><br clear="none">
</span></div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4931">My vote could also be:</span></div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4929">A>B>C</span></div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div dir="ltr" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4502">Does adding C on the end mean that I have in some sense voted for C? I don't think there would actually be any methods where adding
C on the end would have any effect on how the winner is calculated, but the plurality criterion would presumably in theory find it acceptable to do so.</span></div>
<div dir="ltr" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span><br clear="none">
</span></div>
<div dir="ltr" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><span id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4505">But this is more a philosophical objection to the assumptions implicit in the plurality criterion than an an objection to the
results that a method obeying the criterion would produce in practice. But anyway, I put my thoughts about the plurality criterion a while ago (as did Juho) here: </span><a rel="nofollow" shape="rect" class="yiv9431740989" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4693" target="_blank" href="http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247">http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247</a></div>
<div dir="ltr" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><br clear="none">
</div>
<div dir="ltr" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237">But anyway, thank you for the link to the calculator.</div>
<div dir="ltr" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237"><br clear="none">
</div>
<div dir="ltr" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4237">Toby</div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4776"><br clear="none">
</div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4813"><br clear="none">
</div>
<div class="yiv9431740989qtdSeparateBR" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4243">
<br clear="none">
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<div class="yiv9431740989yahoo_quoted" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4264" style="display:block">
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<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4262" style="font-family:HelveticaNeue,Helvetica Neue,Helvetica,Arial,Lucida
Grande,Sans-Serif; font-size:16px">
<div dir="ltr" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4261"><font id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4289" size="2" face="Arial"></font>
<hr size="1">
<b><span style="font-weight:bold">From:</span></b> Chris Benham <a rel="nofollow" shape="rect" class="yiv9431740989moz-txt-link-rfc2396E" target="_blank" href="mailto:cbenhamau@yahoo.com.au">
<cbenhamau@yahoo.com.au></a><br clear="none">
<b><span style="font-weight:bold">To:</span></b> <a rel="nofollow" shape="rect" class="yiv9431740989moz-txt-link-rfc2396E" target="_blank" href="mailto:tdp201b@yahoo.co.uk">
"tdp201b@yahoo.co.uk"</a> <a rel="nofollow" shape="rect" class="yiv9431740989moz-txt-link-rfc2396E" target="_blank" href="mailto:tdp201b@yahoo.co.uk">
<tdp201b@yahoo.co.uk></a>; <a rel="nofollow" shape="rect" class="yiv9431740989moz-txt-link-rfc2396E" target="_blank" href="mailto:cbenham@adam.com.au">
"cbenham@adam.com.au"</a> <a rel="nofollow" shape="rect" class="yiv9431740989moz-txt-link-rfc2396E" target="_blank" href="mailto:cbenham@adam.com.au">
<cbenham@adam.com.au></a>; <a rel="nofollow" shape="rect" class="yiv9431740989moz-txt-link-rfc2396E" target="_blank" href="mailto:election-methods@lists.electorama.com">
"election-methods@lists.electorama.com"</a> <a rel="nofollow" shape="rect" class="yiv9431740989moz-txt-link-rfc2396E" target="_blank" href="mailto:election-methods@lists.electorama.com">
<election-methods@lists.electorama.com></a> <br clear="none">
<b><span style="font-weight:bold">Sent:</span></b> Sunday, 26 May 2019, 18:08<br clear="none">
<b><span style="font-weight:bold">Subject:</span></b> Re: [EM] Losing Votes (equal-ranking whole)<br clear="none">
</div>
<div class="yiv9431740989y_msg_container" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4268">
<br clear="none">
<div id="yiv9431740989">
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4267">
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4266">Toby,<br clear="none">
<br clear="none">
You would like this old online ranked-ballot voting calculator:<br clear="none">
<br clear="none">
<a rel="nofollow" shape="rect" id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4859" target="_blank" href="https://www.cse.wustl.edu/~legrand/rbvote/calc.html">https://www.cse.wustl.edu/~legrand/rbvote/calc.html</a><br clear="none">
<br clear="none">
What do you think are the "false premises" that the Plurality criterion is based on??? It was coined with the assumption<br clear="none">
that voters could only strictly rank from the top however many candidates they wish, and those not truncated had in<br clear="none">
some sense been "voted for". It says that if A has more first-place votes than B has any sort of votes then B can't win.<br clear="none">
No explicit mention of "unranked candidates".<br clear="none">
<br clear="none">
(Adapting it to ballots that allow equal-ranking at the top,?? "first preferences" refers to first-preference score on the
<br clear="none">
ballots symmetrically completed, at least at the top, ballots).<br clear="none">
</div>
<div id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4878">To sensibly claim that it is a "mistake" for an algorithm to do (or apparently "assume") something, I think you need to
<br clear="none">
point to something wrong with an actual result of it doing so.<br clear="none">
<br clear="none">
My answer to your question is no. <br clear="none">
</div>
<div>Chris Benham<br clear="none">
<br clear="none">
</div>
<div class="yiv9431740989moz-cite-prefix"><br clear="none">
On 27/05/2019 1:04 am, Toby Pereira wrote:<br clear="none">
</div>
<blockquote type="cite"></blockquote>
</div>
<div>
<div id="yiv9431740989ymail_android_signature">I think it's a mistake to assume some sort of approval of a ranked candidate. If it's not explicitly part of a method then you should not infer it. As far as I'm concerned:</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884457619"><br clear="none">
</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884457758">46: A</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884462587">44: B>C</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884480116">10: C</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884503906"><br clear="none">
</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884504072">Is the same as:</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884512155"><br clear="none">
</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884512327">46: A>B=C</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884536910">44: B>C>A</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884560941">10: C>A=B</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884616720"><br clear="none">
</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884616935">Presented with these ballots, does this change who you think the winner should be?</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884706281"><br clear="none">
</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884706524">This isn't a defence of margins by me or an argument against anything else in your post, but I think the plurality criterion, by talking about unranked candidates, is based on false premises.</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884772443"><br clear="none">
</div>
<div id="yiv9431740989yMail_cursorElementTracker_1558884772583">Toby</div>
<br clear="none">
<blockquote style="margin:0 0 20px
0">
<div style="font-family:Roboto,sans-serif; color:#6D00F6">
<div>On Sat, 25 May 2019 at 15:31, C.Benham</div>
<div><a rel="nofollow" shape="rect" class="yiv9431740989moz-txt-link-rfc2396E" target="_blank" href="mailto:cbenham@adam.com.au"><cbenham@adam.com.au></a> wrote:</div>
</div>
<div style="padding:10px 0 0
20px; margin:10px 0 0
0; border-left:1px solid
#6D00F6">
<div dir="ltr">There are several Condorcet algorithms that decide the winner by <br clear="none">
</div>
<div dir="ltr">weighing "defeat strengths" and they<br clear="none">
</div>
<div dir="ltr">are all equivalent to MinMax when there are no more than 3 candidates.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">The ones I have in mind that are equal or very nearly equal in merit are
<br clear="none">
</div>
<div dir="ltr">River, Schulze, Ranked Pairs, Smith//MinMax.<br clear="none">
</div>
<div dir="ltr">In public political elections they are very very unlikely to give <br clear="none">
</div>
<div dir="ltr">different winners. River and Smith//MinMax seem to me<br clear="none">
</div>
<div dir="ltr">to be the easiest to understand and explain and use. The other two are
<br clear="none">
</div>
<div dir="ltr">perhaps a bit more elegant and have their<br clear="none">
</div>
<div dir="ltr">enthusiastic supporters.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">This is to make the case that measuring pairwise defeat strength by the
<br clear="none">
</div>
<div dir="ltr">number of votes on the losing side with above-bottom<br clear="none">
</div>
<div dir="ltr">equal-ranking contributing a whole vote to each side (and otherwise as
<br clear="none">
</div>
<div dir="ltr">with normal Winning Votes) is much better than either<br clear="none">
</div>
<div dir="ltr">Winning Votes or Margins.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">The case for Losing Votes(erw) against Margins is that it (in common
<br clear="none">
</div>
<div dir="ltr">with WV) it meets the Plurality criterion and the Non-Drastic<br clear="none">
</div>
<div dir="ltr">Defense criterion.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">The case for Losing Votes(erw) against Winning Votes is that it meets
<br clear="none">
</div>
<div dir="ltr">the Chicken Dilemma criterion and that is much less likely<br clear="none">
</div>
<div dir="ltr">to fail to elect a positionally dominant uncovered candidate. (I don't
<br clear="none">
</div>
<div dir="ltr">see how it can fail to elect such a candidate in the 3-candidate case.)<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">For those who think that Margins might be acceptable:<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">46: A<br clear="none">
</div>
<div dir="ltr">44: B>C<br clear="none">
</div>
<div dir="ltr">10: C<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">A>B 46-44 (margin=2), B>C 44-10 (margin=34), C>A 54-46 (margin=8).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Using Losing Votes (erw) as the measure of defeat strength, the weakest
<br clear="none">
</div>
<div dir="ltr">defeat is the one with the most votes on the losing side.<br clear="none">
</div>
<div dir="ltr">That is the C>A defeat so MinMax drops that and A wins. Conversely the
<br clear="none">
</div>
<div dir="ltr">strongest defeat is the one with the fewest votes on the<br clear="none">
</div>
<div dir="ltr">losing side. That is the B>C defeat so River and Ranked Pairs lock
<br clear="none">
</div>
<div dir="ltr">that. The second strongest is the A>B defeat so those methods<br clear="none">
</div>
<div dir="ltr">also lock that. All but one candidate has been thereby disqualified so B
<br clear="none">
</div>
<div dir="ltr">wins, or we ignore the third pairwise defeat because that<br clear="none">
</div>
<div dir="ltr">makes a cycle, so give a final order A>B>C and A wins.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">To meet both of the Plurality criterion and the Chicken Dilemma <br clear="none">
</div>
<div dir="ltr">criterion A must win.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Winning Votes elects C, violating Chicken Dilemma (which it has to do to
<br clear="none">
</div>
<div dir="ltr">meet the previously fashionable Minimal Defense criterion).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Margins elects B. This fails the Plurality criterion because A has more
<br clear="none">
</div>
<div dir="ltr">exclusive first-place votes than B has any sort of above-bottom<br clear="none">
</div>
<div dir="ltr">votes. It is also an egregious and outrageous failure of Later-no-Help
<br clear="none">
</div>
<div dir="ltr">(assuming that if all the ballots just vote for one candidate we<br clear="none">
</div>
<div dir="ltr">elect the plurality winner).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">To anyone who is remotely positionally or strategically minded or has
<br clear="none">
</div>
<div dir="ltr">any common sense and isn't blind to everything except the<br clear="none">
</div>
<div dir="ltr">Margins pairwise matrix, B is clearly the weakest candidate and a <br clear="none">
</div>
<div dir="ltr">completely unacceptable winner.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">35: A<br clear="none">
</div>
<div dir="ltr">10: A=B<br clear="none">
</div>
<div dir="ltr">30: B>C<br clear="none">
</div>
<div dir="ltr">25: C<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">A>B 45-40 (erw, "normally" 35-30, margin=5), B>C 40-25 (margin=15),
<br clear="none">
</div>
<div dir="ltr">C>A 55-45 (margin=10).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Voted at least equal-top (or Top Ratings) scores: A45, B40, C25.<br clear="none">
</div>
<div dir="ltr">Voted above bottom (or Approval) scores: A45, B40, C55<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">An old Kevin Venzke example. B is neither the most top-rated candidate
<br clear="none">
</div>
<div dir="ltr">or the most approved candidate and is<br clear="none">
</div>
<div dir="ltr">pairwise-beaten and positionally dominated by A (the most top-rated).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Winning Votes and Margins both elect the clearly weakest candidate, B.<br clear="none">
</div>
<div dir="ltr">Losing Votes(erw) elects A.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">For those who prefer to have a method comply with Minimal Defense (which
<br clear="none">
</div>
<div dir="ltr">says that if on more than half the ballots<br clear="none">
</div>
<div dir="ltr">C is voted above A and A no higher than equal-bottom then A can't win)
<br clear="none">
</div>
<div dir="ltr">rather than Chicken Dilemma another method<br clear="none">
</div>
<div dir="ltr">I prefer to WV is Smith//Approval which here elects C.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">25: A>B<br clear="none">
</div>
<div dir="ltr">26: B>C<br clear="none">
</div>
<div dir="ltr">23: C>A<br clear="none">
</div>
<div dir="ltr">26: C<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">C>A 75-25 (margin=50), A>B 48-26 (margin=22), B>C 51-49 (margin=2).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Voted at least equal-top (or Top Ratings) scores: C49, B26, A25.<br clear="none">
</div>
<div dir="ltr">Voted above bottom (or Approval) scores: C75, B51, A48.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">C is an overwhelmingly positionally dominant uncovered candidate. <br clear="none">
</div>
<div dir="ltr">Margins and Losing Votes elect C.<br clear="none">
</div>
<div dir="ltr">WV and IRV elect B.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Now say we change 4 of the 26 C ballots to A>C, thereby making C a bit
<br clear="none">
</div>
<div dir="ltr">weaker.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">25: A>B<br clear="none">
</div>
<div dir="ltr">26: B>C<br clear="none">
</div>
<div dir="ltr">23: C>A<br clear="none">
</div>
<div dir="ltr">22: C<br clear="none">
</div>
<div dir="ltr">04: A>C<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">C>A 71-29 (margin=42), A>B 52-26 (margin=26), B>C 51-49 (margin=2).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Voted at least equal-top (or Top Ratings) scores: C45, B26, A29.<br clear="none">
</div>
<div dir="ltr">Voted above bottom (or Approval) scores: C75, B51, A52.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">The weakening of C has caused WV and IRV to change from B to C, now
<br clear="none">
</div>
<div dir="ltr">agreeing with LV and Margins.<br clear="none">
</div>
<div dir="ltr">Assuming the change was from sincere to insincere, those very lucky
<br clear="none">
</div>
<div dir="ltr">and/or very well informed 4 voters<br clear="none">
</div>
<div dir="ltr">have pulled off a Push-over strategy.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">This is a failure of Mono-raise-delete (more obvious if we reverse the
<br clear="none">
</div>
<div dir="ltr">order of the two situations), which<br clear="none">
</div>
<div dir="ltr">is one of Woodall's mononicity criteria that he says is incompatible
<br clear="none">
</div>
<div dir="ltr">with Condorcet.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Nonetheless in this case C is still the positionally dominant uncovered
<br clear="none">
</div>
<div dir="ltr">candidate and Losing Votes (erw)<br clear="none">
</div>
<div dir="ltr">and Margins both still elect C.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Steve Eppley's old example to illustrate (I think his) Non-Drastic
<br clear="none">
</div>
<div dir="ltr">Defense criterion, which says that if<br clear="none">
</div>
<div dir="ltr">on more than half the ballots B is voted no lower than equal-top and
<br clear="none">
</div>
<div dir="ltr">above A then A can't win.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">46: A>C (sincere may be A>B)<br clear="none">
</div>
<div dir="ltr">10: B>A<br clear="none">
</div>
<div dir="ltr">10: B>C<br clear="none">
</div>
<div dir="ltr">34: C=B (the "defenders", sincere may be C>B)<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">B>A 54-46 (m=8), A>C 56-44 (m=12), C>B (80-54 erw, "normally" 46-20, m=26).<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Voted at least equal-top (or Top Ratings) scores: B54, A46, C34.<br clear="none">
</div>
<div dir="ltr">Voted above bottom (or Approval) scores: B54, A56, C90.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">B is the only candidate top-rated on more than half the ballots. More
<br clear="none">
</div>
<div dir="ltr">than half the voters voted B<br clear="none">
</div>
<div dir="ltr">above A and B not lower than equal-top. Margins and Losing Votes <br clear="none">
</div>
<div dir="ltr">without my recommended<br clear="none">
</div>
<div dir="ltr">"above-bottom equal-ranking whole" bit elect A, violating the <br clear="none">
</div>
<div dir="ltr">Non-Drastic Defense criterion.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Losing Votes (erw) and WV elect B.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">If anyone has some counter-examples where they think that Winning Votes
<br clear="none">
</div>
<div dir="ltr">does better than<br clear="none">
</div>
<div dir="ltr">Losing Votes (erw), I'd be interested in seeing them.<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr">Chris Benham<br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<div dir="ltr"><br clear="none">
</div>
<br>
<div dir="ltr">----<br clear="none">
</div>
<div dir="ltr">Election-Methods mailing list - see <a rel="nofollow" shape="rect" target="_blank" href="https://electorama.com/em">
https://electorama.com/em </a>for list info<br clear="none">
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