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    <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"
      cite="mid:734797744.12568595.1559135275607@mail.yahoo.com">
      <meta http-equiv="content-type" content="text/html; charset=UTF-8">
      <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 style="font-family: Helvetica Neue, Helvetica, Arial,
            Lucida Grande, sans-serif; font-size: 13px;"
            id="yui_3_16_0_ym19_1_1559134455557_8277">
            <div style="font-family: HelveticaNeue, Helvetica Neue,
              Helvetica, Arial, Lucida Grande, Sans-Serif; font-size:
              16px;" id="yui_3_16_0_ym19_1_1559134455557_8276">
              <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"
                            moz-do-not-send="true">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">
                          <br clear="none">
                        </div>
                        <div class="yiv9431740989yahoo_quoted"
                          id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4264"
                          style="display:block;">
                          <div
                            id="yiv9431740989yui_3_16_0_ym19_1_1558893123363_4263"
                            style="font-family:Helvetica Neue,
                            Helvetica, Arial, Lucida Grande,
                            sans-serif;font-size:13px;">
                            <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"
ymailto="mailto:cbenhamau@yahoo.com.au" target="_blank"
                                  href="mailto:cbenhamau@yahoo.com.au"
                                  moz-do-not-send="true"><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"
                                  ymailto="mailto:tdp201b@yahoo.co.uk"
                                  target="_blank"
                                  href="mailto:tdp201b@yahoo.co.uk"
                                  moz-do-not-send="true">"tdp201b@yahoo.co.uk"</a>
                                <a rel="nofollow" shape="rect"
                                  class="yiv9431740989moz-txt-link-rfc2396E"
                                  ymailto="mailto:tdp201b@yahoo.co.uk"
                                  target="_blank"
                                  href="mailto:tdp201b@yahoo.co.uk"
                                  moz-do-not-send="true"><tdp201b@yahoo.co.uk></a>;
                                <a rel="nofollow" shape="rect"
                                  class="yiv9431740989moz-txt-link-rfc2396E"
                                  ymailto="mailto:cbenham@adam.com.au"
                                  target="_blank"
                                  href="mailto:cbenham@adam.com.au"
                                  moz-do-not-send="true">"cbenham@adam.com.au"</a>
                                <a rel="nofollow" shape="rect"
                                  class="yiv9431740989moz-txt-link-rfc2396E"
                                  ymailto="mailto:cbenham@adam.com.au"
                                  target="_blank"
                                  href="mailto:cbenham@adam.com.au"
                                  moz-do-not-send="true"><cbenham@adam.com.au></a>;
                                <a rel="nofollow" shape="rect"
                                  class="yiv9431740989moz-txt-link-rfc2396E"
ymailto="mailto:election-methods@lists.electorama.com" target="_blank"
                                  href="mailto:election-methods@lists.electorama.com"
                                  moz-do-not-send="true">"election-methods@lists.electorama.com"</a>
                                <a rel="nofollow" shape="rect"
                                  class="yiv9431740989moz-txt-link-rfc2396E"
ymailto="mailto:election-methods@lists.electorama.com" target="_blank"
                                  href="mailto:election-methods@lists.electorama.com"
                                  moz-do-not-send="true"><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"
                                        moz-do-not-send="true">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"
ymailto="mailto:cbenham@adam.com.au" target="_blank"
                                            href="mailto:cbenham@adam.com.au"
                                            moz-do-not-send="true"><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>
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