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    <p>Jim,<br>
      <br>
      Yes.  <br>
      <br>
      Chris Benham<br>
      <br>
    </p>
    <div class="moz-cite-prefix">On 1/06/2019 9:45 pm, Faran, James
      wrote:<br>
    </div>
    <blockquote type="cite"
      cite="mid:ee6293fa-7f6a-4312-8add-fa3288a8e099@email.android.com">
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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"
          <a class="moz-txt-link-rfc2396E" href="mailto:cbenham@adam.com.au"><cbenham@adam.com.au></a> 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"
                        moz-do-not-send="true">
                        <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"
                        moz-do-not-send="true">
                        <tdp201b@yahoo.co.uk></a>; <a
                        class="moz-txt-link-rfc2396E"
                        href="mailto:cbenham@adam.com.au"
                        moz-do-not-send="true">
                        "cbenham@adam.com.au"</a> <a
                        class="moz-txt-link-rfc2396E"
                        href="mailto:cbenham@adam.com.au"
                        moz-do-not-send="true">
                        <cbenham@adam.com.au></a>; <a
                        class="moz-txt-link-rfc2396E"
                        href="mailto:election-methods@lists.electorama.com"
                        moz-do-not-send="true">
                        "election-methods@lists.electorama.com"</a> <a
                        class="moz-txt-link-rfc2396E"
                        href="mailto:election-methods@lists.electorama.com"
                        moz-do-not-send="true">
                        <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>
                        </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">
                                    <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"
                                      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"
                                      target="_blank"
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<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>
                                      </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"
                                                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>
                                            <div dir="ltr">Election-Methods
                                              mailing list - see <a
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