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    <div class="moz-cite-prefix">And I took  " the max amount of
      upvotes" to refer to the maximum number of up-votes received by
      any candidate.<br>
      <br>
      Chris Benham<br>
      <br>
      <br>
      On 9/13/2016 10:31 PM, Jameson Quinn wrote:<br>
    </div>
    <blockquote
cite="mid:CAO82iZwt3cyGM1j-V8Yik89XueOTmGV=VKHOncrWdxi6RpPu7g@mail.gmail.com"
      type="cite">
      <div dir="ltr">Chris is correct. "by most" = "by a majority".
        Maximum is "<b><i>the</i></b> most".
        <div><br>
        </div>
        <div>Perhaps I should avoid that word, but I was trying to use
          small words, as in Randall Munroe's "Thing Explainer".</div>
      </div>
      <div class="gmail_extra"><br>
        <div class="gmail_quote">2016-09-13 6:28 GMT-04:00 C.Benham <span
            dir="ltr"><<a moz-do-not-send="true"
              href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>></span>:<br>
          <blockquote class="gmail_quote" style="margin:0 0 0
            .8ex;border-left:1px #ccc solid;padding-left:1ex">
            <div bgcolor="#FFFFFF" text="#000000">
              <div>Kevin,<br>
                <br>
                I take "downvoted by most" to mean down-voted  by most
                of the voters, meaning down-voted on more than half the
                ballots.<br>
                <br>
                Your interpretation would be "the most downvoted".<br>
                <br>
                Chris Benham
                <div>
                  <div class="h5"><br>
                    <br>
                    <br>
                    On 9/13/2016 2:56 PM, Kevin Venzke wrote:<br>
                  </div>
                </div>
              </div>
              <blockquote type="cite">
                <div>
                  <div class="h5">
                    <div
style="color:#000;background-color:#fff;font-family:HelveticaNeue,Helvetica
                      Neue,Helvetica,Arial,Lucida
                      Grande,sans-serif;font-size:12px">
                      <div><font size="+1">Hi Jameson,</font></div>
                      <div><font size="+1"><br>
                        </font></div>
                      <div><font size="+1">"Downvoted by most" means the
                          candidate with the single greatest number of
                          downvotes? This could be the (voted, unique)
                          majority favorite couldn't it?</font></div>
                      <div><font size="+1"><br>
                        </font></div>
                      <div dir="ltr"><font size="+1">How does this
                          violate "irrelevant ballots"? I must be
                          misunderstanding it. Does "max amount of
                          upvotes" mean 100% of the voters, or just the
                          greatest number of upvotes that occurs?</font></div>
                      <div><font size="+1"><br>
                        </font></div>
                      <div><font size="+1">I do like antiplurality
                          mechanisms.</font></div>
                      <div><font size="+1"><br>
                        </font></div>
                      <div><font size="+1">Kevin</font></div>
                      <div><br>
                        <br>
                      </div>
                      <div style="display:block">
                        <div style="font-family:HelveticaNeue,Helvetica
                          Neue,Helvetica,Arial,Lucida
                          Grande,sans-serif;font-size:12px">
                          <div
                            style="font-family:HelveticaNeue,Helvetica
                            Neue,Helvetica,Arial,Lucida
                            Grande,sans-serif;font-size:16px">
                            <div dir="ltr"> <font face="Arial" size="2">
                                <hr size="1"> <b><span
                                    style="font-weight:bold">De :</span></b>
                                Jameson Quinn <a moz-do-not-send="true"
                                  href="mailto:jameson.quinn@gmail.com"
                                  target="_blank"><jameson.quinn@gmail.com></a><br>
                                <b><span style="font-weight:bold">À :</span></b>
                                Kevin Venzke <a moz-do-not-send="true"
                                  href="mailto:stepjak@yahoo.fr"
                                  target="_blank"><stepjak@yahoo.fr></a>;
                                electionsciencefoundation <a
                                  moz-do-not-send="true"
                                  href="mailto:electionscience@googlegroups.com"
                                  target="_blank"><electionscience@googlegroups.<wbr>com></a>
                                <br>
                                <b><span style="font-weight:bold">Cc :</span></b>
                                EM <a moz-do-not-send="true"
                                  href="mailto:election-methods@lists.electorama.com"
                                  target="_blank"><election-methods@lists.<wbr>electorama.com></a><br>
                                <b><span style="font-weight:bold">Envoyé
                                    le :</span></b> Lundi 12 septembre
                                2016 20h37<br>
                                <b><span style="font-weight:bold">Objet :</span></b>
                                Re: [EM] Fwd: Fwd: U/P voting: new name
                                for simple 3-level method.<br>
                              </font> </div>
                            <div><br>
                              <div>
                                <div>
                                  <div dir="ltr">Here's a new proposed
                                    variant of U/P with a simple
                                    default:
                                    <div><br clear="none">
                                    </div>
                                    <div>Voters may rate each candidate
                                      as "unacceptable" (downvote),
                                      "preferred" (upvote), or
                                      "acceptable" (neither). Default is
                                      neither.</div>
                                    <div><br clear="none">
                                    </div>
                                    <div>Any candidate downvoted by
                                      most, or with fewer than half the
                                      max amount of upvotes, is
                                      disqualified, unless that would
                                      disqualify everyone. The winner is
                                      the remaining candidate with the
                                      most upvotes.</div>
                                    <div><br clear="none">
                                    </div>
                                    <div>The "fewer than half the max"
                                      rule prevents dark-horse winners,
                                      without resorting to strange
                                      defaults. It has no effect on a
                                      two-way chicken dilemma. Though in
                                      theory it could affect an
                                      evenly-balanced three-way chicken
                                      dilemma (in a four-way race), I
                                      think there's a negligible chance
                                      that such a scenario would be so
                                      balanced.</div>
                                    <div><br clear="none">
                                    </div>
                                    <div>I know that Chris doesn't like
                                      this method's violation of
                                      "irrelevant ballots". Myself, I
                                      think that no voters are
                                      irrelevant; even if they don't
                                      express an opinion between the two
                                      frontrunners, they may have one.
                                      (True, they may not; but that's
                                      not the first assumption I'd
                                      make.)</div>
                                  </div>
                                  <div><br clear="none">
                                    <div>2016-09-12 20:22 GMT-04:00
                                      Kevin Venzke <span dir="ltr"><<a
                                          moz-do-not-send="true"
                                          rel="nofollow" shape="rect"
                                          href="mailto:stepjak@yahoo.fr"
                                          target="_blank">stepjak@yahoo.fr</a>></span>:<br
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                                      <div>
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                                          <div>
                                            <div
style="color:#000;background-color:#fff;font-family:HelveticaNeue,Helvetica
Neue,Helvetica,Arial,Lucida Grande,sans-serif;font-size:12px">
                                              <div>
                                                <div>
                                                  <div
style="color:#000;background-color:#fff;font-family:HelveticaNeue,Helvetica
Neue,Helvetica,Arial,Lucida Grande,sans-serif;font-size:12px">
                                                    <div><span>Hi
                                                        Jameson,</span></div>
                                                    <div><span><br
                                                          clear="none">
                                                      </span></div>
                                                    <div dir="ltr"><span>I
                                                        think it is a
                                                        positive thing
                                                        that the MTA B/C
                                                        majority
                                                        coalition can
                                                        give their
                                                        sincere
                                                        preferences (!),
                                                        while using the
                                                        strategy they're
                                                        expected to use
                                                        (i.e. middle
                                                        slot as
                                                        tiebreaker given
                                                        multiple
                                                        majorities),
                                                        without risk of
                                                        this strategy
                                                        backfiring.
                                                        (Voters can
                                                        accidentally
                                                        elect the less
                                                        preferred of B
                                                        or C, but that
                                                        is the
                                                        inescapable
                                                        chicken dilemma,
                                                        I would say.)</span></div>
                                                    <div dir="ltr"><span><br
                                                          clear="none">
                                                      </span></div>
                                                    <div dir="ltr"><span>I
                                                        have some
                                                        sympathy for
                                                        your claim that
                                                        C should not be
                                                        able to win with
                                                        few top ratings.
                                                        But that
                                                        sympathy is not
                                                        tied to Borda
                                                        counts, it is
                                                        based on wanting
                                                        to reduce the
                                                        truncation
                                                        incentive for
                                                        the B voters.
                                                        This, U/P does
                                                        not really do,
                                                        because the
                                                        B>C voters
                                                        would be taking
                                                        a large risk
                                                        that they are
                                                        helping to put C
                                                        (alone) over the
                                                        threshold of
                                                        majority
                                                        approval.</span></div>
                                                    <div dir="ltr"><span><br
                                                          clear="none">
                                                      </span></div>
                                                    <div dir="ltr"><span>So
                                                        I don't think
                                                        either of these
                                                        ballot sets is
                                                        likely under
                                                        U/P, and it
                                                        sounds like you
                                                        agree with that
                                                        and think it is
                                                        good (because it
                                                        deters a
                                                        pathological
                                                        ballot set)? Do
                                                        you have a
                                                        stance (or at
                                                        least, see use
                                                        in determining a
                                                        stance) on how
                                                        U/P voters in
                                                        these scenarios
                                                        should be
                                                        voting?</span></div>
                                                    <div dir="ltr"><span><br
                                                          clear="none">
                                                      </span></div>
                                                    <div dir="ltr"><span>Kevin</span></div>
                                                    <div><br
                                                        clear="none">
                                                      <br clear="none">
                                                    </div>
                                                  </div>
                                                </div>
                                              </div>
                                              <div>
                                                <div
                                                  style="font-family:HelveticaNeue,Helvetica
Neue,Helvetica,Arial,Lucida Grande,sans-serif;font-size:12px">
                                                  <div
                                                    style="font-family:HelveticaNeue,Helvetica
Neue,Helvetica,Arial,Lucida Grande,sans-serif;font-size:16px">
                                                    <div dir="ltr"><span>
                                                        <font
                                                          face="Arial"
                                                          size="2"> </font></span>
                                                      <hr size="1"> <b><span
style="font-weight:bold">De :</span></b> Jameson Quinn <<a
                                                        moz-do-not-send="true"
                                                        rel="nofollow"
                                                        shape="rect"
                                                        href="mailto:jameson.quinn@gmail.com"
                                                        target="_blank">jameson.quinn@gmail.com</a>><br
                                                        clear="none">
                                                      <b><span
                                                          style="font-weight:bold">À :</span></b>
                                                      EM <<a
                                                        moz-do-not-send="true"
                                                        rel="nofollow"
                                                        shape="rect"
                                                        href="mailto:election-methods@lists.electorama.com"
                                                        target="_blank">election-methods@lists.
                                                        electorama.com</a>>
                                                      <br clear="none">
                                                      <b><span
                                                          style="font-weight:bold">Envoyé
                                                          le :</span></b>
                                                      Dimanche 11
                                                      septembre 2016
                                                      1h51<br
                                                        clear="none">
                                                      <b><span
                                                          style="font-weight:bold">Objet :</span></b>
                                                      [EM] Fwd: Fwd: U/P
                                                      voting: new name
                                                      for simple 3-level
                                                      method.<br
                                                        clear="none">
                                                    </div>
                                                    <div>
                                                      <div>
                                                        <div><br
                                                          clear="none">
                                                          <div><br
                                                          clear="none">
                                                          <br
                                                          clear="none">
                                                          </div>
                                                          <div>
                                                          <div>
                                                          <div dir="ltr">
                                                          <div>
                                                          <div dir="ltr">
                                                          <div>
                                                          <div><span>2016-09-10
                                                          21:26
                                                          GMT-04:00
                                                          C.Benham <span
                                                          dir="ltr"><<a
moz-do-not-send="true" rel="nofollow" shape="rect"
                                                          href="mailto:cbenham@adam.com.au"
target="_blank">cbenham@adam.com.au</a>></span>:<br clear="none">
                                                          </span>
                                                          <blockquote
                                                          style="margin:0px
                                                          0px 0px
                                                          0.8ex;border-left:1px
                                                          solid
                                                          rgb(204,204,204);padding-left:1ex"><span>On
                                                          9/11/2016 5:02
                                                          AM, Kevin
                                                          Venzke wrote:<br
                                                          clear="none">
                                                          <br
                                                          clear="none">
                                                          </span>
                                                          <blockquote
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                                                          43: A<br
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                                                          24: B>C<br
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                                                          23: C>B<br
                                                          clear="none">
                                                          10: D<br
                                                          clear="none">
                                                          <br
                                                          clear="none">
                                                          Under MTA the
                                                          B and C voters
                                                          are being
                                                          completely
                                                          reasonable:
                                                          They hope for
                                                          majority
                                                          approval but
                                                          can still hope
                                                          for a win if
                                                          they<br
                                                          clear="none">
                                                          don't get it.<br
                                                          clear="none">
                                                          <br
                                                          clear="none">
                                                          Strategy is
                                                          less likely to
                                                          produce these
                                                          ballots under
                                                          U/P because
                                                          the B and C
                                                          voters are
                                                          taking a
                                                          gamble. To get
                                                          a similar
                                                          outcome<br
                                                          clear="none">
                                                          they have to
                                                          vote B=C.
                                                          Anyone who
                                                          doesn't is
                                                          functionally
                                                          defecting!<br
                                                          clear="none">
                                                          </blockquote>
                                                          <br
                                                          clear="none">
                                                           C: A very
                                                          good example! 
                                                           Assuming MTA
                                                          and MCA use
                                                          Top Ratings
                                                          scores to
                                                          break Approval
                                                          ties, they
                                                          both elect the
                                                          Condorcet
                                                          winner B.<br
                                                          clear="none">
                                                          </blockquote>
                                                          <div><br
                                                          clear="none">
                                                          </div>
                                                          <div>But both
                                                          could be
                                                          shifted to C
                                                          with a single
                                                          C-only ballot,
                                                          even if the
                                                          B:C ratio were
                                                          46:1 instead
                                                          of 24:23.</div>
                                                          <span></span>
                                                          <div> </div>
                                                          <blockquote
                                                          style="margin:0px
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                                                          <br
                                                          clear="none">
                                                          U/P's
                                                          under-use of 
                                                          the middle
                                                          ratings slot
                                                          means that it
                                                          relies more on
                                                          its "majority
disqualification" mechanism which seems to make it more<br clear="none">
                                                          vulnerable to
                                                          irrelevant
                                                          ballots, as in
                                                          the example.<br
                                                          clear="none">
                                                          <br
                                                          clear="none">
                                                          Under U/P,
                                                          without the
                                                          irrelevant D
                                                          ballots, A and
                                                          D are
                                                          disqualified
                                                          and B is the
                                                          glorious
                                                          winner. With
                                                          them, B and C
                                                          and D are
                                                          disqualified
                                                          and  (without
                                                          needing<br
                                                          clear="none">
                                                          any others to
                                                          be
                                                          disqualified)
                                                          A wins.<br
                                                          clear="none">
                                                          <br
                                                          clear="none">
                                                          This causes me
                                                          to reject U/P
                                                          as clearly
                                                          worse than MTA
                                                          and MCA. Of
                                                          the three I
                                                          (again) rate
                                                          MTA as the
                                                          least bad.<br
                                                          clear="none">
                                                          </blockquote>
                                                          <div><br
                                                          clear="none">
                                                          </div>
                                                          <div>I think
                                                          MTA is pretty
                                                          darn good. I
                                                          still prefer
                                                          U/P.</div>
                                                          <div><br
                                                          clear="none">
                                                          </div>
                                                          <div>I think
                                                          that scenarios
                                                          like the above
                                                          are
                                                          fundamentally
                                                          pathological;
                                                          any possible
                                                          winner has
                                                          only minority
                                                          approval, so
                                                          that even
                                                          assuming all
                                                          ballots are
                                                          semi-honest,
                                                          any of them
                                                          could be a
                                                          true Condorcet
                                                          loser. Thus, I
                                                          believe that
                                                          it's more
                                                          important for
                                                          a system to
                                                          try to avoid
                                                          scenarios like
                                                          the above,
                                                          than to try to
                                                          find a perfect
                                                          winner in such
                                                          a scenario. In
                                                          fact, in the
                                                          related
                                                          scenario:</div>
                                                          <div><br
                                                          clear="none">
                                                          </div>
                                                          <div><br
                                                          clear="none">
                                                          43: A<br
                                                          clear="none">
                                                          40: B>C</div>
                                                          <div>6: C>B<br
                                                          clear="none">
                                                          1: C<br
                                                          clear="none">
                                                          10: D<br
                                                          clear="none">
                                                          </div>
                                                          <div><br
                                                          clear="none">
                                                          </div>
                                                          <div>... I
                                                          think that a
                                                          case can be
                                                          made for
                                                          either A or B.
                                                          After all,
                                                          they'd be tied
                                                          if we try to
                                                          approximate
                                                          Score by using
                                                          truncatable
                                                          Borda here.
                                                          But no serious
                                                          case can be
                                                          made for C or
                                                          D, even though
                                                          C wins MTA and
                                                          MCA.</div>
                                                          <div><br
                                                          clear="none">
                                                          </div>
                                                          <div>Anyway, I
                                                          think U/P does
                                                          a better job
                                                          trying to
                                                          discourage the
                                                          kind of
                                                          strategy that
                                                          would lead to
                                                          a scenario
                                                          like the
                                                          above. And
                                                          part of that
                                                          is the default
                                                          rule which
                                                          Chris has
                                                          criticized.</div>
                                                          <div><br
                                                          clear="none">
                                                          </div>
                                                          <div>One
                                                          possible
                                                          alternative
                                                          default rule:
                                                          ballots
                                                          alternate
                                                          between
                                                          defaulting to
                                                          "acceptable"
                                                          and to
                                                          "unacceptable".
                                                          Each ballot
                                                          clearly states
                                                          which default
                                                          it uses, and
                                                          there is a
                                                          place on the
                                                          ballot to
                                                          globally
                                                          change that
                                                          default. (I
                                                          doubt Chris
                                                          will like this
                                                          idea, but it
                                                          is at least
                                                          straightforward,
                                                          explicit, and
                                                          easy to
                                                          describe.)</div>
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                                                          </div>
                                                          <blockquote
                                                          style="margin:0px
                                                          0px 0px
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                                                          solid
                                                          rgb(204,204,204);padding-left:1ex">
                                                          <br
                                                          clear="none">
                                                          Chris Benham<br
                                                          clear="none">
                                                          <br
                                                          clear="none">
                                                          <br
                                                          clear="none">
                                                          </blockquote>
                                                          </div>
                                                          <br
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                                                          </div>
                                                          </div>
                                                          </div>
                                                          <br
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                                                          </div>
                                                          </div>
                                                          </div>
                                                          <br
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                                                        </div>
                                                      </div>
                                                      <span>----<br
                                                          clear="none">
                                                        Election-Methods
                                                        mailing list -
                                                        see <a
                                                          moz-do-not-send="true"
                                                          rel="nofollow"
                                                          shape="rect"
                                                          href="http://electorama.com/em"
target="_blank">http://electorama.com/em </a>for list info<br
                                                          clear="none">
                                                        <br clear="none">
                                                        <br clear="none">
                                                      </span></div>
                                                  </div>
                                                </div>
                                              </div>
                                            </div>
                                          </div>
                                        </blockquote>
                                      </div>
                                    </div>
                                    <br clear="none">
                                  </div>
                                </div>
                              </div>
                              <br>
                              <div>----<br clear="none">
                                Election-Methods mailing list - see <a
                                  moz-do-not-send="true" shape="rect"
                                  href="http://electorama.com/em"
                                  target="_blank">http://electorama.com/em
                                </a>for list info<br clear="none">
                              </div>
                              <br>
                              <br>
                            </div>
                          </div>
                        </div>
                      </div>
                    </div>
                    <br>
                    <fieldset></fieldset>
                    <br>
                    <pre>----
Election-Methods mailing list - see <a moz-do-not-send="true" href="http://electorama.com/em" target="_blank">http://electorama.com/em</a> for list info
</pre>
                    <br>
                    <fieldset></fieldset>
                    <br>
                  </div>
                </div>
                <p color="#000000" align="left"><span class="">No virus
                    found in this message.<br>
                    Checked by AVG - <a moz-do-not-send="true"
                      href="http://www.avg.com" target="_blank">www.avg.com</a><br>
                  </span> Version: 2016.0.7797 / Virus Database:
                  4649/13003 - Release Date: 09/12/16</p>
              </blockquote>
              <p><br>
              </p>
            </div>
            <br>
            ----<br>
            Election-Methods mailing list - see <a
              moz-do-not-send="true" href="http://electorama.com/em"
              rel="noreferrer" target="_blank">http://electorama.com/em</a>
            for list info<br>
            <br>
          </blockquote>
        </div>
        <br>
      </div>
      <p class="" avgcert""="" color="#000000" align="left">No virus
        found in this message.<br>
        Checked by AVG - <a moz-do-not-send="true"
          href="http://www.avg.com">www.avg.com</a><br>
        Version: 2016.0.7797 / Virus Database: 4649/13008 - Release
        Date: 09/13/16</p>
    </blockquote>
    <p><br>
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