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    <font face="Helvetica, Arial, sans-serif">A possible explanation for
      the discrepancy between my result and Darlington's is that in my
      evaluation every ballot had the same number of ties and in
      Darlington's the numbers differed.<br>
         On the face of it, WV doesn't treat voters equally. If we
      defined "winning votes" as "the number of voters who prefer A to B
      plus half the number who rank them equally", then every voter
      would contribute m(m-1)/2 winning votes and WV would be equivalent
      (I think) to Margins. But instead we define winning votes
      asymmetrically so that WV is *not* equivalent to margins but
      voters contribute different numbers of winning votes depending on
      the number of ties in their ballots. I can imagine this leading to
      artefacts which Darlington's evaluation would pick up and mine
      would miss. If this is what happened, then even Darlington's
      evaluation must be too lenient to WV since he doesn't include
      effects which would in fact arise, such as voters truncating
      differentially according to their political viewpoint. <br>
         Maybe these things have been taken into account; I have no
      idea, having never seen the thinking behind WV.<br>
            CJC<br>
    </font><br>
    <div class="moz-cite-prefix">On 21/09/2023 03:35, Forest Simmons
      wrote:<br>
    </div>
    <blockquote type="cite"
cite="mid:CANUDvfpjKFS0ndjNdHWMqYeyjhHGDwEufotEa943us6rdyjmFQ@mail.gmail.com">
      <meta http-equiv="content-type" content="text/html; charset=UTF-8">
      <div dir="auto">I think that if you were looking at the success
        rates of unilateral burial options along with the basic burial
        defense of truncation below sincere CW ... then the difference
        between Winning Votes and Margins would be more striking (still
        in favor of wv).</div>
      <br>
      <div class="gmail_quote">
        <div dir="ltr" class="gmail_attr">On Wed, Sep 20, 2023, 2:12 PM
          Michael Ossipoff <<a href="mailto:email9648742@gmail.com"
            moz-do-not-send="true">email9648742@gmail.com</a>> wrote:<br>
        </div>
        <blockquote class="gmail_quote" style="margin:0 0 0
          .8ex;border-left:1px #ccc solid;padding-left:1ex">
          <div dir="auto">Thanks for the experiment. I hope that
            Tideman’s organization won’t be promoting the old margins
            version of RP.  …unless just for maybe choosing between
            pizza-toppings or movies.</div>
          <div><br>
            <div class="gmail_quote">
              <div dir="ltr" class="gmail_attr">On Wed, Sep 20, 2023 at
                07:30 Colin Champion <<a
                  href="mailto:colin.champion@routemaster.app"
                  target="_blank" rel="noreferrer"
                  moz-do-not-send="true">colin.champion@routemaster.app</a>>
                wrote:<br>
              </div>
              <blockquote class="gmail_quote" style="margin:0 0 0
                .8ex;border-left:1px #ccc solid;padding-left:1ex">
                <div> <font face="Helvetica, Arial, sans-serif">Well, I
                    coded up Minimax(WV) for my own evaluation. Rather
                    to my disgust (and contrary to Darlington) I find
                    that it does indeed outperform Margins for truncated
                    sincere ballots. I ran a large number of trials with
                    10001 voters under a spatial model, 8 candidates
                    being truncated to 4. Minimax (margins)=83.35%
                    correct, minimax(wv)=84.09%. Other methods which
                    outperformed standard minimax in the simulation
                    include Approval Sorted Margins (in an ordinal
                    version suggested by Ted Stern): 84.14%; Black:
                    84.22%; Smith,Borda: 84.22%. <br>
                       Hastily written and unreliable code, not to be
                    trusted. <br>
                          CJC<br>
                  </font></div>
                <div><br>
                  <div>On 18/09/2023 22:30, Michael Ossipoff wrote:<br>
                  </div>
                  <blockquote type="cite">
                    <div dir="auto">Hi Colin—</div>
                    <div dir="auto"><br>
                    </div>
                    <div dir="auto">Yes, margins beats wv for
                      social-utility under sincere voting when there’s
                      that vanishingly rare natural top-cycle.</div>
                    <div dir="auto"><br>
                    </div>
                    <div dir="auto">But Darlington & Tideman
                      evidently aren’t considering resistance to
                      offensive strategy, which is a much bigger threat
                      than natural top-cycles.</div>
                    <div dir="auto"><br>
                    </div>
                    <div dir="auto">Protecting the CW from offensive
                      strategy is more important than SU in natural
                      top-cycles.</div>
                    <div dir="auto"><br>
                    </div>
                    <div dir="auto">…& is better for SU.</div>
                    <div><br>
                      <div class="gmail_quote">
                        <div dir="ltr" class="gmail_attr">On Mon, Sep
                          18, 2023 at 07:03 Colin Champion <<a
                            href="mailto:colin.champion@routemaster.app"
                            target="_blank" rel="noreferrer"
                            moz-do-not-send="true">colin.champion@routemaster.app</a>>
                          wrote:<br>
                        </div>
                        <blockquote class="gmail_quote" style="margin:0
                          0 0 .8ex;border-left:1px #ccc
                          solid;padding-left:1ex">
                          <div> <font face="Helvetica, Arial,
                              sans-serif">Thanks to Kevin and Michael
                              for pointing out a feature of minimax I
                              was unaware of. I had however seen Richard
                              Darlington's paper [1] in which he
                              referred to 'several studies' comparing
                              margins with winning votes. He reports
                              that margins 'was the big winner in all of
                              them'. I suppose I'll have to look deeper.<br>
                                 Colin<br>
                              [1]. <a
                                href="https://arxiv.org/abs/1807.01366"
                                target="_blank" rel="noreferrer"
                                moz-do-not-send="true">https://arxiv.org/abs/1807.01366</a><br>
                            </font></div>
                          <div><br>
                            <div>On 18/09/2023 07:57, Michael Ossipoff
                              wrote:<br>
                            </div>
                            <blockquote type="cite">
                              <div><br>
                              </div>
                              <div><br>
                                <div class="gmail_quote" dir="auto">
                                  <div dir="ltr" class="gmail_attr">----------
                                    Forwarded message ---------<br>
                                    From: <strong
                                      class="gmail_sendername"
                                      dir="auto">Michael Ossipoff</strong>
                                    <span dir="auto"><<a
                                        href="mailto:email9648742@gmail.com"
                                        target="_blank" rel="noreferrer"
                                        moz-do-not-send="true">email9648742@gmail.com</a>></span><br>
                                    Date: Sun, Sep 17, 2023 at 22:54<br>
                                    Subject: Re: [EM] Ranked Pairs<br>
                                    To: Forest Simmons <<a
                                      href="mailto:forest.simmons21@gmail.com"
                                      target="_blank" rel="noreferrer"
                                      moz-do-not-send="true">forest.simmons21@gmail.com</a>><br>
                                  </div>
                                  <div class="gmail_quote" dir="auto"><br>
                                  </div>
                                  This was meant to be sent by “Reply
                                  All”, in order to post it. So now I’m
                                  forwarding it to EM.<br>
                                  <br>
                                  <div dir="auto">Forest—</div>
                                  <div dir="auto"><br>
                                  </div>
                                  <div dir="auto">But wv prevents
                                    truncation (strategic or otherwise)
                                    from taking the win from a CW.</div>
                                  <div dir="auto"><br>
                                  </div>
                                  <div dir="auto">…&, with, wv,
                                    refusing to rank anymore you don’t
                                    approve will cause offensive
                                    order-reversal by their preferrers
                                    to backfire.</div>
                                  <div dir="auto"><br>
                                  </div>
                                  <div dir="auto">I’d always take that
                                    precaution, & would advise
                                    others to.</div>
                                  <div dir="auto"><br>
                                  </div>
                                  <div dir="auto">When we discussed
                                    these guarantees years ago they
                                    seemed absolute, & we still have
                                    the guarantee-criteria based on
                                    them…met by wv versions of MinMax,
                                    RP, CSSD, & Smith//MinMax.</div>
                                  <div dir="auto"><br>
                                  </div>
                                  <div dir="auto">…&, with MinMax,
                                    whose winner can come from anywhere,
                                    not just from the top-cycle, &
                                    so, offensive order-reversal, when
                                    there are a fair number of
                                    candidates, is unpredictable &
                                    risky for its perpetrators, even if
                                    the precaution of
                                    deterrent-truncation isn’t taken.</div>
                                  <div><br>
                                    <div class="gmail_quote">
                                      <div dir="ltr" class="gmail_attr">On
                                        Sun, Sep 17, 2023 at 21:17
                                        Forest Simmons <<a
                                          href="mailto:forest.simmons21@gmail.com"
                                          target="_blank"
                                          rel="noreferrer"
                                          moz-do-not-send="true">forest.simmons21@gmail.com</a>>
                                        wrote:<br>
                                      </div>
                                      <blockquote class="gmail_quote"
                                        style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">
                                        <div dir="auto">
                                          <div><br>
                                            <br>
                                            <div class="gmail_quote">
                                              <div dir="ltr"
                                                class="gmail_attr">On
                                                Sat, Sep 16, 2023, 9:42
                                                PM Michael Ossipoff <<a
href="mailto:email9648742@gmail.com" target="_blank" rel="noreferrer"
                                                  moz-do-not-send="true">email9648742@gmail.com</a>>
                                                wrote:<br>
                                              </div>
                                              <blockquote
                                                class="gmail_quote"
                                                style="margin:0px 0px
                                                0px
0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">
                                                <div dir="auto">Is that
                                                  RP(wv), or RP(margins)
                                                  ?</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">RP(wv)
                                                  would thwart &
                                                  deter offensive
                                                  strategy, an important
                                                  property in public
                                                  elections.</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">…&,
                                                  actually, it seems to
                                                  me that MinMax(wv)
                                                  would do that better.</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">That’s
                                                  because, choosing only
                                                  from the Smith Set RP,
                                                  limits it’s choice to
                                                  the strategic
                                                  top-cycle that created
                                                  by the offensive
                                                  strategists.</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">Suppose
                                                  that the CW’s
                                                  preferrers don’t do
                                                  defensive truncation
                                                  (never rank anyone you
                                                  wouldn’t approve in
                                                  Approval, or whose
                                                  preferrers you regard
                                                  as likely to
                                                  offensively
                                                  order-reverse) ?</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">Knowing
                                                  that RP will limit its
                                                  choice to their small
                                                   strategic top-cycle,
                                                  it would be easier for
                                                  the strategists to be
                                                  fairly sur that their
                                                  candidate would win in
                                                  that top-cycle.</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">But,
                                                  with MinMax, the
                                                  winner is chosen more
                                                  broadly, & could
                                                  be anywhere in the
                                                  candidate-set.
                                                   …making it more
                                                  difficult & risky
                                                  to confidently do
                                                  offensive
                                                  order/reversal.</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">RP(margins)
                                                  might the best choice
                                                  for a completely
                                                  honest electorate, but
                                                  MinMax(wv) seems
                                                  better for public
                                                  elections, due to its
                                                  better thwarting &
                                                  deterrence of
                                                  offensive strategy.</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">Yes,
                                                  MinMax doesn’t meet
                                                  the luxury cosmetic
                                                  look-good criteria
                                                  that RP meets. </div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">But for
                                                  one thing, I remind
                                                  you that natural (
                                                  sincere) top-cycles
                                                  are vanishingly-rare.</div>
                                              </blockquote>
                                            </div>
                                          </div>
                                          <div dir="auto"><br>
                                          </div>
                                          <div dir="auto">This is the
                                            same conclusión I have come
                                            around to. </div>
                                          <div dir="auto"><br>
                                          </div>
                                          <div dir="auto">And methods
                                            that break a three member
                                            top cycle at the weakest
                                            link tend to reward the
                                            burier faction.</div>
                                        </div>
                                        <div dir="auto">
                                          <div dir="auto">
                                            <div class="gmail_quote">
                                              <blockquote
                                                class="gmail_quote"
                                                style="margin:0px 0px
                                                0px
0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">So do
                                                  you want to have less
                                                  strategy-protection,
                                                  in order for the
                                                  result to maybe look
                                                  better in a
                                                  vanishingly rare
                                                  natural top/cycle?</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">…&
                                                  how bad is a violation
                                                  of Condorcet-Loser
                                                  anyway.  “Beaten by
                                                  all the other
                                                  alternatives” sounds
                                                  like some kind of
                                                  unanimity, but of
                                                  course it isn’t. It
                                                  isn’t like a
                                                  Pareto-violation. I
                                                  remind you that the
                                                  MinMax winner has
                                                  fewer voters
                                                  preferring some
                                                  particular candidate
                                                  over him than anyone
                                                  else does.</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">Clone-Criterion
                                                  violation? How bad
                                                  that really in MinMax,
                                                  especially when we’re
                                                  talking about a
                                                  vanishingly rare
                                                  natural top-cycle?</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">RP(margins)
                                                  for a completely
                                                  honest electorate.</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">MinMax(wv)
                                                  for public elections.</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">..&
                                                  about a primary to
                                                  reduce the candidates
                                                  to 5: Forget the
                                                  primary. If you think
                                                  people will have
                                                  trouble rank-ordering
                                                  lots of candidates, I
                                                  remind you that, to
                                                  vote among them in a
                                                  primary, they’d still
                                                  have to examine &
                                                  choose among the
                                                  initial many
                                                  candidates.</div>
                                                <div dir="auto"><br>
                                                </div>
                                                <div dir="auto">…harder
                                                  than ranking only the
                                                  ones you know &
                                                  regard as deserving
                                                  & definitely in
                                                  your accepts&
                                                  preferred set.</div>
                                                <div dir="auto"><br>
                                                  <div
                                                    class="gmail_quote"
                                                    dir="auto">
                                                    <div dir="ltr"
                                                      class="gmail_attr">On
                                                      Wed, Sep 13, 2023
                                                      at 00:18 Colin
                                                      Champion <<a
                                                        href="mailto:colin.champion@routemaster.app"
                                                        rel="noreferrer
                                                        noreferrer"
                                                        target="_blank"
moz-do-not-send="true">colin.champion@routemaster.app</a>> wrote:<br>
                                                    </div>
                                                    <blockquote
                                                      class="gmail_quote"
                                                      style="margin:0px
                                                      0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">I
                                                      notice that RP is
                                                      the only election
                                                      method mentioned
                                                      by name in the <br>
                                                      Virginia agenda.<br>
                                                      <br>
                                                      A while ago I ran
                                                      some simulations
                                                      on elections with
                                                      truncated ballots.
                                                      <br>
                                                      Something I
                                                      noticed was that
                                                      the presence of RP
                                                      in the list of
                                                      methods <br>
                                                      made the software
                                                      unacceptably slow.
                                                      I didn't look into
                                                      the cause, but <br>
                                                      there's a natural
                                                      explanation, which
                                                      is the fact that
                                                      RP is known to be
                                                      <br>
                                                      NP-complete when
                                                      it deals correctly
                                                      with tied margins,
                                                      i.e. by <br>
                                                      exhausting over
                                                      all their
                                                      permutations.
                                                      Presumably if some
                                                      candidates <br>
                                                      are unpopular and
                                                      ballots are
                                                      extensively
                                                      truncated, then
                                                      tied margins <br>
                                                      are much likelier
                                                      than with complete
                                                      ballots.<br>
                                                      <br>
                                                      I gather that
                                                      practical
                                                      implementations of
                                                      RP choose a random
                                                      <br>
                                                      permutation rather
                                                      than exhausting.
                                                      This seems to me
                                                      to bring a danger.
                                                      <br>
                                                      The presence of a
                                                      few vanity
                                                      candidates
                                                      (truncated off
                                                      almost all <br>
                                                      ballots) may lead
                                                      to ties, and this
                                                      may lead to a
                                                      comfortable winner
                                                      <br>
                                                      looking as though
                                                      he owes his
                                                      victory to a
                                                      coin-toss.
                                                      Obviously this <br>
                                                      undermines the
                                                      legitimacy of his
                                                      win.<br>
                                                      <br>
                                                      CJC<br>
                                                      ----<br>
                                                      Election-Methods
                                                      mailing list - see
                                                      <a
                                                        href="https://electorama.com/em"
                                                        rel="noreferrer
                                                        noreferrer
                                                        noreferrer"
                                                        target="_blank"
moz-do-not-send="true">https://electorama.com/em</a> for list info<br>
                                                    </blockquote>
                                                  </div>
                                                </div>
                                                ----<br>
                                                Election-Methods mailing
                                                list - see <a
                                                  href="https://electorama.com/em"
                                                  rel="noreferrer
                                                  noreferrer noreferrer"
                                                  target="_blank"
                                                  moz-do-not-send="true">https://electorama.com/em</a>
                                                for list info<br>
                                              </blockquote>
                                            </div>
                                          </div>
                                        </div>
                                      </blockquote>
                                    </div>
                                  </div>
                                </div>
                              </div>
                              <br>
                              <fieldset></fieldset>
                              <pre>----
Election-Methods mailing list - see <a href="https://electorama.com/em" target="_blank" rel="noreferrer" moz-do-not-send="true">https://electorama.com/em</a> for list info
</pre>
                            </blockquote>
                            <br>
                          </div>
                          ----<br>
                          Election-Methods mailing list - see <a
                            href="https://electorama.com/em"
                            rel="noreferrer noreferrer" target="_blank"
                            moz-do-not-send="true">https://electorama.com/em</a>
                          for list info<br>
                        </blockquote>
                      </div>
                    </div>
                  </blockquote>
                  <br>
                </div>
                ----<br>
                Election-Methods mailing list - see <a
                  href="https://electorama.com/em" rel="noreferrer
                  noreferrer" target="_blank" moz-do-not-send="true">https://electorama.com/em</a>
                for list info<br>
              </blockquote>
            </div>
          </div>
          ----<br>
          Election-Methods mailing list - see <a
            href="https://electorama.com/em" rel="noreferrer noreferrer"
            target="_blank" moz-do-not-send="true">https://electorama.com/em</a>
          for list info<br>
        </blockquote>
      </div>
    </blockquote>
    <br>
  </body>
</html>