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    <p>46 A<br class="">
      44 B>C<br class="">
      10 C<br>
      <br>
      The positional information is on the ballots.� You can throw it
      away by refusing to look at anything but a pairwise<br>
      matrix, in this case� A>B 46-44,� B>C 44-10, C>A 54-46
      and then say "oh well, I suppose we just have to break this<br>
      cycle at its weakest link".<br>
      <br>
      A is voted in top position, which in the case of ranked ballots I
      would interpret as being ranked below no other<br>
      candidate, in this case strictly above all other candidates, on
      more ballots than B is ranked above bottom on any<br>
      ballots. <br>
      <br>
      Plus of course A pairwise beats B.�� Given that A is so obviously
      dominant over B, the contention that "B might be<br>
      an ok winner" is absurd and not serious.� What shred of sane
      common-sense explanation could you possibly give<br>
      to the post-election complaining A supporters as to why their
      candidate should have been beaten by B ??!<br>
      <br>
      <blockquote type="cite">does the "positional information" maybe
        refer to some Borda like rating information? (or maybe implicit
        ratings) </blockquote>
      <br>
      I infer some rating from rankings thus: candidates ranked above at
      least one candidate and below no candidate are<br>
      voted in the "top (or first) position", candidates not in the top
      position but also ranked above at least one other candidate<br>
      and below no candidate except those in top position are voted in
      the "second-from-the-top position" and so on<br>
      down to those candidates who are voted above no other candidate
      are in the "bottom position".<br>
      <br>
      I consider that A "positionally dominates" B if A� has more first
      position votes and more first plus second position votes<br>
      and so on down to more above bottom votes.<br>
      <br>
      <blockquote type="cite">If A wins, B and C supporters (54,
        majority) clearly think that C would have been a better choice
        (and 44 voters would prefer B).</blockquote>
      In the scenario as I described it the B voters don't really care
      about C, they were just using C to benefit from Margins' gross
      failure<br>
      of the Later-no-Help criterion.<br>
      <br>
      The A supporters have an undeniable complaint against B but not
      C.� <br>
      <br>
      The B supporters also have no reasonable complaint against C. They
      all voted (above bottom) for C and C is voted above bottom<br>
      on more ballots than B (or A) and C� has a beatpath to B.� They
      can't claim to have been stung by a failure of Later-no-Harm <br>
      because clearly if they had� truncated then A would have won.<br>
      <br>
      The C supporters have some� possible (relatively weak) complaint
      against A. But you want to elect the only candidate whose <br>
      supporters can have no remotely reasonable complaint against the
      election of either of the other candidates.<br>
      <br>
      <blockquote type="cite">It is for example possible that there is
        an election with 5 serious candidates (based on some good
        polling information) and 50 other candidates with no chances to
        win. In that situation it would not be a big problem to limit
        the number of ranked candidates to say 7</blockquote>
      If I sincerely prefer 7 minor candidates before any of the
      "serious" ones, how is this method better for me than plurality?�
      I will either<br>
      have to vote insincerely or put up with my vote having no effect
      on the result.<br>
      <br>
      If Ireland and Australia have no problem allowing voters to fully
      rank then why should the US?<br>
      <br>
      Chris Benham<br>
    </p>
    <div class="moz-cite-prefix">On 6/03/2019 4:31 am, Juho Laatu wrote:<br>
    </div>
    <blockquote type="cite"
      cite="mid:2AE3F757-D372-484B-9B12-FACA6442E9A8@gmail.com">
      <meta http-equiv="Content-Type" content="text/html;
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      <div>
        <blockquote type="cite" class="">
          <div class="">On 05 Mar 2019, at 16:04, Chris Benham <a
              href="mailto:cbenhamau@yahoo.com.au" class=""
              moz-do-not-send="true">cbenhamau@yahoo.com.au</a>
            [ApprovalVoting] <<a
              href="mailto:ApprovalVoting@yahoogroups.com" class=""
              moz-do-not-send="true">ApprovalVoting@yahoogroups.com</a>>
            wrote:</div>
        </blockquote>
        <div><br class="">
        </div>
        <blockquote type="cite" class="">
          <div class="">
            <div text="#000000" bgcolor="#FFFFFF" class="">
              <div class="moz-forward-container">
                <blockquote type="cite" class="">
                  <div class="">Also here you assume that there is an
                    implicit approval cutoff after the ranked
                    candidates. What if the votes are sincere and there
                    is no implicit approval cutoff?</div>
                  <div class=""><br class="">
                  </div>
                </blockquote>
                No, I'm only "assuming" that positional information is
                more meaningful than which candidate is "closer" to
                being the Condorcet winner<br class="">
                according to Margins or which candidate needs the fewest
                additional bullet-votes to become the CW.<br class="">
              </div>
            </div>
          </div>
        </blockquote>
        <div><br class="">
        </div>
        <div>If the added implicit information is not approval of all
          the ranked candidates, does the "positional information" maybe
          refer to some Borda like rating information? (or maybe
          implicit ratings) (I don't really like Borda ratings as
          additional information either because of the associated
          nomination related problems.)<br>
          <br>
        </div>
        <br class="">
        <blockquote type="cite" class="">
          <div class="">
            <div text="#000000" bgcolor="#FFFFFF" class="">
              <div class="moz-forward-container"> <br class="">
                Given that Margins is very vulnerable to Burial strategy
                the argument that it's worth putting up with that
                because with sincere votes B<br class="">
                in this scenario is the best (or a good or even
                acceptable) candidate is .. what??</div>
            </div>
          </div>
        </blockquote>
        <blockquote type="cite" class="">
          <div class="">
            <div text="#000000" bgcolor="#FFFFFF" class="">
              <div class="moz-forward-container"> <br class="">
                Or to put it another way, assuming the votes are
                sincere, you arguments against electing A or C are what?<br
                  class="">
              </div>
            </div>
          </div>
        </blockquote>
        <div><br class="">
        </div>
        <div>I just thought that B might be ok if we take the votes to
          be plain rankings (= pairwise preferences) with no additional
          approval or positional information assumed. The mentioned
          votes are of course very extreme (only three kind if voters),
          so they are not a typical set of votes form a real life
          election.</div>
        <div><br class="">
        </div>
        <div>46 A<br class="">
          44 B>C<br class="">
          10 C</div>
        <div><br class="">
        </div>
        <div>One could think that A is a left wing candidate, C is
          moderate right, and B is far right (because there are 44
          voters that rank them in such linear order). A voters don't
          seem to care which one of the right wing candidates wins (they
          are tied in every single vote). The B voters have a clear and
          understandable position, with full rankings. The C voters have
          not ranked B. Maybe they are so centrist that A and B are
          equally good to them.</div>
        <div><br class="">
        </div>
        <div>Condorcet methods can be said to elect a compromise
          candidate that is not too bad for anyone (sometimes the
          Condorcet winner might have no first preference votes). I
          therefore try to find an explanation to why B might win, from
          this point of view (= elect he best compromise (that is not
          very disliked)).</div>
        <div><br class="">
        </div>
        <div>Since the A voters did not rank C above B, we must assume
          that they are perfectly ok with electing B, if A does not win.
          Same with C voters. B voters have a clear preference C>A
          (if B can not win).</div>
        <div><br class="">
        </div>
        <div>If A wins, B and C supporters (54, majority) clearly think
          that C would have been a better choice (and 44 voters would
          prefer B). If C wins, 46 voters would prefer A, and 44 voters
          would prefer B. If B wins, 46 voters would prefer A, and 10
          voters would prefer C. B doesn't look too bad in this
          comparison. B might be a better compromise than A or C. I.e.
          less complaints and rebellions after the election.</div>
        <div><br class="">
        </div>
        <div>(I tried to avoid the "few votes short of being a Condorcet
          winner" argument since you might not appreciate it.)</div>
        <div><br class="">
        </div>
        <blockquote type="cite" class="">
          <div class="">
            <div text="#000000" bgcolor="#FFFFFF" class="">
              <div class="moz-forward-container"> <br class="">
                <blockquote type="cite" class="">
                  <div class="">One might face problems sooner with
                    sincere voting than with strategic voting.</div>
                  <div class=""><br class="">
                  </div>
                  <div class="">First preferences could be as follows.</div>
                  <div class=""><br class="">
                  </div>
                  <div class="">30: far-left</div>
                  <div class="">21: left</div>
                  <div class="">19: right</div>
                  <div class="">30: far-right</div>
                  <div class=""><br class="">
                  </div>
                  <div class="">If we assume that left hates right, and
                    right hates left, the natural approval limit would
                    be between the left wing and right wing parties. We
                    would get mostly votes that rank only left wing or
                    only right wing candidates. And the winner would be
                    with good probability the far-left candidate, not
                    the expected Condorcet winner (left).</div>
                </blockquote>
                <br class="">
                That doesn't bother me much because (a) far-left may be
                higher "Social Utility" than left </div>
            </div>
          </div>
        </blockquote>
        <div><br class="">
        </div>
        <div>I don't know what "Social Utility" means here. I guess any
          of the candidates could have that. It might not show up in
          rankings nor in approvals.</div>
        <br class="">
        <blockquote type="cite" class="">
          <div class="">
            <div text="#000000" bgcolor="#FFFFFF" class="">
              <div class="moz-forward-container">and (b) probably enough
                right voters would <br class="">
                be aware that the result is unlikely to be decided by
                Approval and so they would not be taking a huge risk by
                sincerely ranking left<br class="">
                over far-left.<br class="">
              </div>
            </div>
          </div>
        </blockquote>
        <div><br class="">
        </div>
        <div>I guess this depends on the method. I can't tell if all
          "ranking + implicit approval" methods would behave well in
          this respect. I also don't like very much the idea of voters
          having to cast strategic votes instead of sincere votes (i.e.
          implicit approvals in the ballots would not mean that the
          voter would approve the candidate, but something strategic
          instead).</div>
        <br class="">
        <blockquote type="cite" class="">
          <div class="">
            <div text="#000000" bgcolor="#FFFFFF" class="">
              <div class="moz-forward-container"> <br class="">
                But having said that, Smith//Approval using ballots
                that� allow voters to rank among candidates they don't
                approve would not be <br class="">
                in my book too bad (and much better than Margins).<br
                  class="">
                <br class="">
                <blockquote type="cite" class="">P.S. I think the
                  STV-BTR method that Robert proposed could make a lot
                  of sense in societies where IRV way of thinking is
                  strong.</blockquote>
                That method doesn't have good criterion compliances.
                It's just a gimmick to smuggle Condorcet compliance past
                IRV enthusiasts.<br class="">
                The alternative of just checking for a CW (among
                remaining candidates) before each elimination is much
                better.<br class="">
              </div>
            </div>
          </div>
        </blockquote>
        <div><br class="">
        </div>
        <div>I'm not a big believer in criterion compliance in real life
          election methods. In theoretical studies different criteria
          are excellent measurement tools, but in real life elections
          nobody cares if the method performs well in some theoretical
          situations. Often slightly modified (heuristic style, not
          necessarily "mathematically clean") methods are close enough
          to meeting those criteria on practice anyway. Also my
          theoretically ideal "maximally strategy resistant method"
          might be one that fails to meet most of the named criteria,
          but does so intentionally in order to violate each one (or
          many) of them just a little bit, so that it can maximise
          resistance against all kind of strategies (and keep its worst
          vulnerability least bad).</div>
        <br class="">
        <blockquote type="cite" class="">
          <div class="">
            <div text="#000000" bgcolor="#FFFFFF" class="">
              <div class="moz-forward-container"> <br class="">
                <blockquote type="cite" class="">P.P.S. Limiting the
                  number of ranking levels or number of ranked
                  candidates could make sense when the number of
                  candidates is very high, or just to keep things simple
                  for the vote counting process, or to keep things
                  simple enough for the voters (not to frighten them
                  with the idea of ranking all 100 candidates). I.e. not
                  theoretically ideal, but in practical situations
                  ranking some candidates may be much better than
                  ranking only one, or not bothering to vote at all.</blockquote>
                <br class="">
                Limiting the number of candidates the voter is allowed
                to rank makes no sense. What has happened to your
                concern<br class="">
                about "removing information" on who the sincere/
                "expected" CW is?<br class="">
              </div>
            </div>
          </div>
        </blockquote>
        <div><br class="">
        </div>
        <div>Typically the intention is not to limit the number of
          candidates that can be ranked (when compared to the situation
          before he change) but to make that number higher, while
          allowing it not to be very high. I am still worried about
          removing information, but I can accept some limitations
          sometimes (when full ranking is not feasible, or when most
          voters would not rank all candidates anyway, or when other
          solutions are not politically possible). The limits should be
          such that they probably do not lead to not electing the
          sincere Condorcet winner (or the best candidate when there is
          no Condorcet winner).</div>
        <div><br class="">
        </div>
        <div>It is for example possible that there is an election with 5
          serious candidates (based on some good polling information)
          and 50 other candidates with no chances to win. In that
          situation it would not be a big problem to limit the number of
          ranked candidates to say 7. The ballots could be simpler that
          way, and voting would not be too tedious. I would not mind
          someone starting even from 3, if that is an improvement e.g.
          to the earlier FPTP.</div>
        <br class="">
        <blockquote type="cite" class="">
          <div class="">
            <div text="#000000" bgcolor="#FFFFFF" class="">
              <div class="moz-forward-container"> <br class="">
                There would be nothing "frightening" about ranking all
                the candidates if doing so is purely optional. But
                voters who wish<br class="">
                to vote a full ranking should be allowed to. <br
                  class="">
              </div>
            </div>
          </div>
        </blockquote>
        <div><br class="">
        </div>
        <div>That is possible, and a positive thing to do, but I do
          understand that sometimes also less perfect methods can be
          "perfect" or "sufficient" for the current real life situation.</div>
        <div><br class="">
        </div>
        <div>Juho</div>
        <div><br class="">
        </div>
        <br class="">
        <blockquote type="cite" class="">
          <div class="">
            <div text="#000000" bgcolor="#FFFFFF" class="">
              <div class="moz-forward-container"> <br class="">
                Chris� Benham<br class="">
                <br class="">
                <br class="">
                <div class="moz-cite-prefix">On 5/03/2019 6:42 pm, Juho
                  Laatu wrote:<br class="">
                </div>
                <blockquote type="cite"
                  cite="mid:4716BB51-8459-4791-AB04-F93B76B8637B@gmail.com"
                  class="">
                  <meta http-equiv="Content-Type" content="text/html;
                    charset=windows-1252" class="">
                  <div class="">
                    <blockquote type="cite" class="">
                      <div class="">On 05 Mar 2019, at 07:45, Chris
                        Benham <a href="mailto:cbenhamau@yahoo.com.au"
                          class="" moz-do-not-send="true">cbenhamau@yahoo.com.au</a>
                        [ApprovalVoting] <<a
                          href="mailto:ApprovalVoting@yahoogroups.com"
                          class="" moz-do-not-send="true">ApprovalVoting@yahoogroups.com</a>>
                        wrote:</div>
                    </blockquote>
                    <div class=""><br class="">
                    </div>
                    <blockquote type="cite" class="">
                      <div class="">
                        <div text="#000000" bgcolor="#FFFFFF" class="">
                          <p class="">Robert,</p>
                        </div>
                      </div>
                    </blockquote>
                    <div class=""><br class="">
                    </div>
                    <blockquote type="cite" class="">
                      <div class="">
                        <div text="#000000" bgcolor="#FFFFFF" class=""><br
                            class="">
                          <blockquote type="cite" class="">in a ranked
                            ballot, what defines an "approved"
                            candidate?� all unranked candidates are
                            tied for last place on a ballot.� is any
                            candidate that is ranked at all "approved"?</blockquote>
                          Yes.<br class="">
                          <br class="">
                          <blockquote type="cite" class="">that would
                            change and complicate the meaning of the
                            ranked ballot.</blockquote>
                          <div class=""><br
                              class="webkit-block-placeholder">
                          </div>
                          <p class="">Arguably "change" somewhat but I
                            don't see how (overly) "complicate".
                            Allowing voters to rank among unapproved<br
                              class="">
                            candidates makes the method more vulnerable
                            to strategy and a lot more complicated.<br
                              class="">
                          </p>
                        </div>
                      </div>
                    </blockquote>
                    <div class="">One might face problems sooner with
                      sincere voting than with strategic voting.</div>
                    <div class=""><br class="">
                    </div>
                    <div class="">First preferences could be as follows.</div>
                    <div class=""><br class="">
                    </div>
                    <div class="">30: far-left</div>
                    <div class="">21: left</div>
                    <div class="">19: right</div>
                    <div class="">30: far-right</div>
                    <div class=""><br class="">
                    </div>
                    <div class="">If we assume that left hates right,
                      and right hates left, the natural approval limit
                      would be between the left wing and right wing
                      parties. We would get mostly votes that rank only
                      left wing or only right wing candidates. And the
                      winner would be with good probability the far-left
                      candidate, not the expected Condorcet winner
                      (left).</div>
                    <div class=""><br class="">
                    </div>
                    <div class="">The problem with "implicit approval
                      cutoff after the ranked candidates" is that voters
                      would be encouraged not to rank all the major
                      candidates. Not good for Condorcet. That would
                      remove some important information. In this example
                      the sincere Condorcet winner could not be
                      identified anymore.</div>
                    <div class=""><br class="">
                    </div>
                    <blockquote type="cite" class="">
                      <div class="">
                        <div text="#000000" bgcolor="#FFFFFF" class="">
                          <p class="">46 A<br class="">
                            44 B>C<br class="">
                            10 C<br class="">
                          </p>
                          <p class="">A>B 46-44
                            (margin=2)���� B>C 44-10
                            (margin=34)�� C>A 54-46 (margin=8)<br
                              class="">
                            <br class="">
                            Now Margins elects B,� rewarding the
                            outrageous Burial strategy.<br class="">
                            <br class="">
                            I can't tolerate any method that elects B in
                            this scenario. Even assuming that all the
                            votes are sincere,<br class="">
                            B is clearly the weakest candidate (the
                            least "approved" and positionally dominated
                            and pairwise-beaten<br class="">
                            by A.)<br class="">
                          </p>
                        </div>
                      </div>
                    </blockquote>
                    <div class="">Also here you assume that there is an
                      implicit approval cutoff after the ranked
                      candidates. What if the votes are sincere and
                      there is no implicit approval cutoff?</div>
                    <div class=""><br class="">
                    </div>
                    <div class="">Juho</div>
                    <div class=""><br class="">
                    </div>
                    <div class=""><br class="">
                    </div>
                    <div class="">P.S. I think the STV-BTR method that
                      Robert proposed could make a lot of sense in
                      societies where IRV way of thinking is strong.</div>
                    <div class=""><br class="">
                    </div>
                    <div class="">P.P.S. Limiting the number of ranking
                      levels or number of ranked candidates could make
                      sense when the number of candidates is very high,
                      or just to keep things simple for the vote
                      counting process, or to keep things simple enough
                      for the voters (not to frighten them with the idea
                      of ranking all 100 candidates). I.e. not
                      theoretically ideal, but in practical situations
                      ranking some candidates may be much better than
                      ranking only one, or not bothering to vote at all.</div>
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