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    <div class="moz-cite-prefix">On 10/19/2016 5:17 AM, Michael Ossipoff
      wrote:<br>
      <br>
      <blockquote type="cite">
        <p dir="ltr">Specifically, how would that pushover strategy
          work? Make a sure-loser win one of the finalist-choosing
          counts, while making your candidate win the other?</p>
        <p dir="ltr">Can you give an example?</p>
      </blockquote>
      Yes, and I'll think about it.<br>
      <br>
      <blockquote type="cite">Suppose the respective finalists are
        chosen by IRV and Implicit Approval, respectively, applied to
        the first set of ballots. </blockquote>
      <br>
      Very easy for this version.  If  you are happy to see the likely
      IRV winner X win, then simply vote X top and then only rank
      candidates that you<br>
      think X can pairwise beat (taking advantage of IRV's compliance
      with Later-no-Harm).<br>
      <br>
      If things go well for you then if X doesn't win both counts then X
      will be the IRV winner and one of the "turkeys" you also approved
      will be the<br>
      Implicit Approval winner and lose in the run-off to X.<br>
      <br>
      (And of course if X doesn't make the final you have the happy
      fall-back of voting sincerely in the run-off).<br>
      <br>
      Chris Benham<br>
      <br>
    </div>
    <blockquote
cite="mid:CAOKDY5BjrWXkdg2PC83o4F2My2wZ5xdxWE2SbvtGQdxTEvHiHg@mail.gmail.com"
      type="cite">
      <p dir="ltr">Specifically, how would that pushover strategy work?
        Make a sure-loser win one of the finalist-choosing counts, while
        making your candidate win the other?</p>
      <p dir="ltr">Can you give an example?</p>
      <p dir="ltr">Surely, strategically putting the right winner in
        both initial counts--especially if both counts operate on the
        same set of ratings--sounds like a daunting task, doesn't it?</p>
      <p dir="ltr">Michael Ossipoff</p>
      <div class="gmail_quote">On Oct 17, 2016 8:36 PM, "C.Benham" <<a
          moz-do-not-send="true" href="mailto:cbenham@adam.com.au">cbenham@adam.com.au</a>>
        wrote:<br type="attribution">
        <blockquote class="gmail_quote" style="margin:0 0 0
          .8ex;border-left:1px #ccc solid;padding-left:1ex">
          <div bgcolor="#FFFFFF" text="#000000">
            <div class="m_-5787891786231176217moz-cite-prefix">This 
              "each voter has two ballots" idea certainly
              (strategically) allows the voter to be completely sincere
              on one of them,<br>
              but the cost is that the overall method becomes a festival
              of fairly easy and obvious Push-over strategising.<br>
              <br>
              Of course one way to monitor this would be to look at the 
              (strategically and so presumably) sincere ballots and
              discover<br>
              who would have won according to various methods on those
              ballots.<br>
              <br>
              (But if that was done openly it might introduce some
              incentives based on fear of embarrassment  and/or fear
              that the<br>
              method will be abolished.)<br>
              <br>
              Chris Benham<br>
              <br>
              <br>
              On 10/18/2016 11:13 AM, Michael Ossipoff wrote:<br>
            </div>
            <blockquote type="cite">
              <p dir="ltr">I think it sounds super. The best yet, with
                the best properties of the best methods, avoiding
                eachother's faults & vulnerabilities.</p>
              <p dir="ltr">More later.</p>
              <p dir="ltr">Michael Ossipoff</p>
              <div class="gmail_quote">On Oct 17, 2016 1:49 PM, "Forest
                Simmons" <<a moz-do-not-send="true"
                  href="mailto:fsimmons@pcc.edu" target="_blank">fsimmons@pcc.edu</a>>
                wrote:<br type="attribution">
                <blockquote class="gmail_quote" style="margin:0 0 0
                  .8ex;border-left:1px #ccc solid;padding-left:1ex">
                  <div dir="ltr">
                    <div>
                      <div>
                        <div>
                          <div>Kristofer,<br>
                            <br>
                            Perhaps the way out is to invite two ballots
                            from each voter. The first set of ballots is
                            used to narrow down to two alternatives.  It
                            is expected that these ballots will be voted
                            with all possible manipulative strategy ...
                            chicken defection, pushover, burial, etc.<br>
                            <br>
                          </div>
                          The second set is used only to decide between
                          the two alternatives served up by the first
                          set.<br>
                          <br>
                        </div>
                        A voter who doesn't like strategic burden need
                        not contribute to the first set, or could submit
                        the same ballot to both sets.<br>
                        <br>
                      </div>
                      <div>If both ballots were Olympic Score style,
                        with scores ranging from blank (=0) to 10, there
                        would be enough resolution for all practical
                        purposes.  Approval voters could simply specify
                        their approvals with 10 and leave the other
                        candidates' scores blank.<br>
                        <br>
                      </div>
                      <div>There should be no consistency requirement
                        between the two ballots.  They should be put in
                        separate boxes and counted separately.  Only
                        that policy can guarantee the sincerity of the
                        ballots in the second set.<br>
                        <br>
                      </div>
                      <div>In this regard it is important to realize
                        that optimal perfect information approval
                        strategy may require you to approve out of
                        order, i.e. approve X and not Y even if you
                        sincerely rate Y higher than X.  [We're talking
                        about optimal in the sense of maximizing your
                        expectation, meaning the expectation of your
                        sincere ratings ballot, (your contribution to
                        the second set).] <br>
                        <br>
                      </div>
                      <div>Nobody expects sincerity on the first set of
                        ballots.  If some of them are sincere, no harm
                        done, as long as the methods for choosing the
                        two finalists are reasonable.<br>
                        <br>
                      </div>
                      <div>On the other hand, no rational voter would
                        vote insincerely on hir contribution to the
                        second set.  The social scientist has a near
                        perfect window into the sincere preferences of
                        the voters.<br>
                        <br>
                      </div>
                      <div>Suppose the respective finalists are chosen
                        by IRV and Implicit Approval, respectively,
                        applied to the first set of ballots.  People's
                        eyes would be opened when they saw how often the
                        Approval Winner was sincerely preferred over the
                        IRV winner.<br>
                        <br>
                      </div>
                      <div>Currently my first choice of methods for
                        choosing the respective finalists would be MMPO
                        for one of them and Approval for the other, with
                        the approval cutoff at midrange (so scores of
                        six through ten represent approval).<br>
                        <br>
                      </div>
                      <div>Consider the strategical ballot set profile
                        conforming to<br>
                        <br>
                      </div>
                      <div>40  C<br>
                      </div>
                      <div>32  A>B<br>
                      </div>
                      <div>28  B<br>
                        <br>
                      </div>
                      <div>The MMPO finalist would be A, and the likely
                        Approval finalist would be B, unless too many B
                        ratings were below midrange.<br>
                        <br>
                      </div>
                      <div>If the sincere ballots were<br>
                        <br>
                      </div>
                      <div>40 C<br>
                      </div>
                      <div>32 A>B<br>
                      </div>
                      <div>28 B>A<br>
                        <br>
                      </div>
                      <div>then the runoff winner determined by the
                        second set of ballots would be A, the CWs.  The
                        chicken defection was to no avail.  Note that
                        even though this violates Plurality on the first
                        set of ballots, it does not on the sincere set.<br>
                        <br>
                      </div>
                      <div>On the other hand, if the sincere set
                        conformed to<br>
                        <br>
                      </div>
                      <div>40 C>B<br>
                      </div>
                      <div>32 A>B<br>
                      </div>
                      <div>28 B>C<br>
                        <br>
                      </div>
                      <div>then the runoff winner would be B, the CWs,
                        and the C faction attempt to win by truncation
                        of B would have no effect.  A burial of B by the
                        C faction would be no more rewarding than their
                        truncation of B.<br>
                        <br>
                      </div>
                      <div>So this idea seems to take care of the
                        tension between methods that are immune to
                        burial and methods that are immune to chicken
                        defection.<br>
                        <br>
                      </div>
                      <div>Furthermore, the plurality problem of MMPO
                        evaporates.  Even if all of the voters vote
                        approval style in either or both sets of
                        ballots, the Plurality problem will
                        automatically evaporate; on approval style
                        ballots the Approval winner pairwise beats all
                        other candidates, including the MMPO candidate
                        (if different from the approval winner).<br>
                        <br>
                      </div>
                      <div>What do you think?<br>
                        <br>
                      </div>
                      <div>Forest<br>
                      </div>
                      <div><br>
                        <br>
                      </div>
                      <div><br>
                      </div>
                      <br>
                    </div>
                    <div class="gmail_extra"><br>
                      <div class="gmail_quote">On Sun, Oct 16, 2016 at
                        1:30 AM, Kristofer Munsterhjelm <span dir="ltr"><<a
                            moz-do-not-send="true"
                            href="mailto:km_elmet@t-online.de"
                            target="_blank">km_elmet@t-online.de</a>></span>
                        wrote:<br>
                        <blockquote class="gmail_quote" style="margin:0
                          0 0 .8ex;border-left:1px #ccc
                          solid;padding-left:1ex"><span>On 10/15/2016
                            11:56 PM, Forest Simmons wrote:<br>
                            > Thanks, Kristofer; it seems to be a
                            folk theorem waiting for formalization.<br>
                            ><br>
                            > That reminds me that someone once
                            pointed out that almost all of the<br>
                            > methods favored by EM list enthusiasts
                            reduce to Approval when only top<br>
                            > and bottom votes are used, in
                            particular when Condorcet methods allow<br>
                            > equal top and multiple truncation votes
                            they fall into this category<br>
                            > because the Approval Winner is the
                            pairwise winner for approval style<br>
                            > ballots.<br>
                            ><br>
                            > Everything else (besides approval
                            strategy) that we do seems to be an<br>
                            > effort to lift the strategical burden
                            from the voter.  We would like to<br>
                            > remove that burden in all cases, but at
                            least in the zero info case.<br>
                            > Yet that simple goal is somewhat
                            elusive as well.<br>
                            <br>
                          </span>Suppose we have a proof for such a
                          theorem. Then you could have a<br>
                          gradient argument going like this:<br>
                          <br>
                          - If you're never harmed by ranking Approval
                          style, then you should do so.<br>
                          - But figuring out the correct threshold to
                          use is tough (strategic burden)<br>
                          - So you may err, which leads to a problem.
                          And even if you don't, if<br>
                          the voters feel they have to burden their
                          minds, that's a bad thing.<br>
                          <br>
                          Here, traditional game theory would probably
                          pick some kind of mixed<br>
                          strategy, where you "exaggerate"
                          (Approval-ize) only to the extent that<br>
                          you benefit even when taking your errors into
                          account. But such an<br>
                          equilibrium is unrealistic (we'd have to find
                          out why, but probably<br>
                          because it would in the worst case require
                          everybody to know about<br>
                          everybody else's level of bounded
                          rationality).<br>
                          <br>
                          And if the erring causes sufficiently bad
                          results, we're left with two<br>
                          possibilities:<br>
                          <br>
                          - Either suppose that the method is
                          sufficiently robust that most voters<br>
                          won't use Approval strategy (e.g. the pro-MJ
                          argument that Approval<br>
                          strategy only is a benefit if enough people
                          use it, so most people<br>
                          won't, so we'll have a correlated equilibrium
                          of sorts)<br>
                          <br>
                          - That any admissible method must have a "bump
                          in the road" on the way<br>
                          from a honest vote to an Approval vote, where
                          moving closer to<br>
                          Approval-style harms the voter. Then a
                          game-theoretical voter only votes<br>
                          Approval style if he can coordinate with
                          enough other voters to pass the<br>
                          bump, which again is unrealistic.<br>
                          <br>
                          But solution #2 will probably destroy quite a
                          few nice properties (like<br>
                          monotonicity + FBC; if the proof is by
                          contradiction, then we'd know<br>
                          some property combinations we'd have to
                          violate). So we can't have it all.<br>
                        </blockquote>
                      </div>
                      <br>
                    </div>
                  </div>
                </blockquote>
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              <pre>----
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