<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 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 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 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>
      </div>
      <br>
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      <br>
      <pre>----
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</pre>
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</blockquote></div>