<div dir="ltr"><div>Chris,<br><br></div><div>good example showing the incompatibility of CD with Semi-Sincerity!<br><br></div><div>It may be that some weaker (but adequate) version of CD is compatible with Semi-sincerity.<br>
<br></div><div>Forest<br></div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Sun, May 18, 2014 at 9:20 AM, C.Benham <span dir="ltr"><<a href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
  
    
  
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      <blockquote type="cite">"The 2nd one, as you said, seems
        closely-related to FBC. Having just now read of it, I don't now
        know how it differs.You say it's somewhat weaker. Then it could
        be useful for comparing methods that don't meet the more
        demanding FBC."</blockquote>
      <br></div>
      Mike,<br>
      <br>
      I don't see how they are similar.<br>
      <br>
      49 C<br>
      27 A>B<br>
      24 B<div class=""><br>
      <br>
      <br>
      <blockquote type="cite">"A method satisfies the Semi-Sincere
        Criterion if and only if each sincere ballot set can be modified
        without any order reversals into a strategic equilibrium ballot
        set that preserves the sincere winner."<br>
      </blockquote>
      <br></div>
      If  Forest's criterion's "sincere ballot sets" allow truncation,
      then it seems to me that it isn't compatible with both of
      Plurality and Chicken Dilemma.  A method meeting Plurality and CD<br>
      must elect C in the above "sincere ballot set", but (assuming the
      method meets Majority Favourite) it doesn't seem to be in
      "strategic equilibrium"  (because there is no "deterrent" to the <br>
      A>B  voters electing B by voting B>A or B).<br>
      <br>
      Or I could be wrong.<br>
      <br>
      49 C<br>
      27 A>B<br>
      24 B=C<br>
      <br>
      Is this a "strategic equilibrium ballot set" for a method that
      meets all of Condorcet, Plurality and CD?   It seems odd to see
      some virtue in a faction being able to rescue the sincere<br>
      method winner... at the expense of its favourite!<br>
      <br>
      <br>
      Chris<div><div class="h5"><br>
      <br>
      <br>
      On 5/16/2014 12:42 AM, Michael Ossipoff wrote:<br>
    </div></div></div><div><div class="h5">
    <blockquote type="cite">
      <div dir="ltr">
        <div class="gmail_extra">Interesting two criteria. For the first
          one, would the magnitude of a change be measured by the total
          number of half-reversals of candidate-order (the matter of
          which is voted over which), where a half-reversal is a move
          from voting X over Y, to voting nether over the other?</div>
        <div class="gmail_extra"> </div>
        <div class="gmail_extra">The 2nd one, as you said, seems
          closely-related to FBC. Having just now read of it, I don't
          now know how it differs.You say it's somewhat weaker. Then it
          could be useful for comparing methods that don't meet the more
          demanding FBC. </div>
        <div class="gmail_extra"> </div>
        <div class="gmail_extra">Do you know how MAM, Benham, Woodall,
          MMLV(erw)M and your sequence based on covering and approval
          do,  by those two new criteria?</div>
        <div class="gmail_extra"> </div>
        <div class="gmail_extra">Michael Ossipoff<br>
          <br>
        </div>
        <div class="gmail_quote">On Wed, May 14, 2014 at 8:11 PM, Forest
          Simmons <span dir="ltr"><<a href="mailto:fsimmons@pcc.edu" target="_blank">fsimmons@pcc.edu</a>></span>
          wrote:<br>
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                                                          <div>Every
                                                          reasonable
                                                          method that
                                                          takes ranked
                                                          ballots has
                                                          the following
                                                          problem: not
                                                          every sincere
                                                          ballot set
                                                          represents a
                                                          strategic
                                                          equilibrium.<br>
                                                          <br>
                                                          </div>
                                                          In other
                                                          words, no
                                                          matter the
                                                          method there
                                                          is some
                                                          scenario where
                                                          a loser can
                                                          change to
                                                          winner through
                                                          unilateral
                                                          insincere
                                                          voting.<br>
                                                          <br>
                                                          </div>
                                                          For example,
                                                          consider the
                                                          following two
                                                          sincere
                                                          scenarios:<br>
                                                          <br>
                                                        </div>
                                                        34 A>B<br>
                                                      </div>
                                                      31 B>A<br>
                                                    </div>
                                                    35 C<br>
                                                    <br>
                                                  </div>
                                                  and <br>
                                                  <br>
                                                </div>
                                                34 X>Y<br>
                                              </div>
                                              31 Y<br>
                                            </div>
                                            35 Z>Y<br>
                                            <br>
                                          </div>
                                          All of the methods that we
                                          currently consider reasonable
                                          (except perhaps IRV) , make A
                                          win in the ABC scenario, and
                                          make Y win in the XYZ,
                                          scenario.<br>
                                          <br>
                                        </div>
                                        Now suppose that the B
                                        supporters unilaterally truncate
                                        A in the first scenario, and the
                                        Z supporters unilaterally
                                        truncate Y in the second
                                        scenario.  The resulting
                                        insincere ballot sets are<br>
                                        <br>
                                        34 A>B<br>
                                        31 B<br>
                                        35 C<br>
                                        <br>
                                      </div>
                                      and<br>
                                      <br>
                                      34 X>Y<br>
                                      31 Y<br>
                                      35 Z .<br>
                                      <br>
                                    </div>
                                    By neutrality, if our method must
                                    pick corresponding winners in the
                                    two scenarios, i.e. either A and X,
                                    or B and Y, or C and Z.<br>
                                    <br>
                                  </div>
                                  But plurality rules out A and X, while
                                  the chicken dilemma criterion  rules
                                  out B and Y.  Therefore our method
                                  must pick C and Z.<br>
                                  <br>
                                </div>
                                That's fine for the first scenario; it
                                means that sincere votes in that
                                scenario could well be a strategic
                                equilibrium.  But making z the winner in
                                the second scenario means that sincere
                                ballots were not a strategic equilibrium
                                position.  The unilateral defection of
                                the Z faction was rewarded by the
                                election of Z.<br>
                                <br>
                              </div>
                              The purpose of this example is to
                              illustrate why sincere votes cannot always
                              be a strategic equilibrium position.<br>
                              <br>
                            </div>
                            Sometimes a faction can take advantage of
                            this problem by making a move (away from
                            sincere ballots) that (if not countered)
                            would improve the outcome from their point
                            of view.  Let's call such a move an
                            offensive move.  Any move by another faction
                            that would make an offensive move
                            unrewarding can be called a defensive move.<br>
                            <br>
                          </div>
                          Now here's the criterion:<br>
                          <br>
                        </div>
                        A method satisfies the Economical Defense
                        Criterion (EDC) if and only if every potential
                        unilateral offensive move away from sincere
                        ballots can be deterred by a smaller unilateral
                        defensive move.<br>
                        <br>
                      </div>
                      How should we measure the size of a move?<br>
                      <br>
                    </div>
                    It should be by the total number of order changes
                    over all changed ballots.  An order reversal of the
                    type X>Y to Y>X should count significantly
                    more than a collapse of the type X>Y to X=Y or
                    the reverse process from X=Y to X>Y.<br>
                    <br>
                  </div>
                  Here's another criterion:<br>
                  <br>
                </div>
                A method satisfies the Semi-Sincere Criterion if and
                only if each sincere ballot set can be modified without
                any order reversals into a strategic equilibrium ballot
                set that preserves the sincere winner.<br>
                <br>
              </div>
              This SSC criterion is similar to the FBC, but easier to
              satisfy.  I think it is just as good as the FBC for
              practical purposes, since rational voters will always aim
              at strategic equilibria.<br>
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                                                  <div>Gotta Go!<span><font color="#888888"><br>
                                                        <br>
                                                      </font></span></div>
                                                  <span><font color="#888888">
                                                      <div>
                                                        Forest<br>
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            <br>
            ----<br>
            Election-Methods mailing list - see <a href="http://electorama.com/em" target="_blank">http://electorama.com/em</a> for list info<br>
            <br>
          </blockquote>
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      <fieldset></fieldset>
      <br>
      <pre>----
Election-Methods mailing list - see <a href="http://electorama.com/em" target="_blank">http://electorama.com/em</a> for list info
</pre>
    </blockquote>
    <br>
  </div></div></div>

</blockquote></div><br></div>