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    <div class="moz-cite-prefix">Forest,<br>
      <br>
      Just because you can contrive some  example  where method X
      appears to resist Burial strategy better than method Y<br>
      is no (or a very very weak) reason to suppose that one couldn't
      just as easily contrive a converse example (i.e. where method<br>
      Y resists Burial strategy better than method X.)<br>
      <br>
      This is especially the case without some sensible
      burial-resistance criterion that you can show is met by X or not
      Y, or failing that<br>
      perhaps some computer simulation that shows that method Y rewards
      Burial strategists significantly more often than method X.<br>
      <br>
      Also, while you are comparing TACC with  Benham/Woodall and IRV I
      think should also be benchmarking it against the other two<br>
      methods that combine pairwise and approval information, 
      Smith//Approval (almost the same thing as another method you
      promoted<br>
      as "Majority Enhanced Approval", where you descend a chain
      starting with the most approved candidate, only adding candidates
      that<br>
      covers all the already added candidates and then elect the last
      added candidate) and Schulze Approval Margins (the same thing, at
      least<br>
      with 3 candidates, as Approval Margins Sort).<br>
      <br>
      Those other methods also deny the buriers in your example, without
      electing a candidate X that is both pairwise-beaten and
      positionally<br>
      dominated by some candidate Y.  (Of course Smith//Approval  fails
      Chicken Dilemma, so we can leave that aside if you like.)<br>
      <br>
      An example that highlights TACC problems:<br>
      <br>
      25 A>B  (sincere may be A or A>C)<br>
      06 A>C<br>
      32 B>C<br>
      27 C>A<br>
      10 C<br>
      <br>
      C>A>B>C,  Approvals C75 > A58 > B57  (Top Ratings 
      C37 > B32 > A31)<br>
      <br>
      TACC  rewards the A>B maybe buriers by electing A, even though
      C positionally dominates and pairwise beats A.   AM/AMS very
      comfortably elects C.<br>
      <br>
      If say, 2 of the 10 C voters change to B ( a Push-over strategy)
      then the TACC winner changes from A to C.<br>
      <br>
      Chris Benham<br>
      <br>
      <br>
      <br>
      On 4/24/2014 5:17 AM, Forest Simmons wrote:<br>
    </div>
    <blockquote
cite="mid:CAP29onfrt4CRFm59reLT57Osp_LLYDgbT5RohAakzxFVGuD1+Q@mail.gmail.com"
      type="cite">
      <div>Chris,</div>
      <div> </div>
      <div>What you say below makes perfect sense in a zero information
        election.</div>
      <div> </div>
      <div>Now suppose the actual ballot set is </div>
      <div> </div>
      <div>35 A>C</div>
      <div>40 B>C</div>
      <div>25 C>A</div>
      <div> </div>
      <div>Then IRV elects A while Woodall/Benham and TACC elect C.</div>
      <div> </div>
      <div>Four years later the polls confirm that public opinion has
        not changed at all from the above ballot set, so candidate
        A convinces her supporters to bury C. The ballot set becomes</div>
      <div> </div>
      <div>35 A>B</div>
      <div>40 B>C</div>
      <div>25 C>A</div>
      <div> </div>
      <div>Neither IRV nor TACC is affected by this burial, but
        Benham&Woodall reward the A faction for their strategic
        order reversal.</div>
      <div> </div>
      <div>It appears that IRV (in general) and TACC (at least in this
        case) are less vulnerable to burial strategy
        than Benham/Woodall.</div>
      <div> </div>
      <div>But let's take this case a little further.  Since the B
        supporters prefer C over A, they have a strong incentive to
        protect C from this obvious threat.  What can they do under IRV
        or Benham/Woodall?  They can betray their favorite B and vote 40
        C>B, which does get C re-elected, thus rewarding their order
        reversal.</div>
      <div> </div>
      <div>Forest</div>
      <div> </div>
      <div class="gmail_quote">On Wed, Apr 23, 2014 at 7:44 AM, C.Benham
        <span dir="ltr"><<a moz-do-not-send="true"
            href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>></span>
        wrote:<br>
        <blockquote style="BORDER-LEFT:#ccc 1px solid;MARGIN:0px 0px 0px
          0.8ex;PADDING-LEFT:1ex" class="gmail_quote">
          <div bgcolor="#FFFFFF" text="#000000">
            <div>Forest,
              <div><br>
                <br>
                <blockquote type="cite">
                  <div class="gmail_extra">40 A>B>C<br>
                  </div>
                  <div class="gmail_extra">35 B>C>A<br>
                  </div>
                  25 C>A>B</blockquote>
                <br>
              </div>
              In this example ballot set of yours (which you say is the
              result of the A faction burying against the sincere
              Condorcet Winner C) there is no reason<br>
              to suppose that any of the ballots are more likely to be
              insincere than any of the others.<br>
              <br>
              In this sort of situation (with 3 candidates in a cycle
              and all the ballots containing the same amount of
              information) we should avoid electing a candidate<br>
              X that is positionally dominated, especially by a
              candidate that pairwise beats X.   In this case that just
              says "not C".<br>
              <br>
              <blockquote type="cite">
                <div class="gmail_extra">35 A>B>C <br>
                </div>
                <div>
                  <div class="gmail_extra">40 B>C>A<br>
                  </div>
                  25 C>A>B</div>
              </blockquote>
              <br>
              In this ballot set (which again you say is the result of
              the A faction burying against C)  TACC elects C.  But
              again there isn't any information on the ballots<br>
              that suggests that some ballots are more likely to be
              insincere than any others.<br>
              <br>
              So the result must be justifiable on the assumption that
              all the votes are sincere. On these ballots C is
              positionally dominated and pairwise beaten by B.<br>
              B also positionally dominates A.<br>
              <br>
              Approval Margins, Approval Margins Sort, IRV, Benham,
              Woodall and all other good  (and/or sane) methods elect B.<br>
              <br>
              Chris Benham
              <div>
                <div class="h5"><br>
                  <br>
                  <br>
                  <br>
                  <br>
                  On 4/23/2014 7:29 AM, Forest Simmons wrote:<br>
                </div>
              </div>
            </div>
            <div>
              <div class="h5">
                <blockquote type="cite">
                  <div dir="ltr"><br>
                    <div class="gmail_extra"><br>
                      <br>
                      <div class="gmail_quote"><br>
                        <blockquote style="BORDER-LEFT:rgb(204,204,204)
                          1px solid;MARGIN:0px 0px 0px
                          0.8ex;PADDING-LEFT:1ex" class="gmail_quote">
                          <div>On 04/21/2014 11:39 PM, C.Benham wrote:<br>
                            <blockquote
                              style="BORDER-LEFT:rgb(204,204,204) 1px
                              solid;MARGIN:0px 0px 0px
                              0.8ex;PADDING-LEFT:1ex"
                              class="gmail_quote">Forest,<br>
                              <br>
                              <blockquote
                                style="BORDER-LEFT:rgb(204,204,204) 1px
                                solid;MARGIN:0px 0px 0px
                                0.8ex;PADDING-LEFT:1ex"
                                class="gmail_quote">48 C<br>
                                27 A>B<br>
                                25 B<br>
                              </blockquote>
                              <br>
                              <blockquote
                                style="BORDER-LEFT:rgb(204,204,204) 1px
                                solid;MARGIN:0px 0px 0px
                                0.8ex;PADDING-LEFT:1ex"
                                class="gmail_quote">Borda, TACC, and IRV
                                based methods like Woodall and Benham
                                elect C.<br>
                                <br>
                                But Borda is clone dependent, and the
                                IRV style elimination based<br>
                                methods fail monotonicity.  So TACC is a
                                leading contender if we<br>
                                really take the Chicken Dilemma
                                seriously.<br>
                              </blockquote>
                              <br>
                              Benham and Woodall are a lot more
                              resistant  to Burial than TACC (and<br>
                              other Condorcet methods that meet
                              mono-raise, aka monotonicity) because<br>
                              they meet<br>
                              "Unburiable Mutual Dominant Third"<br>
                            </blockquote>
                          </div>
                        </blockquote>
                      </div>
                      <br>
                    </div>
                    <div class="gmail_extra">How about the following set
                      of sincere preferences?<br>
                      <br>
                    </div>
                    <div class="gmail_extra">40 A>C>B<br>
                    </div>
                    <div class="gmail_extra">35 B>C>A<br>
                    </div>
                    <div class="gmail_extra">25 C>A>B<br>
                      <br>
                    </div>
                    <div class="gmail_extra">Candidate C is the sincere
                      winner under Benham, Woodall, TACC, or any other
                      method meeting the Condorcet Criterion.<br>
                      <br>
                    </div>
                    <div class="gmail_extra">Suppose that the A faction
                      decides to bury C:<br>
                      <br>
                      <div class="gmail_extra">40 A>B>C<br>
                      </div>
                      <div class="gmail_extra">35 B>C>A<br>
                      </div>
                      25 C>A>B<br>
                      <br>
                    </div>
                    <div class="gmail_extra">Woodall, Benham, Condorcet
                      (both wv and margins) reward this subterfuge by
                      electing A, whereas under TACC  the tactic
                      backfires by getting B elected.<br>
                      <br>
                    </div>
                    <div class="gmail_extra">Under Condorcet (wv) the C
                      faction can defend itself by truncating to 25 C. 
                      This wouldn't help under Woodall/Benham: <br>
                    </div>
                    <div class="gmail_extra"><br>
                      You get the same result if you replace the
                      respective faction sizes 40, 35, 25 with any three
                      positive numbers a, b, c that satisfy both
                      a>b>c and b+c>a.<br>
                      <br>
                    </div>
                    <div class="gmail_extra">Now consider the following
                      example where b>a>c:<br>
                      <br>
                      <div class="gmail_extra">35 A>B>C (sincere
                        A>C>B)<br>
                      </div>
                      <div class="gmail_extra">40 B>C>A<br>
                      </div>
                      25 C>A>B<br>
                      <br>
                    </div>
                    <div class="gmail_extra">Woodall/Benham still
                      rewards the burial.  TACC elects C without any
                      defensive move.  Condorcet elects B without any
                      defensive move.<br>
                      <br>
                    </div>
                    <div class="gmail_extra">Under TACC or Condorcet it
                      never hurts and sometimes helps for the CW
                      supporters to truncate the rest of the candidates.
                      But as you can see in the cases we are dealing
                      with here, only much more drastic defensive action
                      can save the CW under Woodall/Benham.<br>
                      <br>
                    </div>
                    <div class="gmail_extra">Conclusion: although in
                      some cases the UMDT confers a superior defense
                      against burial, that doesn't make Woodall and
                      Benham uniformly more burial resistant than TACC.<br>
                      <br>
                    </div>
                    <div class="gmail_extra">Forest<br>
                    </div>
                  </div>
                </blockquote>
                <br>
              </div>
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          </div>
        </blockquote>
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      <br>
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