<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 abd 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 candidatee 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 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></div></div></blockquote></div><br>