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<div class="moz-cite-prefix">Forest,<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>
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 class="gmail_extra">40 B>C>A<br>
</div>
25 C>A>B</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<br>
<br>
<br>
<br>
<br>
On 4/23/2014 7:29 AM, Forest Simmons wrote:<br>
</div>
<blockquote
cite="mid:CAP29oncJjhsjq=_e-Yeuh5xM7gfcojPHLfPoZS=C_ZSL0jNqrQ@mail.gmail.com"
type="cite">
<div dir="ltr"><br>
<div class="gmail_extra"><br>
<br>
<div class="gmail_quote"><br>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
<div class="">On 04/21/2014 11:39 PM, C.Benham wrote:<br>
<blockquote class="gmail_quote" style="margin:0px 0px
0px 0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
Forest,<br>
<br>
<blockquote class="gmail_quote" style="margin:0px 0px
0px 0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
48 C<br>
27 A>B<br>
25 B<br>
</blockquote>
<br>
<blockquote class="gmail_quote" style="margin:0px 0px
0px 0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
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>
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