<div dir="ltr">Oops; I mis-replied individually, instead of to the list. Here's what I said:<br><div class="gmail_quote">----<br><div dir="ltr">This thread is interesting. However, it's also very heavy on the acronyms. Can I ask that when you use an acronym, you make sure it's explained adequately on the electorama wiki? At a quick check, <a href="http://wiki.electorama.com/wiki/TACC" target="_blank">http://wiki.electorama.com/wiki/TACC</a> is inadequate and <a href="http://wiki.electorama.com/wiki/MAM" target="_blank">http://wiki.electorama.com/wiki/MAM</a> is nonexistent.<div>
<br></div><div>As to the discussion: this is really the heart of the chicken dilemma. I don't think there's any way to look at a set of ballots like </div><div><span style="font-family:arial,sans-serif;font-size:13px"><br>
</span></div><div><span style="font-family:arial,sans-serif;font-size:13px">40 C</span></div><div class=""><div style="font-family:arial,sans-serif;font-size:13px">35 A>B<br></div><span style="font-family:arial,sans-serif;font-size:13px">25 B</span><div>
<span style="font-family:arial,sans-serif;font-size:13px"><br></span></div></div><div><font face="arial, sans-serif">... and get an answer that's not going to be wrong some of the time. If these ballots are honest, then B should win. If the B voters are truncating an honest A second preference, than A would be the ideal winner, but perhaps the system should choose C in order to discourage that strategy. And if enough of the B voters are truncating C, you could make an argument that C is the best winner.</font></div>
<div><font face="arial, sans-serif"><br></font></div><div><font face="arial, sans-serif">The only system I know of where I wouldn't worry about this situation is SODA. Under SODA, since C and B are required to declare second preferences, the ballots above could not occur with lazy voters. So in order to get the ballots above in a chicken dilemma situation, you'd have to have C voters going out of their way to check "Do not delegate", in hopes that [B voters would go out of their way to do so, in mistaken hopes that A voters would not go out of their way to do so]; and then the C voters' hopes would have to be right about the B voters but wrong about the A voters, while the B voters were wrong about the A voters. In other words, as long as there's common information (however complete or incomplete), the ballots above just won't happen in SODA.</font></div>
<div><font face="arial, sans-serif"><br></font></div><div><font face="arial, sans-serif">Short of SODA... I'm interested in the discussion of various preferential methods, but I think that MAV is probably the best answer to the situation, and it's not so great. It would elect B in the above scenario, possibly rewarding a chicken strategy from B voters; but if 3/10 to 4/10 of the A voters truncate, then it's very hard and risky for the B voters to get their way.</font></div>
<div><font face="arial, sans-serif"><br></font></div><div><font face="arial, sans-serif">Jameson</font></div></div><div class="gmail_extra"><br><br><div class="gmail_quote">2014-04-23 10:44 GMT-04:00 C.Benham <span dir="ltr"><<a href="mailto:cbenham@adam.com.au" target="_blank" onclick="window.open('https://mail.google.com/mail/?view=cm&tf=1&to=cbenham@adam.com.au&cc=&bcc=&su=&body=','_blank');return false;">cbenham@adam.com.au</a>></span>:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div class="h5">
<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><br>
<br>
<br>
<br>
<br>
On 4/23/2014 7:29 AM, Forest Simmons wrote:<br>
</div></div></div><div><div>
<blockquote 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>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>
<br>
</div></div></div>
<br></div></div><div class="">----<br>
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<br></div></blockquote></div><br></div>
</div><br></div>