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<TITLE>Re: [Condorcet] Comment on DMC</TITLE>
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<DIV id=idOWAReplyText38049 dir=ltr>
<DIV dir=ltr><FONT face=Tahoma size=2>Here is an "ABC" example that illustrates
Jeff Fisher's concern as I understand it (see below):</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>Sincere zero info ballots:</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>45 A>>C>B</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>20 C>>B>A</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>35 B>>A>C</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>Pairwise cycle is
A>C>B>A.</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr>Approval order is A>B>C.</DIV>
<DIV dir=ltr> </DIV>
<DIV dir=ltr>So the sincere DMC winner is B.</DIV>
<DIV dir=ltr> </DIV>
<DIV dir=ltr>But in the near perfect information case the A
faction might decide to strategically approve C, resulting in</DIV>
<DIV dir=ltr> </DIV>
<DIV dir=ltr>
<DIV dir=ltr><FONT face=Tahoma size=2>45 A>C>>B</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>20 C>>B>A</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>35 B>>A>C</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>and an approval order of
C>A>B,</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>which would make A the DMC
winner.</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>If all three factions resort to this
gratuitous approval strategy, then the approval order becomes A>C>B,
which still gives the win to A.</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>As Jeff notes, the advantage of DMC over
ordinary Condorcet without approval cutoffs seems to be lost, since without the
approval cutoffs River, MinMax, Beatpath, and Ranked Pairs (whether margins or
wv) all agree on A as winner.</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>Here are some of my feelings about
this:</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>1. If DMC does better than the other
methods in the zero-info case, and does just as well in the informed cases, then
DMC is still an improvement over the other methods. (And DMC has all of
the other 14 advantages as well.)</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>2. The largest faction has a
definite advantage in these strategical games. If the other
factions are unwilling to cooperate against the largest faction, then
the largest faction has a strong claim on being the rightful
winner.</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>This second point is also my answer to
those critics of Top Two Approval Runoff that complain that the strongest
faction could get a strawman into the runoff with the highest approval
candidate. I say that if they are that strong, and their opponents that
fragmented, then they deserve to decide the winner.</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>My objection to Top Two Approval Runoff is
that it is a very minor improvement on Approval at a large cost ...
the need for pairwise information. In a small group setting it would be
very reasonable.</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>3. Most people (including Markus
recently) complain that approval cutoffs are apt to be too
stingy. But here's a pressure in the generous approval
direction.</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>4. DFC doesn't suffer from this
strategy problem, since giving C more approval than A gives C (whom the A
supporters do not really approve of) a significant probability of
winning, too.</FONT></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>Forest</FONT></DIV></DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Tahoma size=2>On Thu 9/1/2005 10:50 AM, Jeff Fisher
wrote ...</FONT><FONT size=2></DIV></DIV>
<DIV dir=ltr><BR>I have a problem that I posted in an Electo-wiki discussion
last week; it<BR>has no replies yet:<BR><BR>***<BR><BR>If a faction sees a
Condorcet paradox looming, can it gain an advantage by<BR>insincerely approving
of the contender that it expects to defeat pair-wise?<BR><BR>Your polling data:
Approval runs narrowly A>B>C, but pairings run A>C>B>A,<BR>so 'B'
stands to win under DMC. You're the tactician for faction 'A'. Can<BR>your
supporters insincerely increase approval of 'C' in order to eliminate
'B'?<BR><BR>If so, then it doesn't even matter if you over-do it and push your
spoiler<BR>ahead of yourself in approval: As long as you expect to win head to
head,<BR>you may hand out approval points with impunity and perhaps steal a
victory.<BR><BR>Of course, once your faction's plan leaks out, 'C' will boost
'B', and 'B'<BR>will boost you... and the faction controlling the most first
place votes<BR>will bury its nemesis and prevail.<BR><BR>So, in practice, will
DMC degenerate into basic Condorcet with whatever<BR>limitations that
has?<BR><BR></DIV></FONT>
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