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<TITLE>[Condorcet] Favorite Betrayal in DMC</TITLE>
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<DIV id=idOWAReplyText39134 dir=ltr>
<DIV dir=ltr><FONT face=Arial color=#000000 size=2>Note that in the following
list of conditions for Favorite Betrayal incentive, I did not distinguish
between Strong FBC and Weak FBC, since the conditions are almost identical when
voting under DMC.</FONT></DIV>
<DIV dir=ltr><FONT face=Arial size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Arial size=2>The only difference is in condition
(4).</FONT></DIV>
<DIV dir=ltr><FONT face=Arial size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Arial size=2>If neither approving Compromise
(as in 4 below), nor ranking Compromise equal with Favorite is enough to
stop Favorite from doubly defeating compromise, then (in the presence of the
other six conditions) we're talking about a violation of both weak and
strong FBC, otherwise only a violation of Strong FBC.</FONT></DIV>
<DIV dir=ltr><FONT face=Arial size=2></FONT> </DIV>
<DIV dir=ltr><FONT face=Arial size=2>Because of this, it seems to
me that the gap between weak and strong FBC is smaller in DMC than it is in
Shulze(wv). Shulze(wv) might even do slightly better than DMC with regard
to weak FBC, but I believe that DMC does better with respect to strong FBC,
which is what voters really care about the most.</FONT></DIV></DIV>
<DIV dir=ltr><BR>
<HR tabIndex=-1>
<FONT face=Tahoma size=2><B>From:</B> Condorcet@yahoogroups.com on behalf of
Simmons, Forest <BR><B>Sent:</B> Sat 9/17/2005 3:00 PM<BR><B>To:</B>
election-methods-electorama.com@electorama.com<BR><B>Cc:</B>
Condorcet@yahoogroups.com<BR><B>Subject:</B> [Condorcet] Favorite Betrayal in
DMC<BR></FONT><BR></DIV>
<DIV>
<P><FONT size=2>One of the nice things about DMC is that it is easy to pinpoint
the precise circumstances in which there is a Favorite Betrayal incentive, i.e.
where Favorite Betrayal is more likely to payoff than not. It seems
to be much harder to pin this down in Schulze.<BR><BR>Here are the conditions
that must all obtain simultaneously for there to be a Favorite Betrayal
incentive:<BR><BR>1. There must be a faction V of voters coordinating (by ESP or
otherwise) their strategy trying to decide whether to vote Compromise C above
Favorite F.<BR><BR>2. Without this betrayal by faction V, candidate F beats C
pairwise.<BR><BR>3. With this betrayal by faction V, candidate C beats F
pairwise.<BR><BR>4. Even with full approval of C by faction V, candidate F
has more approval.<BR><BR>5. There must be some candidate X that doubly defeats
F.<BR><BR>6. Candidate C must not be doubly defeated by any candidate other than
F, not even X.<BR><BR>7. The members of V must be convinced that conditions (3)
and (6) are almost surely true despite all of the evidence (conditions 2, 4, and
5) to the contrary.<BR><BR><BR>Think about this. Conditions 2 and 4 say
that F doubly defeats C even when the F supporters that consider C as a
compromise give full approval to C. Condition 5 says that F is doubly
defeated by some other candidate X. If double defeat were transitive, then
we would conclude that X doubly defeated C, too, and there would be no point in
ranking C ahead of F.<BR><BR>Of course, double defeat is not transitive, but in
absence of very strong evidence to the contrary, it is the safest bet. How
would you bet if your were told that X doubly defeats F doubly defeats C?
Would you put your money on C is not doubly defeated by anybody but F, or on C
is doubly defeated by someone other than F (like X)?<BR><BR>But this is not
all. Suppose you were willing to put your money on C not being doubly
defeated by anybody but F. How likely would it be that your betrayal would
help C defeat F, given that your faction V approving C was not enough to raise
C's approval above F's approval?<BR><BR>In sum, because there is a tension of
conditions 2, 4, and 5 versus conditions 3 and 6, it is hard for condition 7 to
hold. But if even one of these conditions is believed to fail, then there
is no betrayal incentive.<BR><BR>I believe that it is practically impossible for
all seven of the above conditions to obtain simultaneously.<BR><BR>Who can make
a similar analysis for Shulze(wv) ?<BR><BR>Forest<BR><BR><BR>[Non-text portions
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