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<TITLE>RE: [Condorcet] Can we come to consensus? (ICA)</TITLE>
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<DIV id=idOWAReplyText69890 dir=ltr>
<DIV dir=ltr><FONT size=2>Kevin, your ICA method interests me. In
particular, your creative use of "equal ranked top" might be called "power top"
analogous to what Mike Ossipoff recently called "power truncation" for equal
(non)ranking at the bottom.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>I suggest that we consider methods that sum two
modified pairwise matrices in addition to the basic pairwise
matrix:</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>(This description is at the ballot level)</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>In the ordinary pairwise matrix M, the (i,j) entry is
a one or a zero depending on whether or not candidate i is ranked ahead of
candidate j on the ballot.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>In the "Pro modification" PM, if candidate
i is ranked equal first, then row i is filled in with ones.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>In the "Con modification" CM, if candidate k is
truncated, then column k is filled in with ones. This is Ossipoff's "power
truncation" matrix.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>I'll leave it as an exercise to restate the definition
of ICA in terms of M and CM, assuming that "least approved rank" is
treated like a candidate.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>Here's another possible application that comes to mind
suggested by the question, "What happens when an irresistible force comes up
against and immoveable object?"</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>We pit the candidate with the strongest offense
against the candidate with the strongest defense:</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>The offensive winner is the candidate for whom the
minimal row element of the PM matrix is maximal, i.e. the MMPO winner with power
truncation.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>The defensive winner is the candidate for whom the
maximal element of the CM matrix is minimal.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>If these two winners are different, then the
ordinary pairwise matrix M decides between them.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>It seems like this method might satisfy the FBC:
the process of picking the offensive winner must satisfy the FBC for the
same reason that MMPO does. And it seems to me that the process of picking
the defensive winner satisfies the FBC for the same reason that ICA
does.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>What do you think?</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>Forest</FONT></DIV></DIV>
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