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<P><FONT SIZE=2 FACE="Arial">Seeing "RRV" used in a post reminded me of some earlier discussions. Analysis of team computer rankings in sports that do NOT have round-robin schedules use "Retrodictive Ranking Violations" to characterize computer ratings with A>B after B has won a match against A. (This is not an "error", since the rating that has A>B may have noticed A has 10 wins over {C}s, each of which has beaten B.)</FONT></P>
<P><FONT SIZE=2 FACE="Arial">But this leads to a thought.</FONT>
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<P><FONT SIZE=2 FACE="Arial">Suppose an Election Method results in an ordered list of alternatives {1st 2nd 3rd....} (trivial for Plurality, and well-defined for any method if we accept {2nd, 2nd, 5th, 5th, 5th,...} for ranked methods that result in "ties")</FONT></P>
<P><FONT SIZE=2 FACE="Arial">For each ranked ballot (for plurality we assume a "ranked ballot" that looks like {1st, last, last, last, ...}, for approval we assume a "ranked ballot" that looks like {1st, 1st, 1st, .... last, last, last} ) we can find RRV(ballot) = SUM over pairs(x,y) (Altx > Alty in EM but Alty > Altx in ballot)</FONT></P>
<P><FONT SIZE=2 FACE="Arial">This is just the Kendall tau rank correlation "distance" = # of swaps required by a bubble sort to turn {ballot} into {EM result}</FONT></P>
<P><FONT SIZE=2 FACE="Arial">Something like that could be exploited to avoid the nebulous notion of utility and define (voter(s) who cast {ballot})'s (lack of) "satisfaction index" unambiguously and entirely with respect to the EM used to form the election results list.</FONT></P>
<P><FONT SIZE=2 FACE="Arial">Paul Kislanko</FONT>
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