[EM] Symmetry and Condorcet

Alex Small asmall at physics.ucsb.edu
Thu Jan 16 09:57:22 PST 2003

If one first cancels out only the reversal symmetry in an electorate, if
there was originall a Condorcet winner there will still be one, AND there
will be no rotationally symmetric part of the electorate to cancel out. 
Moreover, in the 3 candidate case there will be only 2 candidates
remaining with first-place support when there was originally a Condorcet
winner, and that candidate will be the Condorcet winner.

Finally, if there was no Condorcet winner then there will still be a
rotationally symmetric part to cancel out.  You'll be left with the
plurality winner.

I'm not suggesting that plurality completed Condorcet is a perfect system,
but it satisfies the symmetry requirements of Saari without the perverse
strategic incentives of Borda, and also satisfies the majority criterion
(unlike Borda).

I'm curious whether Saari ever considered switching the order in which you
do the symmetry cancellations.


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