[EM] Saari's Basic Argument

Alex Small asmall at physics.ucsb.edu
Wed Jan 15 15:08:39 PST 2003

Forest Simmons said:
> So here's a new method (for three candidate races only): first remove
> all of the symmetry, and then the candidate with a majority of first
> place votes (on the remaining ballots) is the winner.

The order in which one removes symmetry matters.  Canceling out reversal
symmetry before rotational symmetry (cycles) gives a different result than
Saari's recommended order of rotational, then reversal.  I'm not convinced
that symmetry is a particularly compelling reason to pick an election
method, but Forest has shown that Borda is not the only way to respect
symmetry considerations.

I'm curious what Saari would say.  The existence of a majority candidate
in the aftermath of symmetry considerations is a compelling reason to use
Forest's method rather than Borda if one cares about symmetry.  Saari
seems to have a low opinion of the majority criterion, and his attempt to
dismiss it in _Basic Geometry of Voting_ is less than satisfactory.


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