[EM] Saari's Basic Argument

Alex Small asmall at physics.ucsb.edu
Tue Jan 14 15:03:38 PST 2003

Forest Simmons said:
> In the case of full rankings of three candidates, this residual method
> seems to always gives the same result as the Kemeny order, MinMax,
> Ranked Pairs, SSD, etc. for the original problem.

That's what I expected.  It's quite reasonable to assume that a _ranked_
method will give a tie in the case

33 A>B>C
33 B>C>A
33 C>A>B

and that if we add just one more voter, his vote will break the tie, so
that we pick A in the case

34 A>B>C
33 B>C>A
33 C>A>B

Indeed, it makes sense that a Condorcet method would at least respect
reversal symmetry, since adding two voters with opposite preferences does
not change the margin of any pairwise victory (ignore issues of
truncation, so that the word "margin" does not inspire a new round of

I'd have to think a bit before concluding that cancelling out the
rotationally symmetric parts of the electorate would give the same result
as Condorcet in the presence of a CW.  I seem to recall Saari giving an
example to the contrary.  Anyway, thanks, Forest, for pointing out that a
devotion to symmetry need not force one to support Borda a priori.


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