[EM] Saari's Basic Argument

[Steve Barney]

Alex:

You may be thinking of Condorcet's example, the profile which Condorcet used 
to decredit the Borda Count by pointing out that the BC-winner was not the 
Condorcet-winner in that case. Saari argues that "rather than supporting the 
Condorcet winner, these examples expose a flaw," and shows that cancelling out 
the cyclic portion of Condorcet's example makes the Condorcet-winner the same 
as the original BC-winner. Condorcet's profile is:

30:ABC
1:ACB
10:CAB 
1:CBA
10:BCA
29BAC


[source: "EXPLAINING ALL THREE-ALTERNATIVE VOTING OUTCOMES,"
DONALD G. SAARI, section 8.1 - see
<http://citeseer.nj.nec.com/cache/papers/cs/11095/http:zSzzSzwww.math.nwu.eduz
Sz~d_saarizSzvotezSztriple.pdf/saari99explaining.pdf>]

--- In election-methods-list at yahoogroups.com, "Alex Small" <asmall at p...> 
wrote:
[...]
> 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.
>
>
>
> Alex

Steve Barney

Richard M. Hare, 1919 - 2002, In Memoriam: <http://www.petersingerlinks.com/hare.htm>.

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