[EM] Saari's Basic Argument

Forest Simmons fsimmons at pcc.edu
Wed Jan 15 10:40:44 PST 2003

```I've already given an example in which Borda gives the wrong answer after
the symmetry is removed.  Now you have given an example in which symmetry
removal shows the CW to be wrong. So that evens the score :-)

In other words, neither Borda nor Condorcet can claim to be superior on
the basis of symmetry removal.

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.

This method beats both Borda and Condorcet by the "symmetry removal
criterion."

Forest

On Tue, 14 Jan 2003, Steve Barney wrote:

> 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
>

----