[EM] Saari's Basic Argument
Forest Simmons
fsimmons at pcc.edu
Tue Jan 21 09:17:16 PST 2003
On Sat, 18 Jan 2003, Steve Barney wrote:
....
> If you don't like Condorcet's example, how about this one, which I have looked
> at before:
>
> 5 ABC
> 3 BCA
>
>
> Can you give me the decomposition profile, T(p), for this example?
>
This example is essentially the same as the
66% ABC
34% BCA
example. In terms of percentage of the vote, your example is
62.5% ABC
37.5% BCA,
so the majority is only 62.5% instead of 66%, but that doesn't change the
analysis.
Let's add three copies of the symmetric pair {BAC,CAB} to your eight
ballot example to get
5 ABC, 3 BAC, 3 CBA, 3 CAB.
Now subtract three copies of the cycle {ABC,BCA,CAB} to get
2 ABC
3 BAC.
By adding and removing symmetries that are supposed to make no difference,
we have arrived at a ballot set of a completely different character.
Saari makes the assumption that these symmetries are innocuous, whether or
not they respect the actual symmetry or symmetries of the distribution of
ballots.
False assumptions generally lead to ridiculous conclusions.
I agree that Borda has its uses, but not as a public election method
proposal.
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