[EM] Saari's Basic Argument

[Alex Small]

Forest Simmons said:
>
>
> On Thu, 16 Jan 2003, Steve Barney wrote:
>
>> Forest:
>>
>> In your example,
>>
>> >66 A>B>C
>> >34 B>C>A
> No need of giving weights to see all the mischief that could come from
> giving the win to B.

Moreover, if candidate C weren't there then we'd all agree that A trounced
B conclusively.  Then we throw in C, and because the A voters happen to
agree that B is better than C, that point of agreement costs them what was
a decisive victory.  How can you justify that?

Indeed, if C is a single-issue candidate then letting B wins is like
saying that because the A faction agrees with the B faction on one
particular issue, it's OK that B wins.  In that case, I guess it's OK that
Bush won, because even though he got fewer votes than Gore, he at least
agrees with Gore on some things.

Granted, all ranked methods are susceptible to violations of IIA
(Independence from Irrelevant Alternatives) but some methods (e.g.
Condorcet, IRV) at least avoid that problem when somebody has a majority.

So, in the end, as nice as positional methods are for mathematical study,
and as cool as Saari's pictures are, and as impressive and charismatic as
Saari is (I've seen him talk in person), in the end Borda is a horrible
method.



Alex


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