[EM] Saari's Basic Argument

[Forest Simmons]

On Fri, 17 Jan 2003, Alex Small wrote:

> Forest Simmons said:

> >>
> >> >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.

And since C is not in the Smith set, this shows that even in a cycle free
example, Borda doesn't satisfy even the local version of IIAC.

Note that C is the unanimous loser in the ballot set considered equivalent
by Saari (after adding and subtracting "symmetries"):

32 ABC
34 BAC

So all methods satisfying the Pareto Criterion would agree that C is
irrelevant.  Yet when C is removed, the two "equivalent" reduced ballot
sets yield opposite answers.



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