[EM] Borda different than Condorcet?

[Alex Small]

Blake Cretney said:
> On Mon, 2003-02-24 at 11:56, Alex Small wrote:
>
>> Saari:  Anybody who thinks A is the favorite of the electorate really
>> doesn't understand how to deduce the true preferences of the voters.
>> Here's some geometry to show why....
>
> Is that a real Saari quote, or a parody?

Parody, but not too far from the truth.  I don't have his book in front of
me, but he says something to the effect that (paraphrase)

"In profiles where A is the first choice of the majority but B is the
Borda winner, the geometry of the situation strongly suggests that A is
not the true favorite of the electorate."

I think he's referring to the fact that in

66 ABC
34 BCA

the ABC faction has given B second-place support, when they could have put
him in third place.  Meanwhile, the BCA faction has indicated a strong
dislike of A by putting him last.  This indicates that B is a compromise
candidate.

Of course, this seems to hinge on the dubious assumption that relative
rankings in some way reflect absolute utilities.  If A, B, and C are
Great, Awesome, and Awful, there will be little difference in utility
between my first and second choices, but a huge difference in utility
between my second and third.  If the candidates are Awesome, Mediocre, and
Aweful, then they may be more or less evenly spaced in terms of utility.



Alex


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