[EM] Borda different than Condorcet?

Alex Small asmall at physics.ucsb.edu
Mon Feb 24 19:42:36 PST 2003

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

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.


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