[EM] math 103 website - Arrow & Saari

[Markus Schulze]

Dear Steve,

you wrote (8 Jan 2002):
> In this instance, I was referring to Saari's discussion (in
> his book, _Decisions and Elections_) of the intensity of voter
> preferences strictly as it relates to Arrow's Impossibility
> Theorem. Saari shows that Arrow's Theorem can be resolved by
> slightly modifying the Independence from Irrelevant Alternatives
> criterion, so as to require a procedure to take account of the
> intensity of a voter's preferences, as can be determined by the
> Borda Count be noting the number of candidates who are ranked
> in between each pair.

The Borda method doesn't take account of the intensities of the
preferences either. If the intensities of the preferences could
be determined by the number of candidates who are ranked between
each pair of candidates, then this would mean that the intensities
of the preferences are changed when candidates are added. When we
want to check whether a given election method can be manipulated
by strategical nomination, then of course we have to assume that
the opinions of the voters about the already running candidates
don't change. Otherwise we couldn't compare the situation before
with the situation after.

Markus Schulze