[EM] Thoughts on Arrow's Theorem and the IIAC

[Kevin Venzke]

Hi Forest,

--- En date de : Lun 2.5.11, fsimmons at pcc.edu <fsimmons at pcc.edu> a écrit :
> In liberal arts mathematics text
> books Arrow's impossibility theorem is usually
> quoted as saying that no election method can simultaneously
> satisfy (1)
> neutrality, (2) anonymity, (3) decisiveness (4) monotonicty
> (5) the majority
> criterion (6) the Condorcet Criterion, and (7) the
> Independence from Irrelevant
> Alternatives Criterion (the IIAC), as though all of these
> requirements were
> equally to blame for the incompatibility, 

That is the longest list I've ever seen. I'm used to seeing 4+5+6
replaced by Pareto perhaps. Condorcet would already imply majority,
unless this is supposed to be mutual majority.

> when in reality
> conditions one through
> six are perfectly compatible with each other, but condition
> seven is not even
> compatible with the existence of a Condorcet cycle.

Well, we would probably expect "all properties but one" to be compatible.
Drop out #7 and you can have a method. But drop out #6 and you still
don't have a method.

It's clear, as you write, that IIA isn't compatible with Condorcet. It's
not compatible with much of anything. I take that to be the point of
Arrow: If you want IIA you have to do some drastic things. If I could
have IIA (and for real, not on a technicality) I would certainly want 
it...

Kevin