[EM] Criteria and the Smith Set

[Rob Lanphier]

Hmm, my apologies to Blake on the last email.  I went back and read his
earlier mail, and realized he had considered the point that I brought up.

But, hey, while I'm talking about things that may have been brought up, I
have some thoughts on the criteria we often use.  Specifically, I was
filtering through Blake's list of criteria at:
http://www.fortunecity.com/meltingpot/harrow/124/criteria.html

...some of which are criteria that Arrow used in his proof.  Being the
raving Smith//Minmax zealot that I am, I noticed that the criteria that
Smith//Minmax fail seem to involve the case where the Smith set has more
than two candidates in it.  If that's true (haven't checked), then would
it make sense to evaluate which methods pass those criteria when the Smith
set contains only one candidate?

The rationale for this is that the cases where the Smith set has multiple
candidates is a sort of corner case.  At a minimum, it's certainly treated
as a corner case by many methods.  Moreover, I'd argue that many of the
criteria are only intuitively fair and correct when the Smith set is one
(IIAC is an example, since a random pick from the Smith set seems
defensible when Smith>1, yet this clearly violates IIAC).

I suppose that LIIAC came from considering something like the idea I bring
up here, but does it make sense to go down the list and come up with the
Smith=1 versions?

Thoughts?

Rob Lanphier
robla at eskimo.com
http://www.eskimo.com/~robla