[EM] Comments on Alex's 2nd Arrow posting

[Bill Clark]

On 5/17/05, MIKE OSSIPOFF <nkklrp at hotmail.com> wrote:

> If Arrow's elusive definition says something different, then of course
> there's always the possibllity that Approval and Plurality might fail
> Arrow's unposted IIAC.

The full text of Arrow's "Social Choice and Individual Values" (the
book version of his PhD thesis) is available for search on Amazon.com.
 From page 26:

"The Independence of Irrelevant Alternatives

If we consider C(S), the choice function derived from social ordering
R, to be the choice which society would actually make if confronted
with a set of alternatives S, then, just as for a single individual,
the choice made from any fixed environment S should be independent of
the very existence of alternatives outside of S.  For example, suppose
that an election system has been devised whereby each individual lists
all the candidates in order of his preference and then, by a
preassigned procedure, the winning candidate is derived from these
lists.  (All actual election procedures are of this type, although in
most the entire list is not required for the choice.)  Suppose that an
election is held, with a certain number of candidates in the field,
each individual filing his list of preferences, and then one of the
candidates dies.  Surely the social choice should be made by taking
each of the individual's preference lists, blotting out completely the
deadd candidate's name, and considering only the orderings of the
remaining names in going through the procedure of determining the
winner.  That is, the choice to be made among the ser S of surviving
candidates should be independent of the preferences of individuals for
candidates not in S."

-Bill Clark