IIAC (was (Fwd) re: Mike's criticism of Bruce)

Steve Eppley seppley at alumni.caltech.edu
Mon Feb 3 18:28:36 PST 1997

Mike O briefly defined Arrow's Independence from Irrelevant 
Alternatives criterion (IIAC):

>   Removing a non-winning candidate from an election shouldn't
>   change who wins, when the same rankings are re-counted.

The definition of IIAC listed in Ordeshook's book is slightly 
different.  I've posted Ordeshook's version in EM before; briefly,
it states that the social preference order of two given candidates
i and j must depend only on the voters' preferences between i and j
(i.e., only on how they voted in the "i vs. j" pairing).

The two definitions appear substantially the same.

One of the non-obvious ramifications of the Independence axiom is
that expressions of voters' preference *intensities* may not affect
the outcome; only the voters' preference *orders* may affect the

I'm not sure what Mike meant when he suggested we might keep IIAC and 
discard the Pareto criterion instead.  With three or more candidates,
there's always the possibility of circular preferences (e.g., A>B>C>A)
so it appears to be hard to keep IIAC in its pure form.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)

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