[EM] Smith set/IIAC/GSFC

LAYTON Craig Craig.LAYTON at add.nsw.gov.au
Sun Nov 26 18:31:29 PST 2000

Rob Lanphier wrote:

>I'm trying to understand how to make a mathematically credible replacement
>for Arrow's Independence from Irrelavent Alternatives Criterion (IIAC),
>and I'm assuming the key is to understand the nature of the Smith set. 
>Can the Smith set be altered by the introduction of a non-Smith set
>candidate?  If so, what are the conditions when this happens?

Pending further investigation, I will tentatively advance a 'no'.

I would like to get confirmation on how draws are treated in obtaining a
Smith set.  My full (read: convoluted & unnecessary) rules for finding the
Smith set involve taking a candidate, and making them into a 'set', and then
adding all candidates who defeat or draw with candidates already in the set,
repeat until there are no candidates outside the set who defeat or draw with
candidates inside the set.  Repeat for each candidate.  The set with the
smallest number of candidates is the Smith set (my limited knowledge of
programming suggests that this would be a simple way to do it in a program).
However, using a similar method, you could read draws as victories for
candidates already in the set.

A>B, B>C, C>A, A>D, B>D, C=D. (Reading draws as victories for candidates
already in the set yields a Smith set of A,B,C).

Treatment of draws may effect the answer to Rob's question.

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