[logicchop]

I recall that Bordes and Tideman were a good source on this issue; I believe the (relevant) paper is "Independence of Irrelevant Alternatives in the Theory of Voting." -- The upshot is that the condition known as IIA (I think it is sometimes known as Sen's condition-alpha, and the condition that many people harp on, including Michael Dummett) is in fact a stronger condition than is needed for the result; roughly, that instead of needed a condition about consistency among selections over possible ballots (like: if y were selected in ballot [xyz], y should be selected among yz on ballot [yz]..) we simply need a requirement that the selection only involves information on the ballots (and that the relative rankings of candidates not on the ballot are irrelevant to the selection).

[dllthomas]

Ah, I think your phrasing was confusing. "IIA" is considering an attribute of the ballots, but including IIA is stronger than necessary for the theorem to hold - it can be replaced with the much weaker "nothing but the ballots".