[mcphage]

When you say it like that, IIA does sound pretty obvious. But if you change the terms a little bit, you can see why the IIA doesn't match up with how people actually vote:

Say there's an election between a moderate democrat "blueberry pie" and a third party liberal "apple pie". As a liberal, Sidney would rather vote for the third party ("Sidney orders the apple pie"). However, if you introduce a republican candidate "cherry pie", Sidney will probably vote for the democrat (blueberry pie) instead of the third party candidate, because he'd be worried about his vote costing the more moderate candidate the election.

IIA means that you won't vote differently than your preferences—but people do that all the time. And sure, a voting system where that wasn't necessary would be nice, but losing that condition isn't as nonsensical as it seems at first.

[grayclhn]

Arrow's impossibility theorem, and the IIA criterion, is about preferences not about uncertain actions. In particular, IIA doesn't mean that you'll vote differently than your preferences in some sort of election, it means that your preferences themselves don't change when you introduce other irrelevant options. In your example, it wouldn't be about how Sidney would vote in an election given the different menu of candidates, it's about who Sidney would prefer win the election.

(with the caveat that it has been a long time since I've thought about these results.)

[logicchop]

In the context of voting, all IIA represents is the requirement that we only take into account the information on the ballots..

[dllthomas]

I don't see this. Could you elaborate?

[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".