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In the context of voting, all IIA represents is the requirement that we only take into account the information on the ballots..
by logicchop 11y ago
In the context of voting, all IIA represents is the requirement that we only take into account the information on the ballots..
- dllthomas 11y agoI don't see this. Could you elaborate?
- logicchop 11y agoI 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 11y agoAh, 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".