Alex said:
Given that IIA is incompatible with Pareto and non-dictatorship (i.e. impossible for any realistic public election method)
I reply:
IIAC isn't incompatible with Pareto and non-dictatorship. Only for rank methods. That's only a limitation of rank methods. Plurality doesn't have that limitation. Neither does Approval. Arrow's impossibility theorem could be entitled "Arrow's Limitation of Rank Methods".
If that's important to someone then they'd like Plurality better than Condorcet. Mysefl, I prefer Condorcet to Plurality. So then it must be that, at least for some of us, Arrow's limitation of rank methods isn't important.
The above is true if IIAC can be described by my brief votes-only definition. If Arrow's elusive definition says something different, then of course there's always the possibllity that Approval and Plurality might fail Arrow's unposted IIAC.
Alex continues:
, from a practical perspective, IIA is a worthless criterion.
I reply:
Agreed.
Alex continues:
So the value of Arrow's Theorem is not simply that it proves IIA is impossible. It is that he shows that:
1) Seemingly simple properties can be impossible to satisfy, indicating that election methods can be subtle and complicated things
2) Some of these subtleties can be addressed by general statements that transcend any particular method, meaning that election methods need not be studied method-by-method. Sure, there's a place for that approach, but that approach can be supplemented and informed by a more general analysis.
I reply:
Fair enough. Arrow may have been first with demonstrations like that.
Mike Ossipoff
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