Causal Decision Theory violates the Independence of Irrelevant Alternatives

As I’ll use the name here, the independence of irrelevant alternatives (IIA) says that adding an additional option to the menu can’t transform an impermissible choice into a permissible one. An old story from Sidney Morgenbesser illustrates the seeming irrationality of violating this principle: asked to decide between steak and chicken, a man says “I’d rather have the steak”. The waiter tells him that they also have fish, to which he responds: “Oh, in that case, I’ll have the chicken”.

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Teaching Arrow's Impossibility Theorem

I regularly teach undergrads about Arrow’s impossibility theorem. In previous years, I’ve simply presented a statement of the theorem and provided a proof in the optional readings. Arrow’s proof is rather complicated; and while there are several simpler presentations of the proof, they are still too complicated for me to cover with philosophy undergraduates.

Preparing for class this year, I realized that, if Arrow’s theorem is slightly weakened, we can give a proof that is much easier to follow—the kind of proof I’m comfortable presenting to undergraduate philosophy majors. The point of the post today is to present that proof.

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Predictable Poverty in Sequential Decision Problems

Wells (forthcoming) has an really nice example of a sequential decision problem in which an evidential decision theorist will end up predictably poorer than a causal decision theorist. Wells thinks that this case shows that we should reject evidential decision theory. I agree that we should reject evidential decision theory, but I don’t think that a proponent of CDT should use Wells’s case to argue for this conclusion.

The reason is that there are sequential decision problems in which a causal decision theorist will end up predictably poorer than an evidential decision theorist, even when both the causal decision theorist and the evidential decision theorist face this decision problem in the same circumstances. If predictable relative poverty like this gives a sufficient reason to reject EDT, then it likewise gives a sufficient reason to reject CDT. (I think we should tollens—though I won’t be making that case here.)

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