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Chances of a Death Foretold

In Gibbard and Harper’s ‘Death in Damascus’, you must choose to travel to either Damascus or Aleppo, you are rather confident that you will meet Death in whichever city you actually choose, and that traveling to the city you don’t actually choose would save your life. In the standard version of this case, that’s because Death has made a quite reliable prediction about which city you will choose. Today’s post isn’t about ‘Death in Damascus’.

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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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