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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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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