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Deference and Updating

Bas van Fraassen’s principle of Reflection tells you to defer to your future credences. A natural generealization of Christensen’s principle of Rational Reflection tells you to defer to whichever future credence will be rational. Elga’s principle New Rational Reflection is like Christensen’s principle, except that it allows that the rational credences may not be certain that they are rational.

Each of these deference principles is equivalent to a claim about updating—a claim about how your credences should be disposed to change when you learn that some proposition, e, is true. Reflection is equivalent to the claim that you should be disposed to update by conditioning on the proposition that your credences have been updated on e. Rational Reflection is equivalent to the claim that you should be disposed to update by conditioning on the proposition that e is your total evidence. And New Rational Reflection is equivalent to the claim that you should be disposed to update with a Jeffrey shift on the partition of propositions about what your total evidence may be.

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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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