Will_Sawin comments on The Ellsberg paradox and money pumps - Less Wrong

10 Post author: fool 28 January 2012 05:34PM

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Comment author: Will_Sawin 31 January 2012 11:22:13PM 0 points [-]

How do you choose the interval? I have not been able to see any method other than choosing something that sounds good (choosing the minimum and maximum conceivable would lead to silly Pascal's Wager - type things, and probably total paralysis.)

The discontinuity: Suppose you are asked to put a fair price f(N) on a bet that returns N if A occurs and 1 if it does not. The function f will have a sharp bend at 1, equivalent to a discontinuity in the derivative.

An alternative ambiguity aversion function, more complicated to define, would give a smooth bend.

Comment author: fool 01 February 2012 01:15:05AM 0 points [-]

How do you choose the interval? I have not been able to see any method other than choosing something that sounds good

Heh. I'm the one being accused of huffing priors? :-)

Okay, granted, there are methods like maximum entropy for Bayesian priors that can be applied in some situations, and the Ellsberg urn is such a situation.

Yes, you are correct about the discontinuity in the derivative.

Comment author: Will_Sawin 01 February 2012 01:54:11AM 0 points [-]

Yes. Because you're huffing priors. Twice as much, in fact - we have to make up one number, you have to make up two.