Oscar_Cunningham comments on Bayesian probability as an approximate theory of uncertainty? - Less Wrong

16 Post author: cousin_it 26 September 2013 09:16AM

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Comment author: Oscar_Cunningham 28 September 2013 04:40:02PM 1 point [-]

So I think we should look at decision making as primary and then figure out how to decompose decision making into some abstract belief representation plus abstract notion of utility, plus some abstract algorithm for making decisions.

L. J. Savage does this in his book "The Foundations of Statistics." This was mentioned by pragmatist upthread, and is summarised here. This is written in 1954, and so it doesn't deal with weird LW-style situations, but it does found probability in decision theory.

Comment author: cousin_it 28 September 2013 05:50:47PM *  3 points [-]

Just for reference, Wei has pointed out that VNM doesn't work for indexical uncertainty because the axiom of independence is violated. I guess Savage's theory fails for the same reason. Maybe it's worthwhile to figure out what mathematical structures would appear if we dropped the axiom of independence, and if there's any other axiom that can pin down a unique such structure for LW-style problems. I'm trying to think in that direction now, but it's difficult.

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