Comment on Pascal's Mugging for bounded utility functions

Thu, 21 Feb 2013 18:35:50 GMT

Presumably the idea is that 3^^^3 is computable by a fairly short program

Irrelevant.

Solomonoff induction evaluates programs that generate strings of possible future observations conditioned on all your past observations (or equivalently, programs that generate strings of past and future observations, and counts only those that generate a string whose prefix matches your previous observations).
These programs correspond to models of the universe (observed from your particular point of view).

Models of the universe where life goes on as we know it until at a certain point and then suddenly you get 4^^^^4 years of fun are presumbly much more complex than models of the universe where life keeps going on as we know it.

In particular, if Solomonoff induction assigns to models where starting from now you get X years of fun a total probabilty p(X) that asymptotically decreases fast enough with X so that U(X) * p(X) also decreases, it will not be subject to Pascal's mugging.
All reasonable light-tailed probability distribution would have that property w.r.t. any reasonable utility function.
I see no reason to believe that the Solomonoff distribution would behave otherwise.

Discuss