[arielby]

The problem with the original lottery is that most of its value is from high-EV tiny-probability events, e.g. the 2^{-50} probability of winning 2^50 dollars. The practical result of that event does not seem to be worth 2^50 utilons, to say the least. It is hard to think about events worth that many.

However, many perturbations of this lottery can actually be good bets.

For example, suppose you gain 3^n dollars with probability 2^{-n}. Then you have a 1/128 chance of winning $2187, a 1/256 change of winning $6561, and this game starts looking much nicer.

The "Pascal's Mugging" divergence is a different problem, where Solomonoff-style priors imply negative-exponential probabilities of Busy-Beaverish payoffs. Ordinary priors don't really have this problem.

[Houshalter]

It seems like the same class of problems, because they are both about high payoff, low probability bets. Solomonoff induction is just a formalization used to show the result is very general.

Any reasonable prior should have similar cases. Unless you really believe the mugger being a matrix lord has 0 probability, or that God has 0 probability, etc, you are forced to act as if they are true. Which results in wasted effort in the vast majority of possible outcomes, in exchange for a massive payoff in incredibly rare outcomes.

Assigning 0 probability is not something you should do lightly. It would mean you could wake up and find yourself outside of the matrix, and you still would not believe it had any chance of being true. It would mean God himself could come to and say "yeah it's all real." And you would be forced to believe there is still 0 probability he exists.