“Indeed Pascal’s Mugging type issues are already present with the more standard infinities.”
Right, infinity of any kind (surreal or otherwise) doesn’t belong in decision theory.
But Pascal’s Mugging type issues are present with large finite numbers, as well. Do you bite the bullet in the finite case, or do you think that unbounded utility functions don’t belong in decision theory, either?
The latter. It doesn’t even make sense to speak of maximizing the expectation of an unbounded utility function, because unbounded functions don’t even have expectations with respect to all probability distributions.
There is a way out of this that you could take, which is to only insist that the utility function has to have an expectation with respect to probability distributions in some restricted class, if you know your options are all going to be from that restricted class. I don’t find this very satisfying, but it works. And it offers its own solution to Pascal’s mugging, by insisting that any outcome whose utility is on the scale of 3^^^3 has prior probability on the scale of 1/(3^^^3) or lower.
But Pascal’s Mugging type issues are present with large finite numbers, as well. Do you bite the bullet in the finite case, or do you think that unbounded utility functions don’t belong in decision theory, either?
The latter. It doesn’t even make sense to speak of maximizing the expectation of an unbounded utility function, because unbounded functions don’t even have expectations with respect to all probability distributions.
There is a way out of this that you could take, which is to only insist that the utility function has to have an expectation with respect to probability distributions in some restricted class, if you know your options are all going to be from that restricted class. I don’t find this very satisfying, but it works. And it offers its own solution to Pascal’s mugging, by insisting that any outcome whose utility is on the scale of 3^^^3 has prior probability on the scale of 1/(3^^^3) or lower.