Even if you had solid evidence that your utility function was bounded, there would still be a small probability that your utility function was unbounded or bounded at a much higher level than you presumed. Pascal’s mugger simply has to increase his threat to compensate for your confidence in low-level utility bounding.
You can expand out any logical uncertainty about your utility function to get another utility function, and that is what must be bounded. This requires that the weighted average of the candidate utility functions converges to some (possibly higher) bound. But this is not difficult to achieve; and if they diverge, then you never really had a bounded utility function in the first place.
You can expand out any logical uncertainty about your utility function to get another utility function, and that is what must be bounded. This requires that the weighted average of the candidate utility functions converges to some (possibly higher) bound. But this is not difficult to achieve; and if they diverge, then you never really had a bounded utility function in the first place.