You choose some numbers to represent “max goodness” and “max badness”; really good and bad things approach these bounds asymptotically; and when you meet Pascal’s mugger, you take “max badness”, multiply it by an extremely tiny value, and get a very tiny value.
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.
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.
Another approach is to calibrate my estimation of probabilities such that my prior probability for the claim that you have the power to create X units of disutility decreases the greater X is. That is, if I reliably conclude that P(X) ⇐ P(Y)/2 when X is twice the threat of Y, then increasing the mugger’s threat won’t make me more likely to concede to it.
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.
Another approach is to calibrate my estimation of probabilities such that my prior probability for the claim that you have the power to create X units of disutility decreases the greater X is. That is, if I reliably conclude that P(X) ⇐ P(Y)/2 when X is twice the threat of Y, then increasing the mugger’s threat won’t make me more likely to concede to it.