Utilities in decision theory are both scale and translation invariant. It makes no sense to ask what the utility of going extinct “would be” in isolation from the utilities of every other outcome. All that matters are ratios of differences of utilities, since those are all that are relevant to finding the argmax of the linear combination of utilities.
I’m not sure what you mean by “I believe that e has to be 0”, since e is a set of observations, not a number. Maybe you meant P(e) = 0? But this makes no sense either since then conditional probabilities are undefined.
I meant P(e) = 0 and the point was to show that that does not make sense. But I think Donald has shown me exactly where I went wrong. You cannot have a utility function and then not place it in a context within which you have other feasible actions. See my response to Hobson.
Utilities in decision theory are both scale and translation invariant. It makes no sense to ask what the utility of going extinct “would be” in isolation from the utilities of every other outcome. All that matters are ratios of differences of utilities, since those are all that are relevant to finding the argmax of the linear combination of utilities.
I’m not sure what you mean by “I believe that e has to be 0”, since e is a set of observations, not a number. Maybe you meant P(e) = 0? But this makes no sense either since then conditional probabilities are undefined.
I meant P(e) = 0 and the point was to show that that does not make sense. But I think Donald has shown me exactly where I went wrong. You cannot have a utility function and then not place it in a context within which you have other feasible actions. See my response to Hobson.