Assume that the basic reasoning for this is true, but nobody actually does the mugging. Since the probability doesn’t actually make a significant difference to the expected utility, I’ll just simplify and say there equal.
The total expected marginal utility, assuming you’re equally likely to save or kill the people, would be (3^^^3 − 3^^^3) + (3^^^^3 − 3^^^^3) + (3^^^^^3 − 3^^^^^3) + … = 0. At least, it would be if you count it by alternating with saving and killing. You could also count it as 3^^^3 + 3^^^^3 − 3^^^3 + 3^^^^^3 − 3^^^^3 + … = infinity. Or you could count it as −3^^^3 − 3^^^^3 + 3^^^3 − 3^^^^^3 + 3^^^^3 - … = -infinity. Or you could even do 3^^^3 − 3^^^3 + 3^^^^3 − 3^^^^3 + 3^^^^^3 − 3^^^^^3 + … (without parentheses) which doesn’t even converge to anything.
You could also construct hypothetical possibility sets where you can set it to add to any given number by rearranging the possibilities.
It’s one thing when order matters for talking about total utility of an infinitely long universe. It at least has an order, assuming you don’t mind abandoning special relativity, but what order are you even supposed to count expected utility in?
I figure the only way out of this is to use a prior that decreases with expected utility faster than those formulations of Occam’s razor would suggest. I don’t like the idea of doing this, but not doing so just doesn’t add up.
Assume that the basic reasoning for this is true, but nobody actually does the mugging. Since the probability doesn’t actually make a significant difference to the expected utility, I’ll just simplify and say there equal.
The total expected marginal utility, assuming you’re equally likely to save or kill the people, would be (3^^^3 − 3^^^3) + (3^^^^3 − 3^^^^3) + (3^^^^^3 − 3^^^^^3) + … = 0. At least, it would be if you count it by alternating with saving and killing. You could also count it as 3^^^3 + 3^^^^3 − 3^^^3 + 3^^^^^3 − 3^^^^3 + … = infinity. Or you could count it as −3^^^3 − 3^^^^3 + 3^^^3 − 3^^^^^3 + 3^^^^3 - … = -infinity. Or you could even do 3^^^3 − 3^^^3 + 3^^^^3 − 3^^^^3 + 3^^^^^3 − 3^^^^^3 + … (without parentheses) which doesn’t even converge to anything.
You could also construct hypothetical possibility sets where you can set it to add to any given number by rearranging the possibilities.
It’s one thing when order matters for talking about total utility of an infinitely long universe. It at least has an order, assuming you don’t mind abandoning special relativity, but what order are you even supposed to count expected utility in?
I figure the only way out of this is to use a prior that decreases with expected utility faster than those formulations of Occam’s razor would suggest. I don’t like the idea of doing this, but not doing so just doesn’t add up.