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Benquo comments on St. Petersburg Mugging Implies You Have Bounded Utility - Less Wrong
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Comments (163)
Utility doesn't have to take infinity as an argument in order to be infinite. It just has to have a finite output that can be summed over possible outcomes. In other words, if Sum(p X U(a) + (1-p) X U(^a)) is a valid expression of expected utility, then by induction, Sum X U(i)) should also be a valid expression for any finite n. When you take the limit as n->infinity you run into the problem of no finite expectation, but an arbitrarily large finite sum (which you can get with a stopping rule) ought to be able to establish the same point.
I still don't understand 3b. TimFreeman wasn't postulating an acausal universe, just one in which there are things we weren't expecting.
magfrump seems to have nailed it. I find it interesting how controversial that one has been :)
For infinite sums, basically, if the sum is infinite, then any finite probability gives it infinite expected utility (infinity * [1/N] = infinity). If both the sum and probability are finite, then one can argue the details (N * [1/N^2] < 1). The math is different between an arbitrarily large finite and an infinite. Or, at least, I've always assumed Pascal's Wager relied on that, because otherwise I don't see how it produces an infinite expected utility regardless of scepticism.
If the utility can be arbitrarily large depending on N, then an arbitrarily large finite skepticism discount can be overcome by considering a sufficiently large N.
Of course a skepticism discount factor that scales with N might be enough to obviate Pascal's Wager.