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.
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.