Whoops—EV re-updated.
Perhaps I am misunderstanding the setup of the counterfactual mugging—do we live in a world in which Omega is a known being (and just hasn’t yet interacted with us), or do we live in a world in which we have roughly equal credence of the existence of Omega vs Nomega (vs any other arbitrary God-like figure). If it’s the former, then sure UDT says precommit and pay.
But if its the latter, I still don’t see why UDT tells us to pay—not because not precommitting is some sort of default (which is I agree UDT says isn’t relevant) but because when making decisions based on the possible existence of some sort of God while ignoring the possible existence of other God’s isn’t fair or an effective way to maximize you expected utility. Perhaps some sort of Occam’s Razor / Solomon Induction argument could be made that Omega is simpler and thus more likely to exist, but this seems fairly difficult to rigorize.
Hi Vladimir, thanks for your response.
Upon further reflection, I think the crux of my argument is that by precommiting you are essentially pascals wagering yourself—you are making a decision looking to maximize yoir reward should a certain type of God (Omega) exist. Unless (before you get mugged) you have some reason to believe that this type of God is more likley to exist then the opposite type (Nomega), then precommiting is getting wagered (as far as I can tell). You cant wait until you find out that Omega exists to preccomit because by then you have aready learned that the coin is tails—you have to do so blind.
I dont think this proves to much becuase in other problems (Prisoners Dilema, Newcombs Paradox, etc.) considering what to do if a random God shows is wagering, so you just ignore it. Here, though, precommiting is wagering, so (it seems to me) that youshould just ignore it as well and not precommit.
Good point on EV numbers—they are now updated although the actual numbers are not super important to the crux of the argument.