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SilasBarta comments on Thoughts on a possible solution to Pascal's Mugging - Less Wrong Discussion
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This, I think, is the biggest confounding issue on the Pascal's Mugging problem: that one's probability of being approached with that claim is not independent of how one responds to such claims. So if you're "the type to pay up" you will encounter such muggers far out of proportion to the "true" occurrence of beings that are willing and able to create a bunch of minds to torture (whatever that true frequency might be!).
In order to modify the problem to get to the "core" issue here [1], you would have to remove the part where the mugger benefits at your expense, which is what draws in the game-theoretic effects (and, of course, makes them analogous to a mugger in the first place).
So how does the problem look when the "mugger" "only" asks of you something that (as best you can determine?) doesn't cost you anything and doesn't benefit them either? But this part isn't so easily abstracted away either, because whether the mugger can conceal the fact that the proposed course of action benefits them at your expense is itself a game! Argh!
[1] the core issue being how to handle utilities that increase faster than probabilities, relative to the length of the message received
Why even bother with a mugger?
H1 = X sentient creatures will be created and tortured unless you go to the nearest window and throw a quarter into the street.
It's a conceivable hypothesis. If you set the P(H1) >0, you're subject to the same mugging without a mugger as long as you "shut up and multiply". Who needs a mugger to be mugged? Mug yourself! There's almost nothing you can't accomplish by giving credence to arbitrary ideas!
H2 = X sentient creatures will be created and tortured unless you don't go to the nearest window and throw a quarter into the street.
Oh noes! What do I do now?
If you expose pidgeons to intermittent random reward, you can observe the birth of supersticion: the animal will try to correlate the most disparate things to the reward. I long thought this was the kind of mechanism underlying human supersticions, but now it seems more likely that it can also be a self counterfactual mugging: if I open an umbrella in the house, I'm inviting death inside (I don't know if this belief exists outside Italy). Inviting death has such a bigger disutility that even in the tiny probability that the supersticion is real you're better not opening an umbrella in your house.
I've always heard it said that it's "bad luck" to open an umbrella inside (and live in the US), though not specifically that it invites death inside.
I always assumed it originated as a tale to get children not to open umbrellas indoors.
Unless you have some reason to believe H1 over H2 (or vice versa), stop wasting time pondering whether to throw quarters in the street. Introducing spurious infinities that just cancel out doesn't help you reason any.
Or, in other words, a belief is only useful if you have evidence to support it over a belief in the opposite direction.
Attention is a scarce resource. Listenning to the "mugger" already costs me something.
True, but you don't know what the person (not yet known to be a mugger) is saying until you listen! And you can't quite avoid that cost unless you avoid all communication with strangers (though some consider that route reasonable).