In a working paper, Christian Tarsney comes up with a clever resolution to this conflict
Fwiw, I was expecting that the “resolution” would be an argument for why you shouldn’t take the wager.
If you do consider it a resolution: if Alice said she would torture a googol people if you didn’t give her $5, would you give her the $5? (And if so, would you keep doing it if she kept upping the price, after you had already paid it?)
Thanks! I think the “stochastic dominance + background uncertainty” decision criterion makes two claims about muggings:
If the mugging is not too Pascallian, it stochastically dominates “safe” options, which is a pretty strong argument for accepting it (and probably agrees with what an expected value calculation would dictate)
If it is too Pascallian, neither it nor the safe option stochastically dominates, giving a principled reason for rejecting it
The hope is that your example would fall under case (2), but of course this depends on a bunch of particular assumptions about the background uncertainty.
Fwiw, I was expecting that the “resolution” would be an argument for why you shouldn’t take the wager.
If you do consider it a resolution: if Alice said she would torture a googol people if you didn’t give her $5, would you give her the $5? (And if so, would you keep doing it if she kept upping the price, after you had already paid it?)
Thanks! I think the “stochastic dominance + background uncertainty” decision criterion makes two claims about muggings:
If the mugging is not too Pascallian, it stochastically dominates “safe” options, which is a pretty strong argument for accepting it (and probably agrees with what an expected value calculation would dictate)
If it is too Pascallian, neither it nor the safe option stochastically dominates, giving a principled reason for rejecting it
The hope is that your example would fall under case (2), but of course this depends on a bunch of particular assumptions about the background uncertainty.