This isn’t really a problem if the rewards start out high and gradually diminish.
I.e., suppose that you value your life at $L (i.e., you’re willing to die if the heirs of your choice get L dollars), and you assign a probability of 10^-15 to H1 = “I am immune to losing at Russian roulette”, something like 10^ 4 to H2 = “I intuitively twist the gun each time to avoid the bullet”,, and a probability of something like 10^-3 to H3 = “they gave me an empty gun this time”. Then you are offered to play enough rounds of Russian roulette for a price of $L/round until you update to arbitrary levels.
Now, if you play enough times, H3 becomes the dominant hypothesis with say 90% probability, so you’d accept a payout for, say, $L/2. Similarly, if you know that H3 isn’t the case, you’d still assign very high probability to something like H2 after enough rounds, so you’d still accept a bounty of $L/2.
Now, suppose that all the alternative hypothesis H2, H3,… are false, and your only other alternative hypothesis is H1 (magical intervention). Now the original dilemma has been saved. What should one do?
This isn’t really a problem if the rewards start out high and gradually diminish.
I.e., suppose that you value your life at $L (i.e., you’re willing to die if the heirs of your choice get L dollars), and you assign a probability of 10^-15 to H1 = “I am immune to losing at Russian roulette”, something like 10^ 4 to H2 = “I intuitively twist the gun each time to avoid the bullet”,, and a probability of something like 10^-3 to H3 = “they gave me an empty gun this time”. Then you are offered to play enough rounds of Russian roulette for a price of $L/round until you update to arbitrary levels.
Now, if you play enough times, H3 becomes the dominant hypothesis with say 90% probability, so you’d accept a payout for, say, $L/2. Similarly, if you know that H3 isn’t the case, you’d still assign very high probability to something like H2 after enough rounds, so you’d still accept a bounty of $L/2.
Now, suppose that all the alternative hypothesis H2, H3,… are false, and your only other alternative hypothesis is H1 (magical intervention). Now the original dilemma has been saved. What should one do?