Ah, I forgot. You use assumptions where you don’t accumulate the winnings between the different times Sleeping Beauty agrees to the bet.
Well, in that case, if the thirder has certain beliefs about how to handle the situation, you may actually be able to money pump them. And it seems that you expect those beliefs.
My point of view, if adopting the thirder perspective[1], would be for the thirder to treat this situation using different beliefs. Specifically, consider what counterfactually might happen if Sleeping Beauty gave different answers in different awakenings. Possible responses by the bet proposer might be:
a) average the results across the awakenings.
b) accept the bet agreement from one awakening at random.
Regardless of which case (a) or (b) occurs, instrumentally Sleeping Beauty’s betting EV for her bet decision, with non-accumulated bets, should be divided by the number of awakenings to take into account the reduced winnings or reduced chance of influencing whether the bet occurs.
Even if we assume that such disagreement between bet decisions in different awakenings is impossible, it seems strange to assume that a thirder should give different results in that case than the answer they would give where it is not impossible?
This adjustment can be conceptualized as compensating for an “unfair” bet where the bet is unequal between awakenings overall (where parity between awakenings in different scenarios is seen as “fair” by the thirder). I see this as no different in principle to a halfer upweighting trials with more awakenings in the converse scenario where bets are accumulated between trials and are thus “unfair” from the halfer perspective which sees parity between trials as fair, but not awakenings.
reminder: my point of view is that either thirderism or halferism is viable, but I am relatively thirder-adjacent precisely because I find the scenario where the winnings are accumulated between awakenings more natural than if the bet is proposed and agreed at each awakening but not accumulated.
Ah, I forgot. You use assumptions where you don’t accumulate the winnings between the different times Sleeping Beauty agrees to the bet.
Well, in that case, if the thirder has certain beliefs about how to handle the situation, you may actually be able to money pump them. And it seems that you expect those beliefs.
My point of view, if adopting the thirder perspective[1], would be for the thirder to treat this situation using different beliefs. Specifically, consider what counterfactually might happen if Sleeping Beauty gave different answers in different awakenings. Possible responses by the bet proposer might be:
a) average the results across the awakenings.
b) accept the bet agreement from one awakening at random.
Regardless of which case (a) or (b) occurs, instrumentally Sleeping Beauty’s betting EV for her bet decision, with non-accumulated bets, should be divided by the number of awakenings to take into account the reduced winnings or reduced chance of influencing whether the bet occurs.
Even if we assume that such disagreement between bet decisions in different awakenings is impossible, it seems strange to assume that a thirder should give different results in that case than the answer they would give where it is not impossible?
This adjustment can be conceptualized as compensating for an “unfair” bet where the bet is unequal between awakenings overall (where parity between awakenings in different scenarios is seen as “fair” by the thirder). I see this as no different in principle to a halfer upweighting trials with more awakenings in the converse scenario where bets are accumulated between trials and are thus “unfair” from the halfer perspective which sees parity between trials as fair, but not awakenings.
reminder: my point of view is that either thirderism or halferism is viable, but I am relatively thirder-adjacent precisely because I find the scenario where the winnings are accumulated between awakenings more natural than if the bet is proposed and agreed at each awakening but not accumulated.