Yes, Sleeping Beauty has to account for the fact that, even if the result of the coin flip was such that she’s being woken up on both Monday and Tuesday, if she bets on it being Monday, she will surely lose one of the two times. So she needs an extra dollar in the pot from the counterparty: betting $1 to $2 rather than $1 to $1. That pays for the loss when she makes the same bet on Tuesday. In expectation this is a fair bet: she either puts $1 in the pot and loses it, or puts $1 in the pot and gets $3 and then puts $1 in the pot and loses it, getting $2 total.
Anyway, feeling something is an action. I think it’s a mistake when people take “anticipation” as primary. Sure, “Make Beliefs Pay Rent (In Anticipated Experiences)” is good advice, in a similar way as a guide to getting rich is good advice. Predictive beliefs, like money, are good to pursue on general principle, even before you know what you’re going to use them for. But my anticipations of stuff is good for me to the extent that the consequences of anticipating it are good for me. Like any other action.
Yes, Sleeping Beauty has to account for the fact that, even if the result of the coin flip was such that she’s being woken up on both Monday and Tuesday, if she bets on it being Monday, she will surely lose one of the two times. So she needs an extra dollar in the pot from the counterparty: betting $1 to $2 rather than $1 to $1. That pays for the loss when she makes the same bet on Tuesday. In expectation this is a fair bet: she either puts $1 in the pot and loses it, or puts $1 in the pot and gets $3 and then puts $1 in the pot and loses it, getting $2 total.
Anyway, feeling something is an action. I think it’s a mistake when people take “anticipation” as primary. Sure, “Make Beliefs Pay Rent (In Anticipated Experiences)” is good advice, in a similar way as a guide to getting rich is good advice. Predictive beliefs, like money, are good to pursue on general principle, even before you know what you’re going to use them for. But my anticipations of stuff is good for me to the extent that the consequences of anticipating it are good for me. Like any other action.