As I said in the posts surrounding this one, I think we should be asking what the correct decision is, not what the probabilities mean. “Subjective anticipation” is something evolved to deal with standard human behaviour up until now, so we need not expect it to behave properly in copying/deleting cases.
So how to make this into a decision theory? Well, there are several ways, and they each give you a different answer. To get resolution 3, assume that each person in worlds W2 and L2 is to be approached with a bet on which world they are in, with the winnings going to a mutually acceptable charity. Then they would bet at 4:1 odds, as multiple wins in W1 add up.
To get resolution 2, have the same bet offered twice: at W1/L1 and W2/L2. At W1/L1, you would take even odds (since there is a single winning) and at W2/L2 you would take 4:1 odds.
Resolution 1 seems to be similar, but I can’t say, since the problem is incomplete: how altruistic your copies are to one another, for instance, is a crucial component in deciding the right behaviour under these conditions (would one copy take a deal that give it $1 while taking $1000 from each of the other copies?). If the copies are not mutually altruistic, then this leads to a preference reversal (I would not want a future copy to take that deal) which someone can exploit for free money.
But the probabilities don’t mean anything, absent a decision theory (that deals with multiple copies making the same decisions) and a utility. Arguing about them does seem to me like arguing about the sound of trees falling in the forest.
As I said in the posts surrounding this one, I think we should be asking what the correct decision is, not what the probabilities mean. “Subjective anticipation” is something evolved to deal with standard human behaviour up until now, so we need not expect it to behave properly in copying/deleting cases.
So how to make this into a decision theory? Well, there are several ways, and they each give you a different answer. To get resolution 3, assume that each person in worlds W2 and L2 is to be approached with a bet on which world they are in, with the winnings going to a mutually acceptable charity. Then they would bet at 4:1 odds, as multiple wins in W1 add up.
To get resolution 2, have the same bet offered twice: at W1/L1 and W2/L2. At W1/L1, you would take even odds (since there is a single winning) and at W2/L2 you would take 4:1 odds.
Resolution 1 seems to be similar, but I can’t say, since the problem is incomplete: how altruistic your copies are to one another, for instance, is a crucial component in deciding the right behaviour under these conditions (would one copy take a deal that give it $1 while taking $1000 from each of the other copies?). If the copies are not mutually altruistic, then this leads to a preference reversal (I would not want a future copy to take that deal) which someone can exploit for free money.
But the probabilities don’t mean anything, absent a decision theory (that deals with multiple copies making the same decisions) and a utility. Arguing about them does seem to me like arguing about the sound of trees falling in the forest.