This is equivalent to Newcomb’s Problem in the sense that any strategy does equally well on both, where by “strategy” I mean a mapping from info to (probability distributions over) actions.
I don’t see this. For example, the mixed strategy of one-boxing half the time and two-boxing half the time generates very different results in the transformed problem than in the original Newcomb’s Problem.
Though I suppose there may be some ambiguity in the question of what amnesia is supposed to do to the ‘seed’ in your pseudo-random number generator.
Does CDT return the winning answer in such transformed problems?
It does fine on your transformation of Newcomb. I won’t venture a guess on more general problems, because I don’t understand how the general transformation is imagined to work. What is the transformation of the Hitchhiker, for example?
I don’t see this. For example, the mixed strategy of one-boxing half the time and two-boxing half the time generates very different results in the transformed problem than in the original Newcomb’s Problem.
Conventionally, you are not allowed access to a random number generator in Newcomb’s Problem—and so can’t use a mixed strategy. Any such usage would tarnish Omega’s reputation. Omega—being a mind-reading superintelligence—can fairly easily discourage such a tactic by punishing randomising agents economically—and letting the punishment strategy be known.
I don’t see this. For example, the mixed strategy of one-boxing half the time and two-boxing half the time generates very different results in the transformed problem than in the original Newcomb’s Problem.
Nope? Let’s say you flip a coin. Then your expected winnings are
if you one-box with probability p, Omega fills box B with probability p
What is the transformation of the Hitchhiker, for example?
Put the player in front of an ATM and give them the amnesia drug. If they don’t pay you $100, take them to the desert and dump them there. If they paid, put the money from the first round back into their bank account and give them the amnesia drug again. If they pay you again, keep their money. And the player knows these rules.
if you one-box with probability p, Omega fills box B with probability p
Really? I thought Omega would correctly predict the results of the coin flip and whether I called heads or tails. I guess this shows that Omega is better at predicting what I do than I am at predicting what he does.
In any case, thank you for the thought experiment. I agree with Snowyowl that your version is philosophically different from the original, but if we want our philosophical concepts to pay rent, they are going to have to have different consequences than some cheap amnesia drug. Otherwise, why keep them around?
I don’t see this. For example, the mixed strategy of one-boxing half the time and two-boxing half the time generates very different results in the transformed problem than in the original Newcomb’s Problem.
Though I suppose there may be some ambiguity in the question of what amnesia is supposed to do to the ‘seed’ in your pseudo-random number generator.
It does fine on your transformation of Newcomb. I won’t venture a guess on more general problems, because I don’t understand how the general transformation is imagined to work. What is the transformation of the Hitchhiker, for example?
Conventionally, you are not allowed access to a random number generator in Newcomb’s Problem—and so can’t use a mixed strategy. Any such usage would tarnish Omega’s reputation. Omega—being a mind-reading superintelligence—can fairly easily discourage such a tactic by punishing randomising agents economically—and letting the punishment strategy be known.
Nope? Let’s say you flip a coin. Then your expected winnings are
0.5x(0.5x1000000+0.5x(1000000+1000))+0.5x(0.5x0+0.5x(0+1000)) = 500500 dollars
in both versions if Omega follows the rule:
if you one-box with probability p, Omega fills box B with probability p
Put the player in front of an ATM and give them the amnesia drug. If they don’t pay you $100, take them to the desert and dump them there. If they paid, put the money from the first round back into their bank account and give them the amnesia drug again. If they pay you again, keep their money. And the player knows these rules.
I don’t have the general transformation down yet.
Really? I thought Omega would correctly predict the results of the coin flip and whether I called heads or tails. I guess this shows that Omega is better at predicting what I do than I am at predicting what he does.
In any case, thank you for the thought experiment. I agree with Snowyowl that your version is philosophically different from the original, but if we want our philosophical concepts to pay rent, they are going to have to have different consequences than some cheap amnesia drug. Otherwise, why keep them around?