Omega makes a simulation of you. One of you is presented with an offer Omega offers them $1000. 1. If the simulation is offered the $1000 dollars and rejects it, the real you gets a $10,000. 2. If the simulation is offered the $1,000 dollars and accepts it, the real you gets $100. 3. If the real you is offered $1000 and accepts it, the real you gets $1000. 4. If the real you is offered $1000 and rejects it, the real you gets $0.
Immeidately after completion of the decision problem, the simulation is terminated. The probability of selecting simulation or real you by Omega is not known. (OMega may always select one option, select both options with equal probability, or select options with any valid probabilities).
You find yourself in the game, with the rules explained as such to you. You don't know if you're the simulation or real, do you accept the $1000 or reject it?
The payoffs only need be of the form: 1. $k*X (k: 1 < k) (X: 1 < X) 2. $X/k 3. $X 4. $0
If $1000 is irrelevant to you, then substitute for any enticing value of X, and replace $X with X utils. There is no diminishing returns on the utility you gain from the reward Omega gives you.
Do you have a strategy for a general form of this problem?
There's no good reason for assigning 50% probability to game A but neither is there a good reason to assign any other probability. I guess I can say that i'm using something like "fair Omega prior" that assumes that Omega is not trying to trick me.
You and Gurkenglas seem to assume that Omega would try to minimize your reward. What is the reason for that?
You and Gurkenglas seem to assume that Omega would try to minimize your reward
Base rate pessimism and TANSTAAFL. Offers of free money are almost always tricks, so my prior is that the next offer is also a trick. I expect not to be paid at all, so choosing the option that's clearly a violation if I'm not paid is a much clearer cheat than choosing the one where Omega can claim to play by the rules and not pay me.
If you state that I don't know a probability, I have to use other assumptions. 50/50 is a lazy assumption.
Note: this boils down to "where do you get your priors?", which is unsolved in Bayesean rationality.
The idea for this problem is gotten from dmytryl.
The payoffs only need be of the form: 1. $k*X (k: 1 < k) (X: 1 < X)
2. $X/k
3. $X
4. $0
If $1000 is irrelevant to you, then substitute for any enticing value of X, and replace $X with X utils. There is no diminishing returns on the utility you gain from the reward Omega gives you.
Do you have a strategy for a general form of this problem?