Counterfactual mugging doesn’t require spoofing. Consider the following problem:
Suppose no one, given 105 steps of computation, is able to compute any information about the parity of the 1010th digit of π, and everyone, given 10100 steps of computation, is able to compute the 1010th digit of π. Suppose that at time t, everyone has 105 steps of computation, and at a later time t′, everyone has 10100 steps of computation. At the initial time t, Omega selects a probability p equal to the conditional probability Omega assigns to the agent paying $1 at time t′ conditional on the digit being odd. (This could be because Omega is a logical inductor, or because Omega is a CDT agent whose utility function is such that selecting this value of p is optimal). At time t′, if the digit is even, a fair coin with probability p of coming up heads is flipped, and if it comes up heads, Omega pays the agent $10. If instead the digit is odd, then the agent has the option of paying Omega $1.
This contains no spoofing, and the optimal policy for the agent is to pay up if asked.
Counterfactual mugging doesn’t require spoofing. Consider the following problem:
Suppose no one, given 105 steps of computation, is able to compute any information about the parity of the 1010th digit of π, and everyone, given 10100 steps of computation, is able to compute the 1010th digit of π. Suppose that at time t, everyone has 105 steps of computation, and at a later time t′, everyone has 10100 steps of computation. At the initial time t, Omega selects a probability p equal to the conditional probability Omega assigns to the agent paying $1 at time t′ conditional on the digit being odd. (This could be because Omega is a logical inductor, or because Omega is a CDT agent whose utility function is such that selecting this value of p is optimal). At time t′, if the digit is even, a fair coin with probability p of coming up heads is flipped, and if it comes up heads, Omega pays the agent $10. If instead the digit is odd, then the agent has the option of paying Omega $1.
This contains no spoofing, and the optimal policy for the agent is to pay up if asked.