by Jessica Taylor 20 days ago | link | parent Counterfactual mugging doesn’t require spoofing. Consider the following problem: Suppose no one, given $$10^{5}$$ steps of computation, is able to compute any information about the parity of the $$10^{10}$$th digit of $$\pi$$, and everyone, given $$10^{100}$$ steps of computation, is able to compute the $$10^{10}$$th digit of $$\pi$$. Suppose that at time $$t$$, everyone has $$10^5$$ steps of computation, and at a later time $$t'$$, everyone has $$10^{100}$$ 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.

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