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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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