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Jiro comments on Simulation argument meets decision theory - Less Wrong Discussion
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Your utility calculation determines the result of each button, and therefore which button you will press. But the likelihood of being in a simulation determines the result of your utility calculation. And which button you press determines (via the computer simulating you or not) the likelihood of being in a simulation. So your utility calculation is indirectly trying to determine its own result.
Just do it this way:
- Assume you pick "sim" => calculate the probability of being a simulation conditional on picking "sim" => calculate the expected utility conditional on picking "sim" and on the calculated probabilties.
- Assume you pick "don't sim" => calculate the probability of being a simulation conditional on picking "don't sim" => calculate the expected utility conditional on picking "don't sim" and on the calculated probabilities.
Then just pick whichever of the two has the highest expected utility. No infinite regress there!