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.
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!
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!