Suppose Omega forces you to chose a number 0<p<=1 and then, with probability p, you get tortured for 1/(p²) seconds. Assume for any T, being tortured for 2T seconds is exactly twice as bad as being tortured for T seconds. Also assume that your memory gets erased afterwards (this is to make sure there won’t be additional suffering from something like PTSD)
The expected value of seconds being tortured is p * 1/(p²)=1/p, so, in terms of expected value, you should chose p=1 and be tortured for 1 second. The smaller the p you chose, the higher the expected value.
Would you actually chose p=1 to maximize the expected value, or would you rather chose a very low p (like 1/3^^^^3)?
slightly related:
Suppose Omega forces you to chose a number 0<p<=1 and then, with probability p, you get tortured for 1/(p²) seconds.
Assume for any T, being tortured for 2T seconds is exactly twice as bad as being tortured for T seconds.
Also assume that your memory gets erased afterwards (this is to make sure there won’t be additional suffering from something like PTSD)
The expected value of seconds being tortured is p * 1/(p²)=1/p, so, in terms of expected value, you should chose p=1 and be tortured for 1 second. The smaller the p you chose, the higher the expected value.
Would you actually chose p=1 to maximize the expected value, or would you rather chose a very low p (like 1/3^^^^3)?