Nobody has any idea how accurate Omega’s predictions are.
If you interpret that as a uniform prior between 0% accurate and 100% accurate, then Omega’s “prediction” is a coin toss. If Omega’s predictive accuracy is something you have no other reason to care about, take both boxes.
However, being the sort of person who takes the box makes you less likely to exist in worlds where this prediction is accurate, and more likely to exist in worlds where the prediction is inaccurate. So if you think that Omega’s predictive accuracy on this question is correlated with his predictive accuracy on other questions, and you strongly want future predictions to be accurate, don’t take box A.
It seems odd to describe something as a prediction when you believe it uncorrelated with the outcome. Suppose you think Omega’s predictions are somewhere between 50% and 90% accurate.
Being the sort of person that takes both boxes makes you less likely to exist. So don’t take box A unless you think that the universe you are in is exceptionally bad and want to destroy it.
If you interpret that as a uniform prior between 0% accurate and 100% accurate, then Omega’s “prediction” is a coin toss. If Omega’s predictive accuracy is something you have no other reason to care about, take both boxes.
However, being the sort of person who takes the box makes you less likely to exist in worlds where this prediction is accurate, and more likely to exist in worlds where the prediction is inaccurate. So if you think that Omega’s predictive accuracy on this question is correlated with his predictive accuracy on other questions, and you strongly want future predictions to be accurate, don’t take box A.
It seems odd to describe something as a prediction when you believe it uncorrelated with the outcome. Suppose you think Omega’s predictions are somewhere between 50% and 90% accurate.
Being the sort of person that takes both boxes makes you less likely to exist. So don’t take box A unless you think that the universe you are in is exceptionally bad and want to destroy it.