Let’s consider writing a computer program to answer the question instead of doing it ourselves.
Program A: First it prints out 0.5 then it is given one of two inputs “red” or “blue”. If it is given “red” it prints out 0.01 and if it is given “blue” it prints out 0.99.
Program B: Prints out 0.5, ignores input then prints out 0.5 again.
Now we can run the red/blue room simulation many times and see which program makes better guesses.
I didn’t actually write the program, but with this point of view it is easy to see what happens: Strategy A works best in the majority of cases except for the one unlucky guy whose prediction is right off (due to being in a misleading difficult situation), Strategy B works badly in all cases except it’s better than A for that one guy.
So you may have found this a paradox in the sense that (for this one guy who was put into a confusing situation) being more rational can mean you make a much worse prediction!
Let’s consider writing a computer program to answer the question instead of doing it ourselves.
Program A: First it prints out 0.5 then it is given one of two inputs “red” or “blue”. If it is given “red” it prints out 0.01 and if it is given “blue” it prints out 0.99.
Program B: Prints out 0.5, ignores input then prints out 0.5 again.
Now we can run the red/blue room simulation many times and see which program makes better guesses.
I didn’t actually write the program, but with this point of view it is easy to see what happens: Strategy A works best in the majority of cases except for the one unlucky guy whose prediction is right off (due to being in a misleading difficult situation), Strategy B works badly in all cases except it’s better than A for that one guy.
So you may have found this a paradox in the sense that (for this one guy who was put into a confusing situation) being more rational can mean you make a much worse prediction!