Eliezer, the money pump results from circular preferences, which should exist according to your description of the inconsistency. Suppose we have a million statements, each of which you believe to be true with equal confidence, one of which is “The LHC will not destroy the earth.”
Suppose I am about to pick a random statement from the list of a million, and I will destroy the earth if I happen to pick a false statement. By your own admission, you estimate that there is more than one false statement in the list. You will therefore prefer that I play a lottery with odds of 1 in a million, destroying the earth only if I win.
It makes no difference if I pick a number randomly between one and a million, and then play the lottery mentioned (ignoring the number picked.)
But now if I pick a number randomly between one and a million, and then play the lottery mentioned only if I didn’t pick the number 500,000, while if I do pick the number 500,000, I destroy the earth only if the LHC would destroy the earth, then you would prefer this state of affairs, since you prefer “destroy the earth if the LHC would destroy the earth” to “destroy the earth with odds of one in a million.”
But now I can also substitute the number 499,999 with some other statement that you hold with equal confidence, so that if I pick 499,999, instead of playing the lottery, I destroy the earth if this statement is false. You will also prefer this state of affairs for the same reason, since you hold this statement with equal confidence to “The LHC will not destroy the earth.”
And so on. It follows that you prefer to go back to the original state of affairs, which constitutes circular preferences and implies a money pump.
Eliezer, the money pump results from circular preferences, which should exist according to your description of the inconsistency. Suppose we have a million statements, each of which you believe to be true with equal confidence, one of which is “The LHC will not destroy the earth.”
Suppose I am about to pick a random statement from the list of a million, and I will destroy the earth if I happen to pick a false statement. By your own admission, you estimate that there is more than one false statement in the list. You will therefore prefer that I play a lottery with odds of 1 in a million, destroying the earth only if I win.
It makes no difference if I pick a number randomly between one and a million, and then play the lottery mentioned (ignoring the number picked.)
But now if I pick a number randomly between one and a million, and then play the lottery mentioned only if I didn’t pick the number 500,000, while if I do pick the number 500,000, I destroy the earth only if the LHC would destroy the earth, then you would prefer this state of affairs, since you prefer “destroy the earth if the LHC would destroy the earth” to “destroy the earth with odds of one in a million.”
But now I can also substitute the number 499,999 with some other statement that you hold with equal confidence, so that if I pick 499,999, instead of playing the lottery, I destroy the earth if this statement is false. You will also prefer this state of affairs for the same reason, since you hold this statement with equal confidence to “The LHC will not destroy the earth.”
And so on. It follows that you prefer to go back to the original state of affairs, which constitutes circular preferences and implies a money pump.