You’ve profoundly misunderstood McGee’s argument, Eliezer. The reason you need the expectation of the sum of an infinite number of random variables to equal the sum of the expectations of those random variable is exactly to ensure that choosing an action based on the expected value actually yields an optimal course of action.
McGee observed that if you have an infinite event space and unbounded utilities, there are a collection of random utility functions U1, U2, … such that E(U1 + U2 + …) != E(U1) + E(U2) + …. McGee then observes that if you restrict utilities to a bounded range, then in fact E(U1 + U2 + …) == E(U1) + E(U2) + …, which ensures that a series of choices based on the expected value always give the correct result. In contrast, the other paper—which you apparently approve of—happily accepts that when E(U1 + U2 + …) != E(U1) + E(U2) + …, an agent can be Dutch booked and defends this as still rational behavior.
Right now, you’re a “Bayesian decision theorist” who a) doesn’t believe in making choices based on expected utility, and b) accepts Dutch Books as rational. This is goofy.
You’ve profoundly misunderstood McGee’s argument, Eliezer. The reason you need the expectation of the sum of an infinite number of random variables to equal the sum of the expectations of those random variable is exactly to ensure that choosing an action based on the expected value actually yields an optimal course of action.
McGee observed that if you have an infinite event space and unbounded utilities, there are a collection of random utility functions U1, U2, … such that E(U1 + U2 + …) != E(U1) + E(U2) + …. McGee then observes that if you restrict utilities to a bounded range, then in fact E(U1 + U2 + …) == E(U1) + E(U2) + …, which ensures that a series of choices based on the expected value always give the correct result. In contrast, the other paper—which you apparently approve of—happily accepts that when E(U1 + U2 + …) != E(U1) + E(U2) + …, an agent can be Dutch booked and defends this as still rational behavior.
Right now, you’re a “Bayesian decision theorist” who a) doesn’t believe in making choices based on expected utility, and b) accepts Dutch Books as rational. This is goofy.