Added: Just noted that McGee's original formulation used a scenario whose limiting payoff was $.50, not +infinity, and also that the formula I used in the original blog post was not consistent. This has been corrected. You can construct finite-payoff or infinite-payoff versions of McGee's dilemma.

Fun fact: In the finite version of McGee's dilemma, if I take all the odd-numbered bets in the sequence (the first bet $-1 versus $+3, the third bet $-10 versus $+21, etc.) the expected value of my bet approaches a limit of $+1/3, and if I take all the even numbered bets the expected value of my bets approaches a limit of $+1/6. If I take all the bets, this approaches a limit of $+1/2, but according to McGee has an actual expected value of $-1. Or in the infinite-expected-payoff version, McGee has +infinity + +infinity = -1. Never mind having the expectation of a sum of an infinite number of variables not equalling the sum of the expectations; here we have the expectation of the sum of two bets not equalling the sum of the expectations.

If McGee is allowed to do that - who knows, maybe time is infinite and so is physics - then I'm allowed to have a rational Bayesian's infinite strategy not look like their finite strategy.

Infinities are thorny problems for any decision theory - Nick Bostrom has a large paper on this - but as said, using a bounded utility function doesn't solve anything. I can still offer you an infinite series of swaps over infinite time that delays your payoff into the indefinite future, so that the upper bound of the plans is not in the set of plans and there is no optimal (non-dominated) decision.