Utility functions have to be bounded basically because genuine martingales screw up decision theory—see the St. Petersburg Paradox for an example.
Economists, statisticians, and game theorists are typically happy to do so, because utility functions don’t really exist—they aren’t uniquely determined from someone’s preferences. For example, you can multiply any utility function by a constant, and get another utility function that produces exactly the same observable behavior.
One of my mistakes was believing in Bayesian decision theory, and in constructive logic at the same time. This is because traditional probability theory is inherently classical, because of the axiom that P(A + not-A) = 1. This is an embarassingly simple inconsistency, of course, but it lead me to some interesting ideas.
Upon reflection, it turns out that the important idea is not Bayesianism proper, which is merely one of an entire menagerie of possible rationalities, but rather de Finetti’s operationalization of subjective belief in terms of avoiding Dutch book bets. It turns out there are a lot of ways of doing that, because the only physically realizable bets are of finitely refutable propositions.
So you can have perfectly rational agents who never come to agreement, no matter how much evidence they see, because no finite amount of evidence can settle questions like whether the law of the excluded middle holds for propositions over the natural numbers.