It’s worth noting that while the rationality axioms on which Harsanyi’s theorem depends are typically justified by Dutch book arguments, money pumps or the sure-thing principle, an expected utility maximization with an unbounded utility function (e.g. risk-neutral total utilitarianism) with infinitely many possible outcomes is actually vulnerable to Dutch books and money pumps and violates the sure-thing principle. See, e.g. Paul Christiano’s comment with St. Petersburg lotteries. To avoid the issue, you can commit to sticking with the ex ante better option, even though you know you’d later want to break the commitment. But such commitments can be used for other Dutch books, too, e.g. you can commit to never completing the last step of a Dutch book, or, on a more ad hoc basis, anticipate Dutch books and try to avoid them on a more ad hoc basis.
The continuity axiom is also intuitive and I’d probably accept continuity over ranges of individual utilities at least, anyway, but I wouldn’t take it to be a requirement of rationality, and without it, maximin/​leximin/​Rawl’s difference principle and lexical thresholds aren’t ruled out.
It’s worth noting that while the rationality axioms on which Harsanyi’s theorem depends are typically justified by Dutch book arguments, money pumps or the sure-thing principle, an expected utility maximization with an unbounded utility function (e.g. risk-neutral total utilitarianism) with infinitely many possible outcomes is actually vulnerable to Dutch books and money pumps and violates the sure-thing principle. See, e.g. Paul Christiano’s comment with St. Petersburg lotteries. To avoid the issue, you can commit to sticking with the ex ante better option, even though you know you’d later want to break the commitment. But such commitments can be used for other Dutch books, too, e.g. you can commit to never completing the last step of a Dutch book, or, on a more ad hoc basis, anticipate Dutch books and try to avoid them on a more ad hoc basis.
The continuity axiom is also intuitive and I’d probably accept continuity over ranges of individual utilities at least, anyway, but I wouldn’t take it to be a requirement of rationality, and without it, maximin/​leximin/​Rawl’s difference principle and lexical thresholds aren’t ruled out.