It’s worth pointing out that their theorems 2.2 and 3.5 are compatible with Rawls’ difference principle/leximin/maximin (infinite risk-aversion), so their results generalize both Harsanyi’s and Rawls’ approaches, rather than defend utilitarianism against Rawls. They don’t require continuity or cardinal welfare for these theorems, and as far as I know, continuity is not actually an axiom justifiable with Dutch books or money pumps, so I’m not sure what reason we have to believe it other than pure intuition, which is especially suspect in extreme tradeoffs (e.g. involving torture) and because of time-inconsistency in our preferences.
Continuity would of course also fail under utilitarianism with stochastic separability and infinite stakes, i.e. Pascalian problems, although I suppose one defence might be that the physical differences in outcomes are also infinite in these cases, so we might only have continuity starting from finite physical differences and extend it from there.
I don’t think continuity deserves to be called a rationality axiom, and without it and cardinal welfare, the case for utilitarianism as normally conceived falls apart.
It’s worth pointing out that their theorems 2.2 and 3.5 are compatible with Rawls’ difference principle/leximin/maximin (infinite risk-aversion), so their results generalize both Harsanyi’s and Rawls’ approaches, rather than defend utilitarianism against Rawls. They don’t require continuity or cardinal welfare for these theorems, and as far as I know, continuity is not actually an axiom justifiable with Dutch books or money pumps, so I’m not sure what reason we have to believe it other than pure intuition, which is especially suspect in extreme tradeoffs (e.g. involving torture) and because of time-inconsistency in our preferences.
Continuity would of course also fail under utilitarianism with stochastic separability and infinite stakes, i.e. Pascalian problems, although I suppose one defence might be that the physical differences in outcomes are also infinite in these cases, so we might only have continuity starting from finite physical differences and extend it from there.
I don’t think continuity deserves to be called a rationality axiom, and without it and cardinal welfare, the case for utilitarianism as normally conceived falls apart.