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Qiaochu_Yuan comments on Philosophical Landmines - Less Wrong
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The agents that can be modeled as having a utility function are precisely the VNM-rational agents. Having a deontological rule that you always stick to even in the probabilistic sense is not VNM-rational (it violates continuity). On the other hand, I don't believe that most people who sound like they're deontologists are actually deontologists.
That's interesting, can you elaborate?
This is something of a strawman, but suppose one of your deontological rules was "thou shalt not kill" and you refused to accept outcomes where there is a positive probability that you will end up killing someone. (We'll ignore the question of how you decide between outcomes both of which involve killing someone.) In the notation of the Wikipedia article, if L is an outcome that involves killing someone and M and N are not, then the continuity axiom is not satisfied for (L, M, N).
Behaving in this way is more or less equivalent to having a utility function in which killing people has infinite negative utility, but this isn't a case covered by the VNM theorem (and is a terrible idea in practice because it leaves you indifferent between any two outcomes that involve killing people).
I'm trying to avoid eliding the difference between "I think the right thing to do is given by this rule" and "I always stick to this rule"... that is, the difference between having a particular view of what morality is, vs. actually always being moral according to that view.
But I agree that VNM-violations are problematic for any supposedly utilitarian agent, including humans who self-describe as deontologists and I assert above can nevertheless be modeled as utilitarians, but also including humans who self-describe as utilitarians.