This is a linkpost for Von Neumann–Morgenstern utility theorem, which shows that one accepts 4 premises if and only if one maximises expected utility. In my mind, all the 4 premises are self-evident. So I do not see how one can reject maximising expected utility in principle. Relatedly, I think the Repugnant Conclusion follows from 3 self-evident premises.
In 1947, John von Neumann and Oskar Morgenstern proved that any individual whose preferences satisfied four axioms [premises] has a utility function, where such an individual's preferences can be represented on an interval scale [which "allows for defining the degree of difference between measurements"] and the individual will always prefer actions that maximize expected utility.[1] That is, they proved that an agent is (VNM-)rational [has preferences satisfying the 4 axioms] if and only if there exists a real-valued function u defined by possible outcomes such that every preference of the agent is characterized by maximizing the expected value of u, which can then be defined as the agent's VNM-utility (it is unique up to affine transformations i.e. adding a constant and multiplying by a positive scalar). No claim is made that the agent has a "conscious desire" to maximize u, only that u exists.
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Completeness assumes that an individual has well defined preferences:
Axiom 1 (Completeness) For any lotteries and , either or .
(the individual must express some preference or indifference[4]). Note that this implies reflexivity.
Transitivity assumes that preferences are consistent across any three options:
Axiom 2 (Transitivity) If and , then .
Continuity assumes that there is a "tipping point" between being better than and worse than a given middle option:
Axiom 3 (Continuity): If , then there exists a probability such that
where the notation on the left side refers to a situation in which is received with probability and is received with probability .
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Independence assumes that a preference holds independently of the probability of another outcome.
Axiom 4 (Independence): For any and (with the "irrelevant" part of the lottery underlined):
if and only if
In other words, the probabilities involving cancel out and don't affect our decision, because the probability of is the same in both lotteries.
Thanks.
A partly underlying issue here is that it's not clear that the consequentialist/non-consequentialist division is actually all that deep or meaningful if you really think about it. The facts about "utility" in a consequentialist theory, are plausibly ultimately just a kind of short-hand for facts about preferability between outcomes that could be stated without any mention of numbers/utility/maximizing (at least if we allow infinitely long statements). But for non-consequentialist theories, you can also derive a preferability relation on outcomes (where what you do is part of the outcome, not just the results of your action), based on what the theory says you should do in a forced choice. For at least some such theories that look "deontic", in the sense of having rights that you shouldn't violate, even if it leads to higher net well-being, the resulting preferability ranking might happen to obey the 4 axioms and be VNM-rational. For such a deontic theory you could then express the theory as maximizing a relevant notion of utility if you really wanted to (at least if you can cardinalize the resulting ordering of actions by prefertability, via looking at preferences between chance-y prospects I don't know enough to know if meeting the axioms guarantees you can do this.) So any consequentialist theory is sort of really a number/utility-free theory about preferability in disguise, and at least some very deontic feeling theories are in some sense equivalent to consequentialist theories phrased in terms of utility.
Or so it seems to me anyway, I'm certainly not a real expert on this stuff.