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, Michael.
Sorry for the lack of clarity. In principle, I am open to lotteries with arbitrarily large expected utility, but not infinite, and continuity does not rule out arbitratily large expected utilities. I am open to lotteries with arbitrarily many outcomes (in principle), but not to lotteries with infinitely many outcomes (not even in principle).
I think empirical evidence can take us from a very large universe to an arbitrarily large universe (for arbitrarily strong evidence), but never to an infinite universe. An arbitrarily large universe would still be infinitely smaller than an infinite universe, so I would say the former provides no empirical evidence for the latter. So I am confused about why discussions about infinite ethics often mention there is empirical evidence pointing to the existence of infinity[1]. Assigning a probability of 0 to something for which there is not empirical evidence at all makes sense to me.
I have not looked into the post you linked, but you guessed correctly. Which constraints would be forced as a result? I do not think preferential gaps make sense in principle.
Thanks for the links. Plato's section The Challenge from Risk Aversion argues for risk aversion based on observed risk aversion with respect to resources like cups of tea and money. I guess the same applies to Rethink Priorities' section. I am very much on board with risk aversion with respect to resources, but I still think it makes all sense to be risk neutral relative to total hedonistic welfare.
From Bostrom (2011), "Recent cosmological evidence suggests that the world is probably infinite".