The injunction to “maximize expected utility” is entirely capable of incorporating your concerns. It can be “inequality-averse” if you want, simply by making it a concave function of experienced utility
No. I’ve said this 3 times already, including in the very comment that you are replying to. The utility function is not defined across all possible outcomes. A utility function is defined over a single outcome; it evaluates a single outcome. It can discount inequalities within that outcome. It cannot discount across possible worlds. If it operated across all possible worlds, all you would say is “maximize utility”. The fact that you use the word “expected” means “average over all possible outcomes”. That is what “expected” means. It is a mathematical term whose meaning is already established.
You can safely ignore my previous reply, I think I finally see what you’re saying. Not sure what to make of it yet, but I was definitely misinterpreting you.
Repeating your definition of a utility function over and over again doesn’t oblige anybody else to use it. In particular, it doesn’t oblige all those people who have argued for expected utility maximization in the past to have adopted it before you tried to force it on them.
A von Neumann-Morgenstern utility function (which is what people are supposed to maximize the expectation of) is a representation of a set of consistent preferences over gambles. That is all it is. If your proposal results in a set of consistent preferences over gambles (I see no particular reason for it not to, but I could be wrong) then it corresponds to expected utility maximization for some utility function. If it doesn’t, then either it is inconsistent, or you have a beef with the axioms that runs deeper than an analogy to average utilitarianism.
No. I’ve said this 3 times already, including in the very comment that you are replying to. The utility function is not defined across all possible outcomes. A utility function is defined over a single outcome; it evaluates a single outcome. It can discount inequalities within that outcome. It cannot discount across possible worlds. If it operated across all possible worlds, all you would say is “maximize utility”. The fact that you use the word “expected” means “average over all possible outcomes”. That is what “expected” means. It is a mathematical term whose meaning is already established.
You can safely ignore my previous reply, I think I finally see what you’re saying. Not sure what to make of it yet, but I was definitely misinterpreting you.
Repeating your definition of a utility function over and over again doesn’t oblige anybody else to use it. In particular, it doesn’t oblige all those people who have argued for expected utility maximization in the past to have adopted it before you tried to force it on them.
A von Neumann-Morgenstern utility function (which is what people are supposed to maximize the expectation of) is a representation of a set of consistent preferences over gambles. That is all it is. If your proposal results in a set of consistent preferences over gambles (I see no particular reason for it not to, but I could be wrong) then it corresponds to expected utility maximization for some utility function. If it doesn’t, then either it is inconsistent, or you have a beef with the axioms that runs deeper than an analogy to average utilitarianism.
“Expected” means expected value of utility function of possible outcomes, according to the probability distribution on the possible outcomes.