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.
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.