I think you’re underestimating VNM here.
only two of those four are relevant to coherence. The main problem is that the axioms relevant to coherence (acyclicity and completeness) do not say anything at all about probability
It seems to me that the independence axiom is a coherence condition, unless I misunderstand what you mean by coherence?
correctly point out problems with VNM
I’m curious what problems you have in mind, since I don’t think VNM has problems that don’t apply to similar coherence theorems.
VNM utility stipulates that agents have preferences over “lotteries” with known, objective probabilities of each outcome. The probabilities are assumed to be objectively known from the start. The Bayesian coherence theorems do not assume probabilities from the start; they derive probabilities from the coherence criteria, and those probabilities are specific to the agent.
One can construct lotteries with probabilities that are pretty well understood (e.g. flipping coins that we have accumulated a lot of evidence are fair), and you can restrict attention to lotteries only involving uncertainty coming from such sources. One may then get probabilities for other, less well-understood sources of uncertainty by comparing preferences involving such uncertainty to preferences involving easy-to-quantify uncertainty (e.g. if A is preferred to B, and you’re indifferent between 60%A+40%B and “A if X, B if not-X”, then you assign probability 60% to X. Perhaps not quite as philosophically satisfying as deriving probabilities from scratch, but this doesn’t seem like a fatal flaw in VNM to me.
I do not expect agent-like systems in the wild to be pushed toward VNM expected utility maximization. I expect them to be pushed toward Bayesian expected utility maximization.
I understood those as being synonyms. What’s the difference?
Ok, I see what you mean about independence of irrelevant alternatives only being a real coherence condition when the probabilities are objective (or otherwise known to be equal because they come from the same source, even if there isn’t an objective way of saying what their common probability is).
But I disagree that this makes VNM only applicable to settings in which all sources of uncertainty have objectively correct probabilities. As I said in my previous comment, you only need there to exist some source of objective probabilities, and you can then use preferences over lotteries involving objective probabilities and preferences over related lotteries involving other sources of uncertainty to determine what probability the agent must assign for those other sources of uncertainty.
Re: the difference between VNM and Bayesian expected utility maximization, I take it from the word “Bayesian” that the way you’re supposed to choose between actions does involve first coming up with probabilities of each outcome resulting from each action, and from “expected utility maximization”, that these probabilities are to be used in exactly the way the VNM theorem says they should be. Since the VNM theorem does not make any assumptions about where the probabilities came from, these still sound essentially the same, except with Bayesian expected utility maximization being framed to emphasize that you have to get the probabilities somehow first.