Is it just me or is it the case, that not everyone seems to realize that dominance reasoning (at least of actual utilities as opposed to generalized dominance of expected values, but even there what i may say about morgen-besser reasoning may apply) in in-deterministic scenarios  relies on morgen-besser- style reasoning.I had always presumed that dominance reasoning is a distinct principle in own right which often leads to the goal of maximizes expected utility but that is only a consequence and thus could be employed even when probabilities are not defined on the act-state relations so long as there a good reasoning for upholding the notion that changing the act would not change the state, ie had i performed a instead of b, State 1 still would have occurred.

If on the other hand if 'dominances' only job by requiring act-state probabilistic/causal/modal independence so as to ensure that dominating actions maximize expected value, without having to know what the act-state probability is, so that it is supervenient on expected value and is a probabilistic principle. Thus its only role would be to allow one to say that whatever the state probabilities are, it is, it is the same for all acts. Such that dominating options will have higher expected value because whatever their act -state probabilities happen to be, they will be the same and so the contribution to expected utility difference comes from the difference utilities of in the same state. Thus one could use dominance whenever one did not know the probabilities of the states or the expected values of them, just so long as one has enough information to tell you that their probabilities are the same.

Personally, I had always thought that this  requirement (act state independence, probabilistic, modal, causal you name it) was to permit the same kind of inferences that morgenbesser conditionals allow (which generally only hold under probabilistic or causal independence as well), so that we can say if we choose A1 and state one occurs, state one would still have had we of picked A2. The link to maximizing expected value is a benefit in its own right but is only a consequence, or rather usual consequence, as dominance is a rationality principle in its own right; a pre-probabilistic principle which is why I thought that some scholar when trying to derive the probabilistic axioms of the PP use only dominance first

Otherwise if what i said initially (in the second paragraph) is true, all dominance is,, is either (1) just an expected utility principle that speeds up calculations or allows one to calculate which event maximizes expected utility without having to know the act-state probabilities (or to know what that expected value actually is), so long as one knows that whatever they are, they are the same; or (2) that we can treat by the principle of indifference, the same state,  under two acts as the same event or as an equally likely event, so that if one has greater utility it is superior, which relies again on expected utility and an indifference principles, and so it would not be dominance but dominance plus indifference, (which is stochastic dominance) and not a principle in its own right but just a maximization of expected value).

Dominance, does not require indifference for its reasoning to go ahead, the equi-probability assumption i thought was just one way as characterising the idea that a different act cannot change the state (it is to be held fixed), and so could be characterized in non-probabilistic terms (by saying that state would be the same regardless of which other action one would have made on that single case, so long as that can be justified).

And that is technically why some (like me but others also) see dominance as a more fundamental relations as its technically a non-probabilistic relation that involves just relations between super-sets and subsets, and I believe this is why James joyce or at least the Everettians use dominance whenever they use decision theory before they get to probability theory (to either establish the axioms of probability, the probability values or the principle principal, as otherwise it would be circular) because it is a non probabilistic principle in its basic form. However, some see see dominance as equally probabilistic as expected utility (I can link to a paper which suggests this)), whilst others, perhaps the everettians and epistemic utility theorists, who use do not, which is why they apply it, and not expected utility reasoning to (1) to prove the axioms of probability (in the case of epistemic utility theorists) or to (2) prove the PP/born rule or the value of the probabilities from allegedly non-probabilistic constraints in the case of the everettians, by which I mean the dominance related quantum erasure decision theoretic proofs of wallace and deutsch. (I can likewise attach a paper about that as well). Although it would appear that the use of the dominance reasoning in the case of the everettians cannot be justified in the come what may sense, as their states are what I called modally dependent, and thus it may just be expected utility maximization iin disguise). Is this correct?, or is my construal of dominance a conflation with that of ratifiability, which is a kind of post hoc consideration (although it need not involve actual utilities rather than expected utilities or involve in-deterministic scenarios)

In this way as I see it there are case where one cannot use dominance reasoning, and where there is not probabilistic dependence and maybe not even causal but only modal, but in any case if you were to use dominance reasoning the result you would get would match the prescriptions of expected utility and so you would get the right result is supposed  to be is better, despite the fact that you should not be using it, because no options dominates the other in the sense that the same state would have been the case had I done b instead of A, and b has more utility; the implications being that such a scenario could not ground the probability notion itself as its supervenient on expected value; whereas dominance as in the case that one would do better come what may which is dependent on morgen-besser reasoning could (if it could be justified)- as there nothing about the strong law of large number, large collectives, sample averages which occur with only probability one etc involved.

If what I am saying is correct then the morgenbesser counter-factual is more than just a curiosity- all standard 'proper' dominance reasoning under risk- or rather under in-deterministic scenarios would go out the window if the morgenbesser conditional is invalid. Am i missing something here, that is the question I guess I am asking? (and by proper dominance I mean case where the single case results or utilities for one act dominates those of other acts for each and every state, not the expected utilities, but the actual definite results). Likewise I do not mean stochastic dominance for the same reason or stochastic dominance.