What is generally meant by this requirement, A set of states must be a partition of the proposition space that is orthogonal to the act partition???

It appears to be often a prerequisite of dominance reasoning, or to be able to represent an agents preference, probabilities, desirabilities, utilities etc over outcomes, an acts, in such a way that comparisons can be made, or the dictates of rationality (sure thing principle, or expected utility reasoning, or again some form of dominance reasoning can be used) the question is in bold

A set of states must be  a partition of the proposition space that is orthogonal to the act partition??? http://plato.stanford.edu/entries/decision-theory/ (here is a link where the term is used). What is meant by this precisely?(this is the question) I have also described it as act state orthogonality, or act state pair orthogonality I believe. This is also relevant to everettian 'dominance reasoning' where a particular article (which sort of critiqued it and supported it, mentioned this notion not holding in the quantum context, and think there were talking about orthogonality in this decision theoretic sense, given quantum mechanics, not orthogonality as it usually described in geometry or logic, to mean inconsistent/incompatible (the dot product being zero for the two propositions in hilbert space), or in geometry where we are considering the notion of being at 90 degrees (also of course expressible as the dot product between the angles being zero)

By orthogonality do they mean some kind of causal, probabilistic, modal, or linguistic, desirability independence, or to (to some degree) the same thing which is that which is that the acts are mutually exclusive or the states must be, or given the way the states are defined, they are not defined in terms of the probabilities or the utilities themselves, which amount to a form of act state dependence, because given certain distinct acts, A1, A2, S1, S2, A1 in S1, and A2 in S2 amount to the same categorical states of affairs; (as is sometimes done in stochastic dominance, but is then translated as if standard dominance reasoning (better chance, same outcomes, or same chance, but better outcomes, reznick 1987) actually applies, which even if it does, it does not do so for the right, pre-probabilistic reasons for which dominance is probability intuitively supposed to apply (at least pre-theoretically, where the tacit assumptions is that if one commited a different act the same state would have occurred. These conditions need not holkd even if there is probabilistic and causal independence but not complete modal independence; that is even ifdominance reasoning will match up with conditional expected utility calculations, but not for the right reasons (there is no dominance come what may kind of notion going on necessarily) that could be used to derive the notion of probability itself, but only as a kind of short cut method to expected utility maximization once the probability concept is already understood)

For instance,two bets with the same outcomes and the same corresponding utilities but where in one bet the better outcome has a higher chance- where these might where two mutually exclusive albeit equi-probable states are considered the sa, so that two purportedly distinct states (for instance if A1 is bet on heads and A2 is bet on tails,  on a fair die, where both bets pay 1 dollar and nothing otherwise, and I line up the decision table, with state 1 just being that state with outcome given either act which produces  outcome 'win one dollar', and 'state 2 being win nothing', where clearly given A1, state 1 actually means 'heads' occurs, but given A2 state 1 means tails, so that column wise, ie the allegedly the identical states, arent identical at all but orthogonal, and row-wise, the allegedly, the different states which should be disjoint are not, or not always (A1 S1, A2 S2 both lead mean result tails occurs), so that if one were to employ the kind of morgenbesser reasoning) by which dominance reasoning becomes an independent kind of principle from expected utility or probabilistic considerations), one does not have modal or logical independence/linguistic independence because the identification or the partial definability of the states in terms of the acts, or the probabilities or their positive outcomes, leads to act state dependence even if not ontic dependence.

For instance, , presumably, were I to get S1 given A1, I would not still get S1 given A2, but rather S2, even if the States are probabilistically and even causally independent of the acts; they are not modally independent in the sense required by dominance reasoning whereby one can identify a superior act as that act, which leads to a positive outcome in a superset of the set of states in which the other act/s would (where one has some justification for the assumption that if a state occurs, whilst indeterminstically, that same state would have still occurred were I to commit the opposite act), so that without explicit probabilistic considerations (and without saying explicitely what the probability measure is over the states), that whatever it is, if there is one at all, that by logic alone (monotonicity, A implies B, B at least as probable as A) one can say that the first act has a higher 'probability' or degree of possibility for the positive outcome without indifference assumptions, and this because one knows that one if one gets the positive outcome, via the first act, then on that same single case, one may not have gotten such a result had one committed the other act, but if one commits the other act and gets the positive result one would still have gotten it, if one committed the first act(as the same state would occurs and the set of states under which this action leads to a positive result is a subset of the those of the other action)- where one can even use this reasoning prior to the outcome's occurrence (in a weird future directed, past evaluated light)- and the same goes by losses but in the opposite direction (the better outcomes loses only if the worse one alsp does, and the worse one loses when the better one may not have lost)?