I don’t think agents that avoid the money pump for cyclicity are representable as satisfying VNM, at least holding fixed the objects of preference (as we should). Resolute choosers with cyclic preferences will reliably choose B over A- at node 3, but they’ll reliably choose A- over B if choosing between these options ex nihilo. That’s not VNM representable, because it requires that the utility of A- be greater than the utility of B and. that the utility of B be greater than the utility of A-
I don’t think agents that avoid the money pump for cyclicity are representable as satisfying VNM, at least holding fixed the objects of preference (as we should). Resolute choosers with cyclic preferences will reliably choose B over A- at node 3, but they’ll reliably choose A- over B if choosing between these options ex nihilo. That’s not VNM representable, because it requires that the utility of A- be greater than the utility of B and. that the utility of B be greater than the utility of A-