The way I said that may have been too much of a distraction from the real problem, which I’ll restate as: considerations of fairness, which may arise from bargaining or just due to fairness being a terminal value for some people, can imply that the most preferred outcome lies on a flat part of the Pareto frontier of feasible expected utilities, in which case such preferences are not VNM rational and the result described in the OP can’t be directly applied.
The way I said that may have been too much of a distraction from the real problem, which I’ll restate as: considerations of fairness, which may arise from bargaining or just due to fairness being a terminal value for some people, can imply that the most preferred outcome lies on a flat part of the Pareto frontier of feasible expected utilities, in which case such preferences are not VNM rational and the result described in the OP can’t be directly applied.