Before revision:  A natural procedure for determining the collective preferences of a group then is to average its members' beliefs and add up their (0,1)-normalized utility functions . This procedure extends the well-known relative utilitarianism to decision making under uncertainty. We show that it is the only aggregation function that gives tie-breaking rights to agents who join a group and satisfies an independence condition in the spirit of Arrow's independence of irrelevant alternatives as well as four undiscriminating axioms .
After revision:  A natural procedure for determining the collective preferences of a group then is to average its members' beliefs and add up their (0,1)-normalized utility functions and average their beliefs. I show that it is the only aggregation function that gives tie-breaking rights to agents who join a group and satisfies an independence condition in the spirit of Arrow's independence of irrelevant alternatives as well as four undiscriminating axioms .