Purpose - In 1951, Kenneth Arrow proved that it is not possible to have a group decision-making procedure that satisfies reasonable requirements like fairness. From the theoretical viewpoint, this is a great result - welldeserving the Nobel Prize that was awarded to Professor Arrow. However,...

The problem of how to rationally aggregate probability measures occurs in particular (i) when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and (ii) when an individual whose belief system...

In a framework of preferences over lotteries, we show that an axiom system consisting of weakened versions of Arrow's axioms has a unique solution. "Relative Utilitarianism" consists of first normalising individual von Neumann-Morgenstern utilities between 0 and 1 and then summing them. This...