Coalition preferences with individual prospects

We consider a group of individuals, such that each coalition of them is endowed with a preference relation, which may be incomplete, over a given set of prospects, and such that the extended Pareto rule holds. We assume that each singleton coalition has complete vNM preferences. In this setup, Baucells and Shapley (2008) gave a sufficient condition for a coalition to have complete preferences, in terms of the completeness of preferences of certain pairs of individuals. The new property that we introduce of individual prospects requires each individual to have a pair of consequences between which only she is not indifferent. We show that with this property a weaker condition guarantees the completeness of preferences of a coalition: it suffices for a coalition to be a union of a connected family of coalitions with complete preferences.