A linear algebra approach to non-transitive expected utility

Abstract.

The purpose of this paper is twofold. One of the aims is to give a view of P. C. Fishburn's non-transitive expected utility through geometric linear algebra. The other is to give an application of these ideas to a social choice problem. Actually, the problem under consideration arises from the theory of dynamical systems of structures in a society as studied in [All] and [Om1]. A variation of this model as presented in [Om2] leads to the problem of how macro structures of a society form coalitions. Their possible irrational behaviour may be treated using non-transitive expected utility.