Preferences in Abstract Convex Structures

Convexity of preferences is a canonical assumption in economic theory. In this paper we study a generalized definition of convex preferences that relies on the notion of a convex space, that is an abstraction of the standard notion of convexity in a linear space. We introduce also betweenness relations that characterize convex spaces. First we consider a ternary betweenness relation that gives rise to an interval space structure and then we propose a more general definition of betweenness.