Theoretical Economics 14 (2019), 1169–1183

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### "Convex preferences": a new definition

*Michael Richter, Ariel Rubinstein*

#### Abstract

We suggest a concept of convexity of preferences that does not rely on any algebraic structure. A decision maker has in mind a set of orderings interpreted as evaluation criteria. A preference relation is defined to be convex when it satisfies the following: if for each criterion there is an element that is both inferior to b by the criterion and superior to a by the preference relation, then b is preferred to a. This definition generalizes the standard Euclidean definition of convex preferences. It is shown that under general conditions, any strict convex preference relation is represented by a maxmin of utility representations of the criteria. Some economic examples are provided.

Keywords: Convex preferences, abstract convexity, maxmin utility

JEL classification: D01, C60

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