Open AccessConvex preferences: A new definition
Author(s) -
Richter Michael,
Rubinstein Ariel
Publication year - 2019
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te3286
Subject(s) - preference relation , preference , mathematics , mathematical economics , convexity , relation (database) , convex analysis , convex set , set (abstract data type) , regular polygon , algebraic number , revealed preference , element (criminal law) , combinatorics , convex optimization , computer science , economics , econometrics , statistics , mathematical analysis , geometry , database , financial economics , political science , law , programming language
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 condition: 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.