### 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 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.

Original language | English (US) |
---|---|

Pages (from-to) | 1169-1183 |

Number of pages | 15 |

Journal | Theoretical Economics |

Volume | 14 |

Issue number | 4 |

DOIs | |

State | Published - Nov 1 2019 |

### Fingerprint

### Keywords

- abstract convexity
- C60
- Convex preferences
- D01
- maxmin utility

### ASJC Scopus subject areas

- Economics, Econometrics and Finance(all)

### Cite this

*Theoretical Economics*,

*14*(4), 1169-1183. https://doi.org/10.3982/TE3286

**Convex preferences : A new definition.** / Richter, Michael; Rubinstein, Ariel.

Research output: Contribution to journal › Article

*Theoretical Economics*, vol. 14, no. 4, pp. 1169-1183. https://doi.org/10.3982/TE3286

}

TY - JOUR

T1 - Convex preferences

T2 - A new definition

AU - Richter, Michael

AU - Rubinstein, Ariel

PY - 2019/11/1

Y1 - 2019/11/1

N2 - 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.

AB - 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.

KW - abstract convexity

KW - C60

KW - Convex preferences

KW - D01

KW - maxmin utility

UR - http://www.scopus.com/inward/record.url?scp=85076094817&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85076094817&partnerID=8YFLogxK

U2 - 10.3982/TE3286

DO - 10.3982/TE3286

M3 - Article

AN - SCOPUS:85076094817

VL - 14

SP - 1169

EP - 1183

JO - Theoretical Economics

JF - Theoretical Economics

SN - 1555-7561

IS - 4

ER -