### 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) |
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Pages (from-to) | 1169-1183 |

Number of pages | 15 |

Journal | Theoretical Economics |

Volume | 14 |

Issue number | 4 |

DOIs | |

State | Published - Nov 1 2019 |

### Keywords

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

### ASJC Scopus subject areas

- Economics, Econometrics and Finance(all)

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## Cite this

*Theoretical Economics*,

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