## Abstract

I provide an axiomatic foundation for the assumption of specific utility functions in a multidimensional spatial model, endogenizing the spatial representation of the set of alternatives. Given a set of objects with multiple attributes, I find simple necessary and sufficient conditions on preferences such that there exists a mapping of the set of objects into a Euclidean space where the utility function of the agent is linear city block, quadratic Euclidean, or more generally, it is the delta power of one of Minkowski (1886) metric functions. In a society with multiple agents I characterize the set of preferences that are representable. by weighted linear city block utility functions, and I discuss how the result extends to other Minkowski utility functions. (C) 2011 Elsevier B.V. All rights reserved.

Original language | English |
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Pages (from-to) | 200-205 |

Number of pages | 6 |

Journal | Journal of mathematical economics |

Volume | 47 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 2011 |

## Keywords

- Utility representation
- Spatial models
- Multidimensional preferences
- Spatial representation
- VOTING MODELS
- INTRANSITIVITIES
- EQUILIBRIUM