### Abstract

We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteries by means of a set of von Neumann-Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well-defined sense.

Original language | English (US) |
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Pages (from-to) | 118-133 |

Number of pages | 16 |

Journal | Journal of Economic Theory |

Volume | 115 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2004 |

### Keywords

- Expected utility
- Incomplete preference relations

### ASJC Scopus subject areas

- Economics and Econometrics

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## Cite this

Dubra, J., Maccheroni, F., & Ok, E. A. (2004). Expected utility theory without the completeness axiom.

*Journal of Economic Theory*,*115*(1), 118-133. https://doi.org/10.1016/S0022-0531(03)00166-2