Imprecise Probabilities and Their Applications

ISIPTA '03

Lugano, Switzerland

14-17 July 2003

A preference relation on a convex set F is considered. Necessary and sufficient conditions are given that guarantee the existence of a set of affine utility functions { u_i } on F such that the preference relation is represented by U( f ) = u_i ( f ) if f belongs to F_i where each F_i is a convex subset of F. The interpretation is simple: facing a ``non-homogeneous'' set of alternatives F, a decision maker splits it into ``homogeneous'' subsets F_i, and acts as a standard expected utility maximizer on each of them. In particular, when F is a set of simple acts, each u_i corresponds to a subjective expected utility with respect to a finitely additive probability P_i ; while when F is a set of continuous acts, each probability P_i is countably additive.

** Keywords. ** Preference representation, Subjective probability, Nonexpected utility, Integral representation, Multiple priors

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** Authors addresses: **

Fabio Maccheroni

Istituto di Metodi Quantitativi

Università Bocconi

Viale Isonzo, 25

20135 Milano, Italy

Massimo Marinacci

Dipartimento di Statistica e Matematica Applicata

Piazza Arbarello, 8

10122 Torino

Italy

Erio Castagnoli

IMQ

U. Bocconi

viale Isonzo 25

20135 Milano

** E-mail addresses: **

Fabio Maccheroni | fabio.maccheroni@uni-bocconi.it |

Massimo Marinacci | massimo@econ.unito.it |

Erio Castagnoli | erio.castagnoli@uni-bocconi.it |

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