Title: On representation of preferences à la Debreu

Authors: Erio Castagnoli; Marzia De Donno; Gino Favero; Paola Modesti

Addresses: Deceased, formerly of: Department of Decision Sciences, Bocconi University, 20136 Milan, Italy ' Department of Mathematics for Economic, Financial and Actuarial Sciences, Università Cattolica, 20123 Milan, Italy ' Department of Economics and Management, University of Parma, via Kennedy, 6, 43125 Parma, Italy ' Department of Economics and Management, University of Parma, via Kennedy, 6, 43125 Parma, Italy

Abstract: A representation theorem proven by G. Debreu in 1960, although somehow neglected by the literature, implies several deep and unexplored consequences both for Economics and for Decision Theory. This paper focuses on some of them. In particular, possible decompositions of state-dependent utilities à la Debreu (which may equivalently be seen as 'utility-dependent probabilities') are analysed, showing that Debreu's representation is based upon a 'joint' probability/utility function. It is illustrated how Debreu's Theorem can provide a neat geometrical interpretation of Castagnoli and LiCalzi's 'benchmarking' representation of preferences. (Conditional) Certainty Equivalents are defined and studied, and possible implications for attempting representation of incomplete preferences are discussed.

Keywords: Debreu's theorem; representation of preferences; sure thing principle; state-dependent utility; benchmarking; certainty equivalents; incomplete preferences.

DOI: 10.1504/IJDS.2023.132293

International Journal of Data Science, 2023 Vol.8 No.3, pp.175 - 194

Received: 26 Jul 2022
Accepted: 28 Dec 2022
Published online: 17 Jul 2023 *

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