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.
Castagnoli, E., De Donno, M., Favero, G., Modesti, P., On representation of preferences a la Debreu, <<INTERNATIONAL JOURNAL OF DATA SCIENCE>>, 2023; 8 (3): N/A-N/A. [doi:10.1504/IJDS.2023.10054815] [https://hdl.handle.net/10807/235326]
On representation of preferences a la Debreu
De Donno, Marzia;
2023
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.
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