The Rational Core of Preference Relations
Simone Cerreia-Vioglio and
Efe A. Ok
No 632, Working Papers from IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University
We consider revealed preference relations over risky (or uncertain) prospects, and allow them to be nontransitive and/or fail the classical Independence Axiom. We identify the ?rational part ?of any such preference relation as its largest transitive subrelation that satis?fies the Independence Axiom and that exhibits some coherence with the original relation. It is shown that this subrelation, which we call the rational core of the given revealed preference, exists in general, and under fairly mild conditions, it is continuous. We obtain various representation theorems for the rational core, and decompose it into other core concepts for preferences. These theoretical results are applied to compute the rational cores of a number of well-known preference models (such as Fishburn?s SSB model, justi?fiable preferences, and variational and multiplier modes of rationalizable preferences). As for applications, we use the rational core operator to develop a theory of risk aversion for nontransitive nonexpected utility modals (which may not even be complete). Finally, we show that, under a basic monotonicity hypothesis, the Preference Reversal Phenomenon cannot arise from the rational core of one?s preferences. JEL Classifi?cation: D11, D81. Keywords: Transitive core, affine core, nontransitive nonexpected utility, justi?fiable preferences, comparative risk aversion, preference reversal phenomenon.
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