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Updating variational (Bewley) preferences

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Abstract

This paper investigates dynamically consistent updates of weighted unanimity rules given by variational Bewley preferences (VBP), a class of incomplete preferences characterized by pairs of utility index over consequences and ambiguity index over priors. We show that these dynamically consistent updates are also VBP that preserves the same ranking over consequences and feature conditional ambiguity index obtained through the full Bayesian update of the unconditional one. Moreover, we study conditional forced-choice relations, which capture choices that a decision-maker must take after learning some event. Formally, they are monotone continuous weak orders. We show that any conditional forced-choice relation that preserves the ambiguity attitude of a given unconditional VBP has a variational representation with the same affine utility function over consequences and the ambiguity index of its corresponding dynamically consistent update. Thus, our result provides a novel foundation for full Bayesian updating of variational preferences.

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Acknowledgements

We wish to thank Lorenzo Bastianello, Hugo Boff, Alain Chateauneuf, Eduardo Faingold, Gil Riella, and especially three anonymous referees for valuable suggestions and comments. We also thank the participants of seminars at Insper, Université Paris I Panthéon-Sorbonne, Bocconi University, and conferences SAET 2017 and FUR 2018 for their helpful comments. Santos gratefully acknowledges financial support from Fapesp (Grant Nos. 2017/09955-4 and 2018/00215-0). Faro is grateful for financial support from the CNPq-Brazil (Grant No. 308183/2019-3).

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  1. Insper, Rua Quatá 300, Vila Olímpia, São Paulo, 04546-042, Brazil

    José Heleno Faro & Ana Santos

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Faro, J.H., Santos, A. Updating variational (Bewley) preferences. Econ Theory 75, 207–228 (2023). https://doi.org/10.1007/s00199-021-01397-y

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