On the aversion to incomplete preferences

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On the aversion to incomplete preferences Ritxar Arlegi1



Sacha Bourgeois-Gironde2 • Mikel Hualde1

Accepted: 21 September 2020  Springer Science+Business Media, LLC, part of Springer Nature 2020

Abstract We propose an axiomatization of aversion to incomplete preferences. Some prevailing models of incomplete preferences rely on the hypothesis that incompleteness is temporary and that by keeping their opportunity set open individuals reveal a preference for flexibility. We consider that the maintenance of incomplete preference is also aversive. Our model allows us to show how incompleteness induces an aversive attitude in two different ways: intrinsic and instrumental. Intrinsic aversion holds when one instance of incomplete preference in the set suffices to decrease its utility. Instrumental aversion holds only insofar dominating options are affected by incompleteness. Given two partially overlapping sets of axioms on the binary relation over sets we formalize their consistency with the two types of aversion to incompleteness. Finally, we relate our model to the classical Sen’s distinction between tentative and assertive incompleteness. The spelling out of this distinction in the terms of our approach uncovers to what extent aversion to incompleteness may be compatible with a preference for flexibility. Keywords Aversion to incomplete preferences  Preference for flexibility  Ranking sets

Financial support from the Spanish Ministry of Science and Technology (Project ECO2015-65031-R MINECO/FEDER, UE) and the Public University of Navarre is acknowledged. We would like to thank two anonymous referees and an associate editor for their valuable feedback. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11238020-09779-9) contains supplementary material, which is available to authorized users. & Ritxar Arlegi [email protected] 1

Department of economics, Public University of Navarre and Institute for Advanced Research in Business and Economics (INARBE), Campus Arrosadia s/n, 31006 Pamplona, Navarra, Spain

2

Laboratoire d’economie Mathematique et de Microeconomie Appliquee (LEMMA), Universite Paris 2 Pantheon-Assas, 12 place du Pantheon, 75005 Paris, France

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R. Arlegi et al.

1 Introduction Incompleteness of preferences may relate to different sources: objective or subjective, i.e. either pointing to incomparable features among the alternatives themselves, or to an epistemic state of decision uncertainty of the individual (for example, due to lack of information). In the former case incompleteness is, in principle, unsolvable. In the latter case, elucidating what the expectations of the individual about the solvability of incompleteness are turns to be crucial to evaluate its welfare implications. The interpretation and resolution of incompleteness in terms of preference for flexibility (Kreps 1979; Arlegi and Nieto 2001a; Danan and Ziegelmeyer 2006) and some choice-deferral models (Gerasimou 2017) indicate that the i

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