Theoretical Economics 15 (2020), 1509–1546

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### An explicit representation for disappointment aversion and other betweenness preferences

*Simone Cerreia-Vioglio, David Dillenberger, Pietro Ortoleva*

#### Abstract

One of the most well-known models of non-expected utility is Gul (1991)'s
model of Disappointment Aversion. This model, however, is defined implicitly,
as the solution to a functional equation; its explicit utility representation
is unknown, which may limit its applicability. We show that an explicit
representation can be easily constructed, using solely the components of the
implicit one. We also provide a more general result: an explicit
representation for preferences in the Betweenness class that also satisfy
Negative Certainty Independence (Dillenberger, 2010) or its counterpart.
We show how our approach gives a simple way to behaviorally identify the parameters of the representation and to study the consequences of disappointment
aversion in a variety of applications.

Keywords: Disappointment Aversion, Betweenness, Cautious Expected Utility, utility representation

JEL classification: D80, D81

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