Representing Preferences with a Unique Subjective State Space: A Corrigendum

Abstract

Dekel, Lipman and Rustichini (2001) (henceforth DLR) axiomatically characterized three representations of preferences that allow for a desire for flexibility and/or commitment. In one of these representations (ordinal expected utility), the independence axiom is stated in a weaker form than is necessary to obtain the representation; in another (additive expected utility), the continuity axiom is too weak. In this erratum we provide examples showing that the axioms used by DLR are not sufficient, and provide stronger versions of these axioms that, together with the other axioms used by DLR, are necessary and sufficient for these two representations.

A Reference-Dependent Representation with Subjective Tastes

“…Therefore we assume throughout an additional axiom on preferences called Monotonicity, which imposes that weakly larger sets in the partial order given by inclusion be weakly preferred by the decision maker. 5 This is a condition consistent with the assumption of the agent not experiencing commitment problems. Theorem 6 When the set Z is …nite, the preference has an additive expected utility representation with a measure which is always positive if and only if it satis…es Weak Order, Independence, Continuity, and Monotonicity.…”

“…6 Axiom 7 (Finiteness) Every menu A 2 K( (Z)) has a …nite critical set, where a critical set of a menu A is a any set A 0 such that for all B with A 0 hull(B) hull(A) we have B A. 5 The Monotonicity axiom is part of the axiomatization of the preference for ‡exibility in Kreps (1979). 6 hull(A) = fz 2 Z : z = P k i=1 i z i with i 0, P k i=1 i = 1 and z i 2 Ag denotes the convex hull of a set A.…”

Eliciting Temptation and Self-Control Through Menu Choices: A Lab Experiment

“…25 It is worth noting that NPR is generally not a restriction of axiomatic models of preference for flexibility such as Dekel et al (2001Dekel et al ( , 2007. To see this, suppose that the DM expects to be in one of two states during the task: with probability p, he expects to choose according to utility v such that v(1) > v(0); with probability 1 − p, he expects to choose according to u such that u(0) > u(1).…”

The price of flexibility: Towards a theory of Thinking Aversion

“…In recent years a large number of papers have extended the realm of traditional decision theory to the framework of preferences over menus, and have obtained rigorous models of phenomena like preference for flexibility (Kreps (1979)), temptation and self control (Gul and Pesendorfer (2001), Dekel et al (2007a)), regret (Sarver (2007)), or a potential combination of these elements (Dekel, Lipman, and Rustichini (2001), henceforth DLR01, Dekel et al (2007b), henceforth DLRS). Some of these papers offer different explanations as to why an agent might prefer a smaller set: she might want to avoid the presence of a tempting item, or to feel regret had she made the "wrong" choice.…”