Representing Preferences with a Unique Subjective State Space

Abstract

Ž. We extend Kreps' 1979 analysis of preference for flexibility, reinterpreted by Kreps Ž . 1992 as a model of unforeseen contingencies. We enrich the choice set, consequently obtaining uniqueness results that were not possible in Kreps' model. We consider several representations and allow the agent to prefer commitment in some contingencies. In the representations, the agent acts as if she had coherent beliefs about a set of possible future Ž . ex post preferences, each of which is an expected-utility preference. We show that this set of ex post preferences, called the subjecti¨e state space, is essentially unique given the restriction that all ex post preferences are expected-utility preferences and is minimal even without this restriction. Because the subjective state space is identified, the way ex post utilities are aggregated into an ex ante ranking is also essentially unique. Hence when a representation that is additive across states exists, the additivity is meaningful in the sense that all representations are intrinsically additive. Uniqueness enables us to show that the size of the subjective state space provides a measure of the agent's uncertainty about future contingencies and that the way the states are aggregated indicates whether these contingencies lead to a desire for flexibility or commitment.

State dependent choice

“…The definition here is similar, but we allow the choice in a state, γ (A, < m ), to be multi-valued. 14 This means that, at a substantive level, the models differ, as there may not be a one-to-one correspondence between the frames and the states that explain a given set of observations. Details are in section 6.…”

“…For example, the relationship between 'mood' and choice is documented in an impressively large body of empirical evidence from psychology and economics. 2 In the large literature on menu choice (Kreps [34]; Dekel, Lipman and Rustichini [14]), an agent anticipates being in one of different preference determining states. And there exist several models of the effects on choice of specific psychological states, such as 'anticipatory feelings' (Caplin and Leahy [8]).…”

Lexicographic expected utility with a subjective state space

“…Think of a hypothesis as a (singed) measure over contingencies that is used to weight the valuation of outcomes across states. 4 She may view one hypothesis as "infinitely less relevant" than another. Think of this as being captured by a hierarchy of hypotheses.…”

“…In the following, we identify S * as the smallest finite subset of S B satisfying the condition (4).…”

“…Kreps [9,10] shows how the ranking of menus of alternatives reveals subjective uncertainty. Building on that, Dekel, Lipman, and Rustichini [4] (henceforth, DLR) endogenize the state space in an Archimedean framework. DLR take preference over menus of lotteries as a primitive and derive a unique subjective state space, corresponding to possible future preferences over lotteries.…”