Chernoff's dual axiom,revealed preference and weak rational choice functions

A new and a weaker concept of rationalizability is introduced and its implications on the properties of individual choice are investigated. Especially, (i) it is shown that a property of choice functions, called Chernoff's dual axiom in this paper, plays a crucial role for the rationality of choice, and (ii) weakening the concept of rationalizability facilitates characterization of revealed preference relations.     

‘Regular’ choice and the weak axiom of stochastic revealed preference

We explore the relation between two ‘rationality conditions’ for stochastic choice behavior: regularity and the weak axiom of stochastic revealed preference (WASRP). We show that WASRP implies regularity, but the converse is not true. We identify a restriction on the domain of the stochastic choice function, which suffices for regularity to imply WASRP. When the universal set of alternatives is finite, this restriction is also necessary for regularity to imply WASRP. Furthermore, we identify necessary and sufficient domain restrictions for regularity to imply WASRP, when the universal set of alternatives is finite and stochastic choice functions are all degenerate. Results in the traditional, deterministic, framework regarding the relation between Chernoff’s condition and the weak axiom of revealed preference follow as special cases. Thus, general conditions are established, under which regularity can substitute for WASRP as the axiomatic foundation for a theory of choice behavior.     

The demand functions that satisfy the weak axiom of revealed preference and generalized monotonicity

We prove that the individual demand function satisfying the Weak Axiom of Revealed Preference and the excess demand function satisfying the Wald’s Axiom are pseudomonotone_*⁺, a new class of generalized monotonicity. With this new concept, we refine the characterization of Zhou for the individual demand function. In particular, a full characterization for the excess demand functions satisfying the Wald’s Axiom is derived.     

What kind of preference maximization does the weak axiom of revealed preference characterize?

A (multivalued) choice is justified if no two chosen alternatives are preferred to each other, and if all chosen alternatives are preferred to all rejected alternatives. This concept permits a connection between the behavioral property expressed by WARP and a weak form of preference maximization. I am grateful to Michele Lombardi, Michael Mandler, Paola Manzini and an anonymous referee for useful discussions and comments.     

Self-control,revealed preference and consumption choice

We provide a time-consistent model that addresses the preference reversals that motivate the time-inconsistency literature. The model subsumes the behavior generated by the time-inconsistency approach in finite settings but, unlike the time-inconsistent models, allows for self-control. This paper provides a brief summary of theoretical results shown elsewhere [Gul and Pesendorfer, Econometrica 69 (2001) 1403; Econometrica, (2002), in press; Rev. Econ. Stud. (2002), in press] and contrasts the predictions and welfare implications of our model and the time-inconsistent β−δ model.     

A revealed preference test of rationing

This paper derives a revealed preference test for utility maximization under rationing and can detect, for which goods rationing is binding without specifying a functional form or imposing rationing constraints prior to estimation. For UK data from 1920–55, we find evidence of utility maximization under rationing with rationing binding for food and other services. Estimated virtual prices exceed observed food prices by 16.5% in 1947 and observed prices of other services by 10.9% in 1952.     

Equivalence of the weak and strong axioms of revealed preference without demand continuity assumptions: A “regularity condition” approach

The main result of this paper is that, provided the range of the demand function is convex and the whole budget is spent, the strong axiom of revealed preference holds if and only if the weak axiom of revealed preference and a certain “regularity” condition both hold. The regularity condition is a relationship between two definitions of expenditure compensation function that must hold if the strong axiom holds. The paper distinguishes itself from previous work in that no continuity assumptions are made on the demand function. It also discusses the relationship of the regularity condition used in this paper to the one used by Uzawa and van Moeseke.     

Public choice interpretations of distributional preference

This essay examines, from the perspective of both economics and ethics, the logical foundations of income transfers in a democratic society that allocates resources, in the large, through free markets. Such transfers, enacted through the public choice process, modify the market-determined distribution of income, as a reflection of the distributional preferences of the members of a society. Both constitutional and post-constitutional explanations of redistributions are considered. A discussion of recent experimental evidence of distributional preferences leads into a critique of simple equality, built on Michael Walzer's distinction between monopoly and dominance, as a criterion of distributive justice.     

Consumer choice and revealed bounded rationality

We study two boundedly rational procedures in consumer behavior. We show that these procedures can be detected by conditions on observable demand data of the same type as standard revealed preference axioms. This provides the basis for a non-parametric analysis of boundedly rational consumer behavior mirroring the classical one for utility maximization.     

Characterization of generalized weak orders and revealed preference

Summary This short paper provides an alternative framework to axiomatize various binary preference relations such as semiorder, weak semiorder etc. A set of simple axioms is presented in terms of revealed-preferred and revealed-inferior alternatives which makes the connection between various binary preference relations transparent; and every single axiom is necessary and sufficient for the existence of a binary preference relation of a specified type.We thank Bhasker Dutta, Peter Fishburn, Prasanta Pattanaik, Robert Russell and Thomas Schwartz for helpful suggestions     

The dynamics and revealed preference of status-quo optimality

Summary In a preceding companion paper, a static model of individual decision making was proposed that, due to imprecise perceptions, induces simple and inertial behavior at equilibrium (status-quo optimal) points. This paper addresses two complementary issues. Firstly, it studies the learning dynamics induced by the model and shows that its well-defined limit behavior ranges from status-quo optimal to fully optimal, depending on the underlying features of the problem. Secondly, the paper characterizes the behavioral implications of the model and compares them with those derived from standard decision-theoretic frameworks. Specifically, it is shown that, from a Revealed-Preference perspective, status-quo optimal behavior may be identified with that rationalizable by an acyclic preference relation, possibly intransitive.     

The subjective expected utility hypothesis and revealed preference

Summary A choice behavior of a decision maker is said to satisfy the subjective expected utility hypothesis if there exist a utility and a subjective probability such that a decision maker chooses acts with the highest expected utility. We present a revealed preference characterization of choice behavior that is consistent with the subjective expected utility hypothesis. Our result applies to any state space and compact sets of prizes and observations (either finite or infinite).     

Stochastic preference and randomized strategies for consumer choice

In this article a stochastic model of choice is developed that is based on game theory. The model is developed to demonstrate that a basic stochastic model can yield results similar to phenomena discovered in consumer behavior. In particular, a definition of brand loyalty is developed along with a basis for rational intransitivity of preferences, which is noted by brand switching. A measurement approach is also presented along with an example. The basic intent is to demonstrate that stochastic approaches to choice do have a foundation in both theoretical development beside observations in empirical studies.     

Characterization of certain choice functions

We characterize rationality of certain choice functions C by C(A) ∩ C(B) ? C(A ∪ B) ? C(A) ∪ C(B). We also characterize choice functions coming from preference relations which are partial orders and some other types of relations. Furthermore, we also characterize the admissible set of a binary relation by the fact it is invariant under certain changes in the relation.     

A simplified test for preference rationality of two-commodity choice

We provide a simplified test to determine if choice data from a two-commodity consumption set satisfies the Generalized Axiom of Revealed Preference (GARP), and thus the preference or utility maximization hypothesis. We construct an algorithm for this test and illustrate its application on experimental choice data. JEL Classification C91, D11, D12 An erratum to this article is available at .