Continuous choice functions and the strong axiom of revealed preference

Summary In this note, it is shown that a result due to Uzawa showing that the weak axiom of revealed preference together with a regularity condition implies the strong axiom of revealed preference can be derived from the regularity conditionalone, if the choice function is continuous in prices and in income. The observation that the weak axiom of revealed preference is not needed suggests that this regularity condition is remarkably strong. The main result of the paper is quite general in the sense that the only additional assumption on the choice function is that the whole budget be spent.I thank Charles Blackorby for his comments on an earlier version.     

‘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.     

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     

强偏好、弱偏好与制度演化

通过区分强偏好与弱偏好,来分析制度的演化轨迹。强、弱偏好对制度的演化有不同的影响。由于与生存竞争关系密切,基于强偏好的制度更容易服从于进化选择,好的制度最终将被普遍接受,从而在一个同一的环境内,基于强偏好的制度将趋同。相反,弱偏好则更容易多样化。在制度形成的过程中,不同的人的影响是不对称的,而且环境是开放性的还是封闭性的,对制度形成也关系重大。在开放的环境中,好制度更容易被选择;而在封闭的环境中,个人有可能将自己不好的偏好强加于社会,形成不好的制度。     

Strategy-proof and individually rational social choice functions for public good economies

Summary We consider the problem of choosing an allocation in an economy in which there are one private good and one public good. Our purpose is to identify the class of procedures of choosing an allocation which satisfy strategy-proofness, individual rationality, no exploitation and non-bossiness. Any such procedure is a scheme of semi-convex cost sharing determined by the minimum demand principle.I wish to thank Professors Salvador Barbera, Matthew Jackson, Herve Moulin and William Thomson for their helpful suggestions and two anonymous referees for their detailed comments. Conversations with Professors Hideo Konishi, Shinji Oseto Ken-ichi Shimomura and Stephen Ching were helpful. This work is supported by the Japan Economic Research Foundation and Research Grants PB89-0294 and PB89-0075 from the Direcion General de Investigacion Cientifica y Tecnica, Spanish Ministry of Education.     

Strategy-proof and individually rational social choice functions for public good economies

Summary This note is to inform about a mistake in my paper (Serizawa, 1996). In that paper, I characterized strategy-proof, individually rational, budget-balancing, non-exploitative and non-bossy social choice functions for economies with one public good and one private good. I established as Theorem 3 (page 507) that a social choice function is strategy-proof, individually rational with respect to endowment, budget-balancing, non-exploitative and non-bossy if and only if it is a scheme of semi-convex cost sharing determined by the minimum demand principle. I also exposed one example (Example 2, page 507) in order to emphasize that non-bossiness is indispensable for this characterization. I claimed that the social choice function in that example satisfies the above axioms except for non-bossiness, and is not a scheme of semi-convex cost sharing. However, the social choice function in the example is actually not strategy-proof, as shown in the simple discussion below. Therefore it is an open question whether or not a similar characterization theorem holds without non-bossiness.I thank Professor Rajat Deb, who kindly pointed out my mistake.     

Some Hicksian and Marshallian consumer's surplus estimates in discrete choice

This note describes the theory and practice of applying the Hicksian approach to cost-benefit analysis to discrete choice models. It illustrates the technique with numerical estimates of Hicksian and Marshallian consumer's surplus measures based on computer simulations using real-world data.     

Between mathematical formalism,normative choice rules,and the behavioural sciences: The emergence of rational choice theories in the late 1940s and early 1950s

Abstract

This paper discusses why mathematical economists of the early Cold War period favored formal-axiomatic over behavioral choice theories. One reason was that formal-axiomatic theories allowed mathematical economists to improve the conceptual and theoretical foundations of economics and thereby to increase its scientific status. Furthermore, the separation between mathematical economics and other behavioral sciences was not as clear-cut as often argued. While economists did not modify their behavioral assumptions, some acknowledged the empirical shortcomings of their models. The paper reveals the multifaceted nature of rational choice theories reflected in the changing interpretations and roles of the theories in those early years.     

Strategy-proof and individually rational social choice functions for public good economies: A note

Summary. Serizawa [3] characterized the set of strategy-proof, individually rational, no exploitative, and non-bossy social choice functions in economies with pure public goods. He left an open question whether non-bossiness is necessary for his characterization. We will prove that non-bossiness is implied by the other three axioms in his characterization. Received: October 17, 1997; revised version: January 19, 1998