A characterization of the Walras rule

This paper has three purposes. First, we refine the characterization of the Walras rule proposed by Nagahisa (JET 1991) over a more natural and simple domain than the one he employed. We show that the Walras rule is the only social choice rule defined over the domain and satisfying Individual Rationality, Pareto Efficiency, and Local Independence. Second, assuming endowments to be collectively owned, we show that the Walras rule operated from equal division is the only social choice rule satisfying No Envy, Pareto Efficiency, and Local Independence. Third, we show that for every social choice rule satisfying Individual Rationality and Pareto Efficiency, Local Independence is equivalent to a condition of Nash implementation with a game form satisfying convexity.This article is a revised version of Toyama University Working Paper No. 141. We are grateful to Professors William Thomson, Shinsuke Nakamura, Tomoichi Shinotsuka and two anonymous referees for their detailed comments. Nagahisa is grateful for hospitality of the economics department of the University of Rochester.     

Vetoer and tie-making group theorems for indifference-transitive aggregation rules

A binary relation is indifference-transitive if its symmetric part satisfies the transitivity axiom. We investigated the properties of Arrovian aggregation rules that generate acyclic and indifference-transitive social preferences. We proved that there exists unique vetoer in the rule if the number of alternatives is greater than or equal to four. We provided a classification of decisive structures in aggregation rules where the number of alternatives is equal to three. Furthermore, we showed that the coexistence of a vetoer and a tie-making group, which generates social indifference, is inevitable if the rule satisfies the indifference unanimity. The relationship between the vetoer and the tie-making group, i.e., whether the vetoer belongs to the tie-making group or not, determines the power structure of the rule.     

Acyclic and continuous social choice in T 1 connected spaces

In this paper, we prove some versions of the Arrovian impossibility theorem in T ₁ connected alternatives spaces, with the collective rationality condition weakened from transitivity to acyclicity, the Pareto condition replaced by some weaker conditions, and a continuity condition of social preferences imposed. Moreover these impossibility theorems are applied to a distributive problem of private goods in economic environments.This is a revised version of my Working Paper No. 111. I would like to thank two anonymous referees of the journal for their insightful comments. This paper was reported at the Western Meeting of Japan Association of Economics and Econometrics, held at Tezukayama University June 1990, and at Second Annual Southeastern Economic Theory Meetings, held at Florida University October 1990. I am grateful to Professors Tetsuya Kishimoto, Makoto Okamura, Koichi Suga, and Donald Campbell for their insightful comments. This paper is supported in part by the Tokyo Center for Economic Research.     

An axiomatization of the Kalai-Smorodinsky solution when the feasible sets can be finite

We axiomatize the Kalai-Smorodinsky solution (1975) in the Nash bargaining problems if the feasible sets can be finite. We show that the Kalai-Smorodinsky solution is the unique solution satisfying Continuity (in the Hausdorff topology endowed with payoffs space), Independence (which is weaker than Nash's one and essentially equivalent to Roth (1977)'s one), Symmetry, Invariance (both of which are the same as in Kalai and Smorodinsky), and Monotonicity (which reduces to a little bit weaker version of the original if the feasible sets are convex). Received: 4 November 1999/Accepted: 6 June 2001     

Identification of domain restrictions over which acyclic, continuous-valued, and positive responsive social choice rules operate

We consider a social choice problem in various economic environments consisting of n individuals, 4≤n<+∞, each of which is supposed to have classical preferences. A social choice rule is a function associating with each profile of individual preferences a social preference that is assumed to be complete, continuous and acyclic over the alternatives set. The class of social choice rules we deal with is supposed to satisfy the two conditions; binary independence and positive responsiveness. A new domain restriction for the social choice rules is proposed and called the classical domain that is weaker than the free triple domain and holds for almost all economic environments such as economies with private and/or public goods. In this paper we explore what type of classical domain that admits at least one social choice rule satisfying the mentioned conditions to well operate over the domain. The results we obtained are very negative: For any classical domain admitting at least one social choice rule to well operate, the domain consists only of just one profile.