Ryo-ichi Nagahisa

A local independence condition for characterization of Walrasian allocations rule

Abstract The purpose of this paper is to characterize Walrasian resource allocations in terms of social choice axioms. We prove that the Walras rule is the only social choice rule satisfying individual rationality, Pareto principle, non-discrimination, and local independence. In the last part of this paper, we discuss the relation between our result and Nash implementation. We introduce a new condition, called Nash implementation with strong star shapedness around Nash equilibria, and show that it is equivalent to the local independence.

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

Abstract. 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 Nashs 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).

Acyclic and continuous social choice in T1 connected spaces

In this paper, we prove some versions of the Arrovian impossibility theorem in T1 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.

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.

Walrasian social choice in a large economy

Abstract The purpose of this paper is to characterize Walrasian allocations with infinite agents in terms of social choice axioms. We prove that the Walras rule is the only social choice rule satisfying the core property, non-discrimination, and weak monotonicity.

Rational performance and gibbard's pareto-consistent libertarian claim

Abstract The purpose of this paper is to introduce a new condition, called the rational performance, and hereby point out that the Gibbards Pareto-consistent libertarian claim has a certain defect from this point of view.

Acyclic and positive responsive social choice with infinite individuals: An alternative ‘invisible dictator’ theorem

Abstract In this paper, we investigate some versions of Arrovian Impossibility Theorem with infinite individuals, and with the collective rationality condition weakened from transitivity into acyclicity. We have an ‘invisible dictator’ theorem, being different from Kirman and Sondermanns one.

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.