Gibbardian libertarian claims revisited

Two resolution schemes for the impossibility theorems on the Gibbard-Kelly claims of libertarian rights, which are rather contrasting with each other, are proposed and their implications discussed. The first scheme asserts that there exists a collective choice rule satisfying the Pareto principle and the Gibbard-Kelly libertarian claims if there exists at least one socially unconcerned individual. The second scheme asserts existence of an eligible collective choice rule if there exists at least one liberal individual.     

Quasi-transitive and Suzumura consistent relations

We examine properties of binary relations that complement quasi-transitivity and Suzumura consistency in the sense that they, in conjunction with the original axiom(s), are equivalent to transitivity. In general, the conjunction of quasi-transitivity and Suzumura consistency is weaker than transitivity but in the case of collective choice rules that satisfy further properties, this conjunction implies transitivity of the social relation. We prove this observation by characterizing the Pareto rule as the only collective choice rule such that collective preference relations are quasi-transitive and Suzumura consistent, and standard social choice axioms are satisfied.     

Recoverability of choice functions and binary relations: some duality results

Banerjee and Pattanaik (1996) proved a theorem that the maximal set with respect to a quasi-ordering can be fully recovered by defining the greatest sets with respect to each and every ordering extension thereof and taking their union. Donaldson and Weymark (1998) proved a theorem that a quasi-ordering can be fully recovered by taking the intersection of all the ordering extensions thereof. These recoverability theorems are obviously related, but their exact relationship has never been clarified in the literature. This paper examines the issue of choice-functional recoverability and relational recoverability in a general framework, and establishes several remarkable duality relationships. Thanks are due to Professors Walter Bossert, Prasanta K. Pattanaik, Clemens Puppe, Amartya K. Sen, and John Weymark, with whom we had several opportunities to discuss this and related issues. The first author also would like to express his gratitude to the Andrew Young School of Policy Studies, Georgia State University, and the Scientific Research Grant for Policy Areas (B) Number 603 from the Ministry of Education, Science and Culture of Japan for their financial support which made this collaborative research possible. We are also grateful to the referees whose comments have led to several improvements of the paper.     

Rationalizability of choice functions on general domains without full transitivity

The rationalizability of a choice function by means of a transitive relation has been analyzed thoroughly in the literature. However, not much seems to be known when transitivity is weakened to quasi-transitivity or acyclicity. Such weakenings are particularly relevant in the context of social choice. We describe the logical relationships between the different notions of rationalizability involving, for example, the transitivity, quasi-transitivity, or acyclicity of the rationalizing relation. Furthermore, we discuss sufficient conditions and necessary conditions for rational choice on arbitrary domains. Transitive, quasi-transitive, and acyclical rationalizability are fully characterized for domains that contain all singletons and all two-element subsets of the universal set.     

On the voluntary exchange of libertarian rights

Harel and Nitzan recently formulated a resolution scheme for Sen's Pareto libertarian paradox, where libertarian decision-making entitlements actually change hands through the voluntary exchange of rights-endowments. Being a rigorous formalization of the strong libertarian tradition of free contract as advocated by Buchanan and Barry, this scheme serves as a natural target for our attempt to evaluate the logical capability and ethical nature of this tradition. It will be shown that this proposed scheme can hardly qualify, logically as well as ethically, as a libertarian resolution of the Pareto libertarian paradox.This paper was presented at the Murphy Conference on Liberty and Rights, Murphy Institute of Political Economy, Tulane University, September 16–17, 1989 and the VIth World Congress of the Econometric Society, Barcelona, August 22–28, 1990. Thanks are due to Professors Wulf Gaertner, Jerry S. Kelly, Prasanta K. Pattanaik, Amartya K. Sen, and K. Suga for their helpful comments and discussions. Thanks are also due to the referees of Social Choice and Welfare, whose comments greatly helped me to improve my exposition. By the time I completed the first draft of this paper, I was unaware of a related paper by Breyer (1990). I will comment on the partial overlap between our works at a later stage.     

The informational basis of the theory of fair allocation

The theory of fair allocation is often favourably contrasted with the social choice theory in the search for escape routes from Arrow’s impossibility theorem. Its success is commonly attributed to the fact that it is modest in its goal vis-à-vis social choice theory, since it does not aspire for a full-fledged ordering of options, and settles with a subset of ‘fair’ options. We show that its success may rather be attributable to a broadened informational basis thereof. To substantiate this claim, we compare the informational basis of the theory of fair allocation with the informational requirements of social choice theory.This paper is derived from a part of an earlier draft of our paper entitled ‘Informational requirements for social choice in economic environments’. The authors thank A. Trannoy, an associate editor and three referees for comments, and participants at seminars in University of Cergy-Pontoise, University of Rochester, Hitotsubashi University, and Waseda University, and the 5th International Meeting of the Society for Social Choice and Welfare in Alicante. Financial support from the Ministry of Education of Japan through Grant-in-Aid No. 10045010 (‘Economic Institutions and Social Norms: Evolution and Transformation’) and the 21st Century Center of Excellence Project on the Normative Evaluation and Social Choice of Contemporary Economic Systems is gratefully acknowledged.     

Rationality,external norms,and the epistemic value of menus

Ever since Sen’s criticism of internal consistency properties of choice, there exists a perception that the standard rational choice approach has difficulties in coping with the existence of external norms, or the information a menu of choice might convey to a decision maker. This article provides a brief survey of possible responses to these criticisms of traditional rational choice theory. We review approaches to the internalization of external norms as well as ways to formulate norm-conditional rationalizability. Furthermore, we illustrate how the epistemic value of an opportunity set can be incorporated into rational choice theory.