[Show abstract][Hide abstract] ABSTRACT: 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.
Social Choice and Welfare 11/2006; 27(3):435-458. · 0.44 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We analyze infinite-horizon choice functions within the setting of a simple linear technology. Time consistency and efficiency are characterized by stationary consumption and inheritance functions, as well as a transversality condition. In addition, we consider the equity axioms Suppes-Sen, Pigou-Dalton, and resource monotonicity. We show that Suppes-Sen and Pigou-Dalton imply that the consumption and inheritance functions are monotone with respect to time—thus justifying sustainability—while resource monotonicity implies that the consumption and inheritance functions are monotone with respect to the resource. Examples illustrate the characterization results.
[Show abstract][Hide abstract] ABSTRACT: Although the theory of greatest-element rationalizability and maximal-element rationalizability under general domains and without full transitivity of rationalizing relations is well-developed in the literature, these standard notions of rational choice are often considered to be too demanding. An alternative definition of rationality of choice is that of non-deteriorating choice, which requires that the chosen alternatives must be judged at least as good as a reference alternative. In game theory, this definition is well-known under the name of individual rationality when the reference alternative is construed to be the status quo. This alternative form of rationality of individual and social choice is characterized in this paper on general domains and without full transitivity of rationalizing relations.
[Show abstract][Hide abstract] ABSTRACT: This Version: August 2006 Most, if not at all, practitioners of welfare economics and social choice theory are presumed to be welfaristic in their conviction. Indeed, they evaluate the goodness of an economic policy and/or economic system in terms of the welfare that people receive at the culmination outcomes thereby generated. Recent years have witnessed a substantial upsurge of interest in the non-welfaristic bases, or even the non-consequentialist bases, of welfare economics and social choice theory. Capitalizing on the axiomatic approach which we explored in the recent past, we try to provide a coherent analysis of consequentialism vis-à-vis non-consequentialism. To begin with, we develop an abstract framework in which the primitive of our analysis is a preference ordering held by an evaluator over the pairs of culmination outcomes and opportunity sets from which those culmination outcomes are chosen. As a partial test to see how much relevance can be claimed of the axiomatized concepts of consequentialism and non-consequentialism, two simple applications of this abstract framework are worked out. The first application is to the Arrovian social choice theory and the second application is to the analysis of ultimatum games. 科学研究費補助金（特別推進研究） = Grant-in-Aid for Specially Promoted Research
[Show abstract][Hide abstract] ABSTRACT: In this paper we consider variations of Koopmans' (1960) postulates and demonstrate that these lead to a class of social preferences that is wider than discounted utilitarianism. We formulate a utilitiarian condition (PFL), and introduce a one-sided equity condition (HEF) stating that a sacrifice of the present generation leading to a uniform gain for all future generations is weakly desirable if the present remains better off than the future. We investigate the consequences of imposing HEF, and obtain a new axiomatization of discounted utilitarianism by assuming that PFL holds and HEF does not hold., and seminar participants in Tokyo, Ascona, Osaka and Madrid, and financial support from the Research Council of Norway (Ruhrgas grant).
[Show abstract][Hide abstract] ABSTRACT: We examine the possibility of constructing social ordering func- tions, each of which associates a social ordering over the feasible pairs of allocations and allocation rules with each simple production econ- omy. Three axioms on the admissible class of social ordering func- tions are introduced, which embody the values of procedural fair- ness, non-welfaristic egalitarianism, and welfaristic consequentialism, respectively. The logical compatibility of these axioms and their lexi- cographic combinations subject to constraints are examined. Two so- cial ordering functions which give priority to procedural values rather than to consequential values are identified, which can uniformly ra- tionalize a nice allocation rule in terms of the values of procedural fairness, non-welfaristic egalitarianism, and Pareto efficiency.
International Journal of Economic Theory 02/2005; 1(1):21-41. · 0.38 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We examine the maximal-element rationalizability of choice functions with arbitrary domains. While rationality formulated in terms of the choice of greatest elements according to a rationalizing relation has been analyzed relatively thoroughly in the earlier literature, this is not the case for maximal-element rationalizability, except when it coincides with greatest-element rationalizability because of properties imposed on the rationalizing relation. We develop necessary and sufficient conditions for maximal-element rationalizability by itself, and for maximal-element rationalizability in conjunction with additional properties of a rationalizing relation such as reflexivity, completeness, P-acyclicity, quasi-transitivity, consistency and transitivity. Copyright Springer 2005
Theory and Decision 02/2005; 58(4):325-350. · 0.48 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The rationalizability of a choice function on an arbitrary domain under various coherence properties has received a considerable amount of attention both in the long-established and in the recent literature. Because domain closedness conditions play an important role in much of rational choice theory, we examine the consequences of these requirements on the logical relationships among different versions of rationalizability. It turns out that closedness under intersection does not lead to any results differing from those obtained on arbitrary domains. In contrast, closedness under union allows us to prove an additional implication.
[Show abstract][Hide abstract] ABSTRACT: Arrow's celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and non-dictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about indifference surfaces is needed to construct social ordering functions satisfying the weak Pareto principle and anonymity. We show that local information such as marginal rates of substitution or the shapes “within the Edgeworth box” is not enough, and knowledge of substantially non-local information is necessary.
[Show abstract][Hide abstract] ABSTRACT: 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--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.
Social Choice and Welfare 02/2005; 24(2):311-341. · 0.44 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Consistency of a binary relation requires any preference cycle to involve indifference only. It has been shown that consistency is necessary and sufficient for the existence of an ordering extension of a binary relation. It is therefore of interest to examine the rationalizability of choice functions by means of consistent relations. We describe the logical relationships between the different notions of rationalizability obtained if reflexivity or completeness are added to consistency. All but one such notion are characterized for general domains, and all are characterized for domains that contain all two-element subsets of the universal set. Copyright (c) The London School of Economics and Political Science 2005.
[Show abstract][Hide abstract] ABSTRACT: The rationalizability of a choice function on arbitrary domains by means of a transitive relation has been analyzed thoroughly in the literature. Moreover, characterizations of various versions of consistent rationalizability have appeared in recent contributions. However, not much seems to be known when the coherence property of quasi-transitivity or that of P-acyclicity is imposed on a rationalization. The purpose of this paper is to fill this significant gap. We provide characterizations of all forms of rationalizability involving quasi-transitive or P-acyclical rationalizations on arbitrary domains.
[Show abstract][Hide abstract] ABSTRACT: This Version June 2004 Bibliography: p. 27-29 We examine the possibility of constructing social ordering functions, each of which associates a social ordering over the feasible pairs of allocations and allocation rules with each simple production economy. Three axioms on the admissible class of social ordering functions are introduced, which embody the values of procedural fairness, non-welfaristic egalitarianism, and welfaristic consequentialism, respectively. The logical compatibility of these axioms and their lexicographic combinations subject to constraints are examined. Two social ordering functions which give priority to procedural values rather than to consequential values are identified, which can uniformly rationalize a nice allocation rule in terms of the values of procedural fairness, non-welfaristic egalitarianism, and Pareto efficiency.
[Show abstract][Hide abstract] ABSTRACT: This paper revisits Diamond’s classical impossibility result regarding the ordering of infinite utility streams. We show that if no representability condition is imposed, there do exist strongly Paretian and finitely anonymous orderings of intertemporal utility streams with attractive additional properties. We extend a possibility theorem due to Svensson to a characterization theorem and we provide characterizations of all strongly Paretian and finitely anonymous rankings satisfying the strict transfer principle. In addition, infinite horizon extensions of leximin and of utilitarianism are characterized by adding an equity preference axiom and finite translation-scale measurability, respectively, to strong Pareto and finite anonymity.
[Show abstract][Hide abstract] ABSTRACT: Two features of Arrow’s social choice theory are critically scrutinized. The first feature is the welfarist-consequentialism, which not only bases social judgements about right or wrong actions on the assessment of their consequences, but also assesses consequences in terms of people’s welfare and nothing else. The second feature is a similarity of people’s attitudes towards social outcomes as a possible resolvent of the Arrow impossibility theorem. Two extended frameworks, one consequentialist and the other non-consequentialist, are developed. Both frameworks are shown to admit some interesting resolutions of Arrow’s general impossibility theorem, which are rather sharply contrasting with Arrow’s own perspective. Copyright Springer-Verlag 2004
Social Choice and Welfare 02/2004; 22(1):237-251. · 0.44 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Revised Version: November 7, 2002 We would like to thank Professor Prasanta K. Pattanaik for numerous discussions on this and related subjects we have had over the years. It is our great pleasure as well as honour to dedicate this paper to celebrate his 60th birthday. Financial support through a Grant-in-Aid for Scientific Research for Priority Areas Number 603 from the Ministry of Education, Science and Culture of Japan is gratefully acknowledged. Thanks are also due to the anonymous referee of this journal, whose incisive comments greatly improved the exposition of the paper. In a recent paper ["Paretian Welfare Judgements and Bergsonian Social Choice," Economic Journal, Vol. 109, 1999, pp. 204-220], Suzumura proposed a possible way of relating the two schools of "new" welfare economics. According to his proposal, the logical possibility of the Paretian "new" welfare economics can be reduced to the constrained dual choice-functional recoverability of the Pareto-compatible Bergson-Samuelson social welfare ordering by means of the Pareto-compatible and consistent sub-relations thereof. He also identified the necessary and sufficient condition for this crucial property to hold. However, he posed but left open the problem of the constrained dual choice-functional recoverability of the Pareto-compatible Bergson-Samuelson social welfare ordering by means of the Pareto-compatible and transitive sub-relations thereof. The first purpose of this paper is to settle this open question. The second purpose of this paper is to pose and settle related problems of the constrained dual relational recoverability of the Pareto-compatible Bergson-Samuelson social welfare ordering by means of the Pareto-compatible and either consistent or transitive sub-relations thereof. 科学研究費補助金（特定領域研究） = Grant-in-Aid for Scientific Research on Priority Areas
Mathematical Social Sciences 02/2003; 45(2):143-154. · 0.45 Impact Factor