On the Closeness Aspect of Three Voting Rules: Borda – Copeland – Maximin

This paper provides a comparison of three voting rules, the Borda rule, the Copeland rule and the maximin rule. Our analysis based on the rankings derived from those voting rules will shed new light on existing comparisons based on “closeness” between the three voting rules under investigation. In particular it will be shown that both, the rankings derived from the Borda rule and the maximin rule and the rankings derived from the Copeland rule and the maximin rule, will be exactly the opposite for certain preference profiles.     

Pareto Optimal Trade in an Uncertain World: GMOs and the Precautionary Principle

Optimal trade policy in an uncertain world is examined. Decision-maker attitudes toward uncertainty are represented in terms of the Gilboa–Schmeidler (1989) maximin expected-utility (MMEU) model. The central result is that in a two-country, general-equilibrium setting with both trading partners possessing an MMEU preference structure, Pareto optimality can require one trading partner to absorb all uncertainty in the economy if its set of priors is a subset of its trading partners. An immediate corollary is that autarky is Pareto optimal if the trading partner with the more inclusive set of priors either chooses or is endowed with a nonstochastic technology.     

A class of fair distribution rules à la Rawls and Sen

Summary. This paper discusses and develops “non-welfaristic” arguments on distributive justice à la J. Rawls and A. K. Sen, and formalizes, in cooperative production economies, “non-welfaristic” distribution rules as game form types of resource allocation schemes. First, it conceptualizes Needs Principle which the distribution rule should satisfy if this takes individuals' needs into account. Second, one class of distribution rules which satisfy Needs Principle, a class of J-based Capability Maximum Rules, is proposed. Third, axiomatic characterizations of the class of J-based Capability Maximum Rules are provided. Received: July 30, 1999; revised version: March 11, 2002 RID="*" ID="*" We are grateful to an anonymous referee of this journal, Professors Marc Fleurbaey, Nicolas Gravel, Ryo-ichi Nagahisa, Prasanta Pattanaik, Kotaro Suzumura, Koich Tadenuma, and Yongsheng Xu for their fruitful comments. An earlier version of this paper was published with the title name, “A Game Form Approach to Theories of Distributive Justice: Formalizing Needs Principle” as the Discussion Paper No. 407 of the Institute of Social and Economic Research, Osaka University, and in the proceedings of the International Conference on Logic, Game, and Social Choice held at Oisterwijk in May 1999. That version was also presented at the 3rd Decentralization Conference in Japan held at Hitotsubashi University in September 1997, at the annual meeting of the Japan Association of Economics and Econometrics held at Waseda University in September 1997, and the 4th International Conference of Social Choice and Welfare held at University of British Colombia in July 1998. This research was partially supported by the Japanese Ministry of Education and the Ministry of Health and Welfare. Correspondence to: N. Yoshihara     

Extended social ordering functions for rationalizing fair allocation rules as game forms in the sense of Rawls and Sen

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 that give priority to procedural values rather than to consequential values are identified. These two can uniformly rationalize a nice allocation rule in terms of the values of procedural fairness, non-welfaristic egalitarianism, and Pareto efficiency.     

The utilitarian–maximin social welfare function and anomalies in social choice

Two major criteria of distributive justice are the utilitarian criterion and the maximin criterion. We offer a simple axiomatic characterization of a mixed utilitarian–maximin social welfare function. This social welfare function explains recent empirical violations of the standard cardinal social choice theory such as the social Allais paradox and the social common ratio effect. In addition, it offers a new foundation for the positively skewed wealth distributions in society. It also provides an objective function for mechanism design applications that trades off maximizing surplus and minimizing inequality.     

Optimal number of accrual groups and accrual group sizes in longitudinal trials with discrete‐time survival endpoints

In longitudinal trials, the number of accrual groups and their sizes should carefully be chosen to ensure a desired power to detect a specified treatment effect. Methods are proposed to obtain a cost‐effective combination of the number and size of accrual groups that provides high efficiency at minimal cost. We focus on trials where an event occurs at any point in time, but it is recorded on a discrete scale. The Weibull survival function is considered for modeling the underlying time to event. By using a cost function, it is shown that the ratio of the cost of recruiting and treating subjects to the cost of measuring them and also the survival pattern highly influence the optimal combination of the number and size of accrual groups. A maximin approach is further presented to obtain robust designs with respect to poor specification of these modeling parameters. We also show the application of the proposed optimal design methodology using real examples.     

On the Irrelevance of Risk Attitudes in Repeated Two-Outcome Games

We study equilibrium and maximin play in supergames consisting of the sequential play of a finite collection of stage games, where each stage game has two outcomes for each player. We show that for two-player supergames in which each stage game is strictly competitive, in any Nash equilibrium of the supergame, play at each stage is a Nash equilibrium of the stage game provided preferences over certain supergame outcomes satisfy a natural monotonicity condition. In particular, equilibrium play does not depend on risk attitudes. We establish an invariance result for games with more than two players when the solution concept is subgame perfection. Journal of Economic Literature Classification Numbers: C72, C9.     

Comment on "Ellsberg's two-color experiment, portfolio inertia and ambiguity"

In the setting of Ellsberg's two-color experiment, Mukerji and Tallon (2003) claim, without relying on particular representations, that ambiguity-averse behavior implies subjective portfolio inertia. In this note, we point out using a counterexample that their axioms are not enough to establish the result. We fill in the gap in their argument using additional axioms and argue that these axioms are of their own interest in that they behaviorally separate two prominent models of ambiguity: the maximin expected utility and smooth ambiguity models.     

A stability property in social choice theory

A social choice function g is stable if whenever an alternative x is selected at profile u and then profile is constructed from u by only switching x with yfor one individual i who has y just below x at u, then rule g selects either x or y at and not some third alternative. Stability is strictly weaker than strategy‐proofness but strong enough to establish two kinds of impossibility theorems.