A generalization of Condorcet’s Jury Theorem to weighted voting games with many small voters

We extend Condorcet’s Jury Theorem (Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. De l’imprimerie royale, 1785) to weighted voting games with voters of two kinds: a fixed (possibly empty) set of ‘major’ voters with fixed weights, and an ever-increasing number of ‘minor’ voters, whose total weight is also fixed, but where each individual’s weight becomes negligible. As our main result, we obtain the limiting probability that the jury will arrive at the correct decision as a function of the competence of the few major players. As in Condorcet’s result the quota q = 1/2 is found to play a prominent role. I wish to thank Maurice Koster, Moshé Machover, Guillermo Owen and two anonymous referees for helpful comments.     

Game-theoretic properties of Final-Offer Arbitration

Final-Offer Arbitration (FOA) is a dispute settlement procedure in which an arbitrator chooses one side's final position as the resolution. Game-theoretic models of FOA in two-sided interest disputes are reviewed, especially models of the disputants' final offer choices under uncertainty about the arbitrator's preferences. The extent to which the Brams-Merrill Theorem (1986) reveals optimal strategic behavior under FOA, and the implications for efficiency and equity, are assessed. Analysis of a model not satisfying the hypotheses of the Theorem suggests that, for some arbitrators, FOA can have an undesirable tendency. Another game model is used to address the question of how disputants' differential risk-aversion is reflected in their strategic behavior, and in the fairness of FOA outcomes. This calculation clarifies some apparently contradictory empirical evidence about FOA.     

关于基尼系数若干问题的再研究--与部分学者商榷

基尼系数是测量收入不平等的一个重要指标，近年来有很多学者对此进行了深入研究，本文主要对有关学者的研究内容进行商榷与补充。首先，实际计算基尼系数应首选离散公式，并且根据具体的抽样方法选择无偏或有效的估计公式；其次，本文论证了对数正态分布下基尼系数G与标准差d的关系式：G=2Ф（σ/√2）-1；再次，针对基尼系数存在的不足，改进基尼系数成为一些学者的研究重点，本文发现一些改进并没有解决基尼系数与洛伦茨曲线的非一一对应问题，并且可操作性较差，通过介绍S基尼系数和E基尼系数，本文说明了基尼系数改进的总体思路；最后，针对学者提出的“部分分布决定性定理（PD定理）”，本文论证了其推理过程中存在的问题，说明该定理是错误的。     

Reduced Form Auctions Revisited

This note uses the Theorem of the Alternative to prove new results on the implementability of general, asymmetric auctions, and to provide simpler proofs of known results for symmetric auctions. The tradeoff is that type spaces are taken to be finite.     

Kuhn’s Theorem for extensive form Ellsberg games

We propose the notions of mixed and behavioral Ellsberg strategies for extensive form games and prove that these strategies are outcome-equivalent if and only if mixed Ellsberg strategies satisfy a certain rectangularity condition. In addition, we show that not only the profile of Ellsberg strategies must be appropriately chosen but also the extensive form must satisfy further restrictions beyond those implied by perfect recall in order to ensure that each player will respect his ex ante strategy choice with the evolution of play.     

On Minimally-supported <Emphasis Type="Italic">D</Emphasis>-optimal Designs for Polynomial Regression with Log-concave Weight Function

This paper studies minimally-supported D-optimal designs for polynomial regression model with logarithmically concave (log-concave) weight functions. Many commonly used weight functions in the design literature are log-concave. For example, and exp(−x ²) in Theorem 2.3.2 of Fedorov (Theory of optimal experiments, 1972) are all log-concave. We show that the determinant of information matrix of minimally-supported design is a log-concave function of ordered support points and the D-optimal design is unique. Therefore, the numerically D-optimal designs can be constructed efficiently by cyclic exchange algorithm.     

Another Graphical Proof of Arrow's Impossibility Theorem

Arrow's (1951) Impossibility Theorem is the idea that, given several well-known assumptions, the social orderings of particular alternatives that are meant to reflect individuals' preferences must match the preferences of an arbitrary individual (the dictator). A social-choice rule other than dictatorship is impossible. Following from Fountain (2000), the author presents another graphical proof of the theorem that is intended to be more accessible to students and teachers of economics. The principal strength of this approach is that the patterns of agreements and conflicts over all possible combinations of two individuals' rankings of alternatives are transparent; appreciating these patterns is the key to intuitively understanding Arrow's theorem. A self-test for readers (or a classroom exercise for students) is included.     

Estimation of the change point of a distribution based on the number of failed test items

This paper discusses the family of life distributions with failure rate functions which decrease initially until a change point and remain constant thereafter. The paper focuses on the estimation for the change point of the failure rate function. While point estimation of the change point of the failure rate function has been discussed by some authors, one can hardly find any existing work on the interval estimation of the change point. In this paper, a method for constructing approximate confidence intervals for the change point is proposed. The proposed approximate confidence intervals are based on the number of failed test items at or before a fixed inspection time. Received: September 1999