A characterization and an impossibility of finite length anonymity for infinite generations

In the context of ranking infinite utility streams, the impartiality axiom of finite length anonymity requires the equal ranking of any two utility streams that are equal up to a finite length permutation ( Fleurbaey and Michel, 2003). We first characterize any finite length permutation as a composition of a fixed step permutation and an “almost” fixed step permutation. We then show that if a binary relation satisfies finite length anonymity, then it violates all the distributional axioms that are based on a segment-wise comparison. Examples of those axioms include the weak Pareto principle and the weak Pigou-Dalton principle.     

Unanimity,anonymity, and infinite population

This paper is concerned with the implications of unanimity and anonymity for the Arrovian social choice theory when population is infinite. Contrary to the finite population case, various unanimity and anonymity axioms can be formulated. We show a tension between unanimity and anonymity by providing possibility and impossibility results. We also examine the case in which social preferences are allowed to be quasi-transitive.     

Transversals, systems of distinct representatives, mechanism design, and matching

A transversal generated by a system of distinct representatives (SDR) for a collection of sets consists of an element from each set (its representative) such that the representative uniquely identifies the set it belongs to. Theorem 1 gives a necessary and sufficient condition that an arbitrary collection, finite or infinite, of sets, finite or infinite, have an SDR. The proof is direct, short. A Corollary to Theorem 1 shows explicitly the application to matching problems. In the context of designing decentralized economic mechanisms, it turned out to be important to know when one can construct an SDR for a collection of sets that cover the parameter space characterizing a finite number of economic agents. The condition of Theorem 1 is readily verifiable in that economic context. Theorems 2–5 give different characterizations of situations in which the collection of sets is a partition. This is of interest because partitions have special properties of informational efficiency.     

Differentiability as convergence to perfectly competitive equilibrium

A concept of convergence to perfectly competitive equilibrium, called asymptotically no-surplus, is demonstrated for a sequence of exchange economies in which both the number of agents and the number of commodities is increasing. The no-surplus criterion for perfect competition represents an ordinal extension of the marginal productivity theory of distribution. Its asymptotic definition resembles a Fréchet derivative.     

Gumbel’s Identity,Binomial Moments,and Bonferroni Sums

Gumbel’s Identity equates the Bonferroni sum with the k ‐ th binomial moment of the number of events M_n which occur, out of n arbitrary events. We provide a unified treatment of familiar probability bounds on a union of events by Bonferroni, Galambos–Rényi, Dawson–Sankoff, and Chung–Erdös, as well as less familiar bounds by Fréchet and Gumbel, all of which are expressed in terms of Bonferroni sums, by showing that all these arise as bounds in a more general setting in terms of binomial moments of a general non‐negative integer‐valued random variable. Use of Gumbel’s Identity then gives the inequalities in familiar Bonferroni sum form. This approach simplifies existing proofs. It also allows generalization of the results of Fréchet and Gumbel to give bounds on the probability that at least t of n events occur for any A further consequence of the approach is an improvement of a recent bound of Petrov which itself generalizes the Chung–Erdös bound.     

The topological equivalence of the pareto condition and the existence of a dictator

The paper studies two standard properties of rules for aggregating individual into social preferences: non-dictatorship and the Pareto condition. Together with the condition of independence of irrelevant alternatives, these are the three basic axioms of Arrow's social choice paradox.We prove the topological equivalence between the Pareto condition and the existence of a dictator for continuous rules. The axiom of independence of irrelevant alternatives is not required.The results use a topological framework for aggregation introduced in Chichilnisky (1980), but under different conditions. In Chichilnisky (1980) rules are anonymous and respect unanimity. Since anonymity is strictly stronger than the condition of non-dictatorship, while respect of unanimity is strictly weaker than the Pareto condition, the two sets of conditions are not comparable.     

Sociological Models Based on Fréchet Random Variables

Products of random variables are of both practical and theoretical significance to social scientists. This has increased the need to have available the widest possible range of statistical results on products of random variables. In this note, the distribution of the product XY is derived when X and Y are independent Fréchet random variables. Extensive tabulations of the associated percentage points are also given.     

On the computability of quasi-transitive binary social choice rules in an infinite society and the halting problem

This paper investigates the computability problem of the existence of a vetoer and an oligarchy for quasi-transitive binary social choice rules (Mas-Colell and Sonnenschein in Rev Econ Stud 39:185–192, 1972) in a society with an infinite number of individuals (infinite society) according to the computable calculus (or computable analysis) by Aberth (Computable analysis, McGraw-Hill, New York, 1980; Computable calculus, Academic Press, Dublin, 2001). We will show the following results. The problem whether a quasi-transitive binary social choice rule which satisfies Pareto principle and independence of irrelevant alternatives (IIA) has a vetoer or has no vetoer in an infinite society is a nonsolvable problem, that is, there exists no ideal computer program for a quasi-transitive binary social choice rule which satisfies Pareto principle and IIA that decides whether it has a vetoer or has no vetoer. And it is equivalent to nonsolvability of the halting problem. We also show that if for any quasi-transitive binary social choice rule there exists an oligarchy in an infinite society, whether it is finite or infinite is a nonsolvable problem. A vetoer is an individual such that if he strictly prefers an alternative to another alternative, then the society prefers the former to the latter or is indifferent between them regardless of the preferences of other individuals, and an oligarchy is the minimal set of individuals which has dictatorial power and its each member is a vetoer. It will be shown that an oligarchy is a set of vetoers if it exists. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 20530165, and the Grant-in-Aid from the Zengin Foundation for Studies on Economics and Finance in Japan.     

An Empirical Test of Cognitive Style and Strategic Decision Outcomes*

abstract We examine how cognitive style, as measured by the MBTI, affects strategic decision outcomes. Executives participated in a simulated strategic decision making environment that allowed controlled collection of decision outcomes, including manager decisiveness, decision quality, and perceived effectiveness. We found that iNtuiting/Thinking managers used their intuition to make cognitive leaps based on objective information to craft more decisions of higher quality than other managers. In contrast, Sensing/Feeling types used time to seek socially acceptable decisions, which led to the lowest number of decisions and the lowest perceived effectiveness of all. We found no effect on decisiveness or perceived effectiveness based on a manager's preference for Perceiving or Judging. However, we found that others perceived Extraverted managers as being more effective than Introverted managers when, in fact, the Extraverts were no more decisive than Introverts. Thus, cognitive style influences actual decision outcomes as well as how others perceive one's decision performance.     

Testing conditional independence via empirical likelihood

We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother functions. We show that the test statistics are asymptotically normal under the null hypothesis and a sequence of Pitman local alternatives. We also show that the tests possess an asymptotic optimality property in terms of average power. Simulations suggest that the tests are well behaved in finite samples. Applications to some economic and financial time series indicate that our tests reveal some interesting nonlinear causal relations which the traditional linear Granger causality test fails to detect.     

Revealed preferences: A topological approach

The purpose of this paper is to study the relationship between the axiomatic foundations of revealed preference theory and the continuity properties of choice. The main result of this paper shows that the continuity of a set-to-point choice function is equivalent to the weak axiom of revealed preference and openness of the strict revealed relation, provided that the collection of budget sets is endowed with a topology used widely by economists.     

Optimal control with an unbounded horizon

This paper extends existence results for finite and infinite horizon control problems to ‘unbounded horizon’ problems where both finite and infinite terminal times are feasible and there are non-trivial payoff implications (in particular, because of a non-zero terminal valuation) in making this choice. The classical approach used in the paper leads to simple and fairly intuitive conditions for existence involving direct assumptions about the objective function, state dynamics, and control constraints which are accessible to applied users of control techniques. In addition, the results are proved under fairly weak concavity assumptions and thus have potential applicability to ‘increasing returns’ problems.     

Nonlinear supporting prices : The superadditive case

Assumptions on allocations and preferences sufficient to allow superadditive price support are considered for an exchange economy with a finite number of traders when the commodity space is an ordered topological vector space. The main requirements are a uniformmonotonicity assumption on preferences and that no permutation of the allocation among agents yields a Pareto improvement. No convexity assumption on preferences is used, the positive orthant need not have interior, while the proof is constructive. Applications to finite and infinite dimensional commodity spaces are discussed.     

A law of large numbers for abstract random variables

Summary It was emphasized by Fréchet [8] that in many of the practical applications, we get, as a result of a random experiment, an abstract random variableX belonging to a setX. Givenn determinations of the variableX, an arithmetic meanZ _n is introduced in 2-. It reduces to the classical arithmetic mean, whenX is the set of real numbers. Moreover, if the random variableX is Gaussian, having a meanM(X), and belongs to a certain (4-) familyF, the introduced arithmetic meanZ _n constitutes an exhausting estimation [5] of the meanM(X).     

Ratchet consumption over finite and infinite planning horizons

Ratchet consumers want their spending to always increase and never decrease. We find an optimal consumption rule for ratchet consumers by maximizing an expected utility that eschews spending declines, yet permits a range of choices for felicity and time preference functions. This solution can be tailored to fit both retirees with finite planning horizons and endowments with infinite planning horizons. We assume complete markets modeled by a pricing kernel generated by a Lévy process. When the kernel is log-normal, we obtain closed-form solutions for both finite and infinite horizons.     

Conditional feature screening for mean and variance functions in models with multiple-index structure

The existing methods for feature screening focus mainly on the mean function of regression models. The variance function, however, plays an important role in statistical theory and application. We thus investigate feature screening for mean and variance functions with multiple-index framework in high dimensional regression models. Notice that some information about predictors can be known in advance from previous investigations and experience, for example, a certain set of predictors is related to the response. Based on the conditional information, together with empirical likelihood, we propose conditional feature screening procedures. Our methods can consistently estimate the sets of active predictors in the mean and variance functions. It is interesting that the proposed screening procedures can avoid estimating the unknown link functions in the mean and variance functions, and moreover, can work well in the case of high correlation among the predictors without iterative algorithm. Therefore, our proposal is of computational simplicity. Furthermore, as a conditional method, our method is robust to the choice of the conditional set. The theoretical results reveal that the proposed procedures have sure screening properties. The attractive finite sample performance of our method is illustrated in simulations and a real data application.     

Generalizing weak instrument robust IV statistics towards multiple parameters,unrestricted covariance matrices and identification statistics

We generalize the weak instrument robust score or Lagrange multiplier and likelihood ratio instrumental variables (IV) statistics towards multiple parameters and a general covariance matrix so they can be used in the generalized method of moments (GMM). The GMM extension of Moreira's [2003. A conditional likelihood ratio test for structural models. Econometrica 71, 1027–1048] conditional likelihood ratio statistic towards GMM preserves its expression except that it becomes conditional on a statistic that tests the rank of a matrix. We analyze the spurious power decline of Kleibergen's [2002. Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70, 1781–1803, 2005. Testing parameters in GMM without assuming that they are identified. Econometrica 73, 1103–1124] score statistic and show that an independent misspecification pre-test overcomes it. We construct identification statistics that reflect if the confidence sets of the parameters are bounded. A power study and the possible shapes of confidence sets illustrate the analysis.     

On games without side payments arising from a general class of markets

The class of games without side payments obtainable from finite trader markets having possibly infinite dimensional commodity spaces, individual compact, convex consumption and production sets, and concave upper-semicontinuous utility functions is considered. It is shown that these market games are precisely the totally balanced games. In fact, each totally balanced game is shown to have both a finite commodity representation and an infinite commodity ‘simple’ representation.     

Nash-implementation of the weak Pareto choice rule for indecomposable environments

A feasible mechanism is constructed which weakly Nash-implements the weak Pareto choice rule over a certain class of indecomposable pure-exchange environments, where there may be no private goods whose consumption has no external effects. Received: 30 November 1995 / Accepted: 24 June 1997