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.     

Background Risk and the Performance of Insurance Markets under Adverse Selection

Background risk can influence the performance of insurance markets that must deal with adverse selection when applicants are risk vulnerable, since they are more averse to bearing the insurable risk as a result of their exposures to background risk. We show that background risk always results in a lower deductible for the incentive constrained contract, and that a broader range of markets attains the stable sequential equilibrium cross-subsidized pair of separating contracts. We conclude that background risk always improves the performance of markets for coverage against (insurable) foreground risks that must deal with adverse selection. We also find, however, that these improvements are never sufficient to offset the cost to insureds of bearing the background risk.     

The product elimination function

Historically, major consideration given to product management has focused on research and development or the introductory stage of the product life cycle. The authors present an empirical study delineating the variables to be considered in the product elimination process. More specifically, the elimination process is evaluated under a situation of poor product performance despite a generally viable market. The basic objectives of the study were: to determine the significant variables in the product elimination process of the Small Appliance Industry; to determine the relative importance of the variables; to examine the interaction among variables. The data obtained through personal structured questionnaire interviews were analyzed and provided a ranking of twenty-six variables relevant to the elimination process. Moreover, the Johnson's Hierarchical Clustering Schemes was applied to determine the interaction among variables. The results indicate that profitability and financial variables are most significant in the elimination decision-process. Second, the primary clusters of importance are concerned with market share, market growth rate, consumer awareness, and competitive action.     

Marginal distributions of sequential and generalized order statistics

Expressions for marginal distribution functions of sequential order statistics and generalized order statistics are presented without any restrictions imposed on the model parameters. The results are related to the relevation transform, to the distribution of the product of Beta distributed random variables, and to Meijers G-functions. Some selected applications in the areas of moments, conditional distributions, recurrence relations, and reliability properties are shown. Key words:Order statistics; Generalized order statistics; Sequential order statistics; Record values; Distribution theory; Meijers G-function; Recurrence relations; Reliability properties.     

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.     

Money in the pure consumption loan model

The purpose of this paper is to show how modern techniques of Temporary competitive equilibrium analysis can be applied to models of the “pure consumption loan model” type. One considers Samuelson's simplest model where traders live two periods and where money is the only store of value. It is proved that a temporary equilibrium exists if price expectations are sufficiently independent of current prices. A stationary market equilibrium is shown to exist if there is a set of traders (i) whose total resources are greater when they are young than when they are old, (ii) who are indifferent between present and future consumption. It is proved that this existence theorem still holds if the economy is sufficiently “close” to an economy which has this property. A stationary market equilibrium is shown to be Pareto optimal if all traders hold positive cash balances. It may be inefficient if this condition is not satisfied, for some traders may then be willing to borrow, which they cannot do in this model.