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.     

The politics of redistributive social insurance

This paper analyses the political support for a social insurance that includes elements of redistribution when there exists an imperfect private insurance alternative. Individuals differ both in their income and risk. The social insurance is compulsory and charges an income-related contribution with pooling of risks. The private insurance is voluntary and charges a contribution based on individual risks. However due to the adverse selection problem, private insurance companies provide only partial insurance. Adopting a non-expected utility model, we show that there is a general majority support for social insurance and that this support is increasing with risk aversion. We also show that a mixed insurance is politically impossible, regardless of the degree of redistribution of social insurance and the joint distribution of risk and income in the population. Lastly, we analyse how the political support for social insurance is affected by any change in its redistributive component and the possibility of using genetic tests.     

The Borda rule,Condorcet consistency and Condorcet stability

Summary. The Borda rule is known to be the least vulnerable scoring rule to Condorcet inconsistency, Saari (2000). Such inconsistency occurs when the Condorcet winner (the alternative which is preferred to any other alternative by a simple majority) is not selected by the Borda rule. This note exposes the relationship between the Borda rule and the Condorcet q-majority principle as well as the Condorcet q-majority voting rule. The main result establishes that the Borda rule is Condorcet q-majority consistent when where k is the number of alternatives. The second result establishes that is the minimal degree of majority decisiveness corresponding to the Borda rule under sincere voting. The same majority is required to ensure decisiveness under the Borda rule and to ensure that a q-rule (the generalized q-majority Condorcet rule) is a voting rule. Received: April 8, 2002; revised version: July 17, 2002 Correspondence to:S. Nitzan     

On the dynamic selection of mechanisms for provision of public projects

How do individuals' spatial decisions affect the institutions for public goods provision over time? This paper describes a dynamic model in which the provision mechanism for a public project is itself the object of locational choice of individuals. Individuals in an ongoing society must choose between a location with a Majority Rule mechanism and one with a Voluntary Contribution mechanism. Each mechanism determines a funding decision for a local public project which is repeated over time. Generations of individuals asynchronously supercede their ‘parents’, creating an entry/exit process that allows individuals with possibly different beliefs to enter society. A self-confirming equilibrium (SCE) belief process describes an evolution of beliefs in this society consistent with a self-confirming equilibrium (Fudenberg and Levine, 1993) of the repeated location/provision game. It is shown that the process with belief mutation as new individuals enter society results in a globally absorbing state in which the Majority Rule mechanism is the unique survivor of the two.     

An analysis of majority owner‐managed companies in the UK

This paper investigates the characteristics of 73 UK companies in which managers have an ownership stake of greater than 50 per cent. We find that majority owner‐managed companies make less use of alternative corporate control systems and are less likely to remove their chief executive officer or other board members following poor performance. However, our sample firms actually outperform diffusely held companies of similar size in the same industry. The determinants of majority control appear more closely related to the characteristics of the controlling shareholders rather than the firm's operating environment. Changes in the ownership structure of our sample companies owe more to changes in owner‐specific characteristics and security issuance than they are related to changes in the company's operating environment or company performance. We conclude that despite the obvious agency costs of managerial entrenchment for closely held companies, for the present sample at least the incentive alignment benefits of large director shareholdings are beneficial to outside shareholders.     

Majority cycles in a multi-dimensional setting

Summary. We consider a set of alternatives (electoral platforms, bills, etc. ...) defined as a Cartesian product of k finite discrete sets. We assume that the preferences of the individuals (voters) are marginally single-peaked and separable. The main result of this paper states that the pairwise majority relation satisfies these two properties but that it might exhibit several cycles. This result is important when related to classical problems of multi-dimensional decisions such as logrolling and vote trading. We relate our result with a continuous version of it (McKelvey, 1976). Received: March 21, 2000; revised version: April 12, 2001     

Winning probabilities in a pairwise lottery system with three alternatives

Summary. The pairwise lottery system is a multiple round voting procedure which chooses by lot a winner from a pair of alternatives to advance to the next round where in each round the odds of selection are based on each alternatives majority rule votes. We develop a framework for determining the asymptotic relative likelihood of the lottery selecting in the final round the Borda winner, Condorcet winner, and Condorcet loser for the three alternative case. We also show the procedure is equivalent to a Borda lottery when only a single round of voting is conducted. Finally, we present an alternative voting rule which yields the same winning probabilities as the pairwise lottery in the limiting case as the number of rounds of the pairwise lottery becomes large.Received: 5 June 2003, Revised: 17 June 2004, JEL Classification Numbers: D71. Correspondence to: Jac C. HeckelmanWe thank Keith Dougherty and Andrew Yates for their comments.