On the real voting power index

Both formal and real voting power indices completely disregard the significance of voting methods to processes of coalition formation. This may result in misleading figures of voting strength if estimated probabilities of certain coalitions are utilized in the indices. It is shown that application of the real voting power index of Stenlund, Lane and Bjurulf (a measure closely related to the Banzhaf index) to parliaments using the amendment voting procedure, is problematical. If a parliament votes upon three or more alternatives, the winning coalition on the issue depends more or less on the order of voting. The measurement of real voting power is distorted both if the formation of the voting order is based on application of general voting order rules, or if it is totally unregulated.     

A note on power,satisfaction and group cohesiveness in a voting body

This essay discusses the power of an m-member subgroup of an N-member (N = 2n + 1) voting body, whose members vote either ‘yes’ or ‘no’ to a given issue. Passage or defeat of an issue is determined by simple majority. The power of the subgroup is defined as the probability that the outcome of a vote changes if all the members of the group reverse their votes. We assume that across a sequence of issues voters' behavior can be described by a Pólya-Eggenberger probability model, containing a parameter interpretable as group cohesiveness. Special cases are bloc voting and completely independent voting.Our model allows us to study interesting intermediate cases, i.e., situations where group cohesiveness is less than that of bloc voting yet stronger than in the case of independence. Satisfaction, defined as the probability of voting with the majority, and individual power are discussed in the light of the model.     

Cost sharing with multiple technologies

We study cost sharing problems where gains from cooperation can come from the presence of other agents, such as when agents share their technologies. A simple model is built, where economies of scale are eliminated in order to study this effect. We use as the key axiom the property that, if an agent does not improve the technology of any coalition he joins, he should not get any part of the gain from cooperation. With properties of linearity and symmetry, this axiom characterizes a well-defined set of rules. From this set, we propose a rule derived from the familiar Shapley value. We show that it is the only rule in that set satisfying an upper-limit property on individual cost allocations or a monotonicity property when technology improves. We also derive a distinct rule using a property that ensures that no coalition has an incentive to manipulate the individual demands of its members.     

Cost sharing with multiple technologies

We study cost sharing problems where gains from cooperation can come from the presence of other agents, such as when agents share their technologies. A simple model is built, where economies of scale are eliminated in order to study this effect. We use as the key axiom the property that, if an agent does not improve the technology of any coalition he joins, he should not get any part of the gain from cooperation. With properties of linearity and symmetry, this axiom characterizes a well-defined set of rules. From this set, we propose a rule derived from the familiar Shapley value. We show that it is the only rule in that set satisfying an upper-limit property on individual cost allocations or a monotonicity property when technology improves. We also derive a distinct rule using a property that ensures that no coalition has an incentive to manipulate the individual demands of its members.     

Public goods,voting, and growth

We study a parametric politico‐economic model of economic growth with productive public goods and public consumption goods. The provision of public goods is funded by a proportional tax. Agents are heterogeneous in their initial capital endowments, discount factors, and the relative weights of public consumption in overall private utility. They vote on the shares of public goods in gross domestic products (GDP). We propose a definition of voting equilibrium, prove the existence and provide a characterization of voting equilibria, and obtain a closed‐form solution for the voting outcomes. Also we introduce a “fictitious” representative agent and interpret the outcome of voting as a choice made by a central planner for his benefit. Finally, we undertake comparative static analysis of the shares of public goods in GDP and of the rate of balanced growth with respect to the discount factors and the preferences for public consumption. The results of this analysis suggest that the representative‐agent version of our model is capable of capturing the interaction between many voting heterogeneous agents only if the heterogeneity is one‐dimensional.     

Committee Design with Endogenous Information

Identical agents gather costly information, and then aggregate it through voting. Because information is a public good, information is underprovided relative to the social optimum. A "good" voting rule must give incentives to acquire information, as well as aggregate information efficiently. A voting rule that requires a large plurality (in the extreme, unanimity) to upset the status quo can be optimal only if the information available to each agent is sufficiently accurate. This result is independent of the preferences of voters and of the cost of information.     

The (sub-)optimality of the majority rule

We consider collective choice from two alternatives. Ex-ante, each agent is uncertain about which alternative she prefers, and may be uncertain about the intensity of her preferences. An environment is given by a probability distribution over utility vectors that is symmetric across agents and neutral across alternatives. In many environments, the majority voting rule maximizes agents? ex-ante expected utilities among all anonymous and dominant-strategy implementable choice rules. But in some environments where the agents? utilities are stochastically correlated, other dominant-strategy choice rules are better for all agents. If utilities are stochastically independent across agents, majority voting is ex-ante optimal among all anonymous and incentive-compatible rules. We also compare rules from an interim-viewpoint.     

Core equivalence with congested public goods

Summary This paper examines a model of an infinite production economy with a finite number of types of agents andsemi- public goods, which are subjected to crowding and exclusion. The utility of an agent depends not only on the vector of public commodities produced by the coalition to which she belongs, but also on the mass of agents of her type who are the members of this coalition. The main purpose of the paper is to derive necessary and sufficient conditions on the local degrees of congestion which would guarantee the equivalence between the core and the set of equal treatment Lindahl equilibria. We prove that this equivalence holdsif and only if there are constant returns to group size for each type of agents. It implies that linearity of each agent's congestion function with respect to the mass of the agents of her own type is necessary for the core equivalence to hold.The final version of this paper was written while Shlomo Weber was visiting the Technical University of Dresden as the Fellow of the Alexander von Humboldt Foundation, whose support is gratefully acknowledged. The authors are grateful to Peter Meyer, Nicholas Yannelis and the anonymous referees for useful remarks and suggestions.     

Information transmission in coalitional voting games

A core allocation of a complete information economy can be characterized as one that would not be unanimously rejected in favor of another feasible alternative by any coalition. We use this test of coalitional voting in an incomplete information environment to formalize a notion of resilience. Since information transmission is implicit in the Bayesian equilibria of such voting games, this approach makes it possible to derive core concepts in which the transmission of information among members of a coalition is endogenous. Our results lend support to the credible core of Dutta and Vohra [Incomplete information, credibility and the core, Math. Soc. Sci. 50 (2005) 148-165] and the core proposed by Myerson [Virtual utility and the core for games with incomplete information, Mimeo, University of Chicago, 2005] as two that can be justified in terms of coalitional voting.     

A simple model of coalitional bidding

Summary. We analyze a model of coalitional bidding in which coalitions form endogenously and compete with each other. Since the nature of this competition influences the way in which agents organize themselves into coalitions, our main aim is to characterize the equilibrium coalition structure and the resulting bids. We do so in a simple model in which the seller may have good reason to allow joint bidding. In particular, we study a model in which the agents are budget constrained, and are allowed to form coalitions to pool their finances before engaging in the first price auction. We show that if the budget constraint is very severe, the equilibrium coalition structure consists of two coalitions, one slightly larger than the other; interestingly, it is not the grand coalition. This equilibrium coalition structure is one which yields (approximately) the maximum expected revenue. Thus the seller can induce the optimal (revenue maximizing) degree of cooperation among budget constrained buyers simply by permitting them to collude. Received: June 25, 1999; revised version: November 13, 2000     

Group identification with (incomplete) preferences

We consider the problem of identifying members of a group based on individual opinions. Since agents do not have preferences in the model, properties of rules that concern preferences (e.g., strategy‐proofness and efficiency) have not been studied in the literature. We fill this gap by working with a class of incomplete preferences derived directly from opinions. Our main result characterizes a new family of group identification rules, called voting‐by‐equitable‐committees rules, using two well‐known properties: strategy‐proofness and equal treatment of equals. Our family contains as a special case the consent rules (Samet & Schmeidler. J. Econ. Theory, 110 (2003), pp. 213–233), which are symmetric and embody various degrees of liberalism and democracy; and it also includes dictatorial and oligarchic rules that value agents’ opinions differently. In the presence of strategy‐proofness, efficiency turns out to be equivalent to non‐degeneracy (i.e., any agent may potentially be included or excluded from the group). This implies that a rule satisfies strategy‐proofness, efficiency, and equal treatment of equals if, and only if, it is a non‐degenerate voting‐by‐equitable‐committees rule.     

Bargaining in committees as an extension of Nash's bargaining theory

This paper addresses the following issue: if a set of agents bargain on a set of feasible alternatives ‘in the shadow’ of a voting rule, that is, any agreement can be enforced if a ‘winning coalition’ supports it, what general agreements are likely to arise? In other words: what influence can the voting rule used to settle (possibly nonunanimous) agreements have on the outcome of consensus? We model the situation as an extension of the Nash bargaining problem in which an arbitrary voting rule replaces unanimity. In this setting a natural extension of Nash's solution is characterized.     

Waiting to settle: Multilateral bargaining with subjective biases

We study multilateral bargaining games where agents disagree over their bargaining power. We show that if agents are extremely optimistic, there may be costly delays in an arbitrarily long finite game but if optimism is moderate, all sufficiently long games end in immediate agreement. We show that the game with extreme optimism is highly unstable in the finite-horizon, and we examine the ramifications of this instability on the infinite-horizon problem. Finally, we consider other voting rules, and show that the majority-rule may be more efficient than the unanimity rule when agents are optimistic.     

Uniqueness of stationary equilibrium payoffs in coalitional bargaining

We study a model of sequential bargaining in which, in each period before an agreement is reached, the proposer?s identity is randomly determined, the proposer suggests a division of a pie of size one, each other agent either approves or rejects the proposal, and the proposal is implemented if the set of approving agents is a winning coalition for the proposer. The theory of the fixed point index is used to show that stationary equilibrium expected payoffs of this coalitional bargaining game are unique. This generalizes Eraslan [34] insofar as: (a) there are no restrictions on the structure of sets of winning coalitions; (b) different proposers may have different sets of winning coalitions; (c) there may be a positive probability that no proposer is selected.     

A note on feasible implementations

This paper is concerned with the problem of individually feasible outcomes in decentralized allocation mechanisms. We consider a well-known mechanism which achieves efficient allocations in equilibrium. This mechanism, however, may leave agents bankrupt, if they fail to reach equilibrium. It is shown that the bankruptcy problem can be avoided, if a voting stage is added to the original mechanism.     

How to win a large election

We consider the optimization problem of a campaign trying to win an election when facing aggregate uncertainty, where agentsʼ voting probabilities are uncertain. Even a small amount of uncertainty will in a large electorate eliminate many of counterintuitive results that arise when voting probabilities are known. In particular, a campaign that can affect the voting probabilities of a fraction of the electorate should maximize the expected difference between its candidateʼs and the opposing candidateʼs share of the fractionʼs potential vote. When a campaign can target only finitely many voters, maximization of the same objective function remains optimal if a convergence condition is satisfied. When voting probabilities are certain, this convergence condition obtains only at knife-edge combinations of parameters, but when voting probabilities are uncertain the condition is necessarily satisfied.     

Demand bargaining and proportional payoffs in majority games

We study a majoritarian bargaining model in which players make payoff demands in decreasing order of voting weight. The unique subgame perfect equilibrium outcome is such that the minimal winning coalition of the players that move first forms with payoffs proportional to the voting weights. This result advances previous analysis in terms of one or more of the following: a) the simplicity of the extensive form (finite horizon with a predetermined order of moves); b) the range of the majority games covered; c) the equilibrium concept (subgame perfect equilibrium is sufficient for a unique prediction).     

THE POLITICAL CHOICE OF THE EXCHANGE RATE REGIME*

The purpose of this paper is to present a model in which the choice of the optimal exchange rate regime is envisaged in a political setting. We consider a country whose voting population comprises three types of agents, importers, exporters and speculators, who select their position on exchange rate policy according to welfare maximization. As a result, well-defined interest groups are shown to emerge. Each coalition makes contributions to one of two political candidates running for political office in support for their optimal policy intervention. When policy pronouncements by the two candidates are made in terms of exchange rate volatility, the equilibrium consists of two extremes: a fixed versus flexible exchange regime, the latter with bounded volatility [JEL D72, F31].     

Dominance solvability of dynamic bargaining games

We formulate and study a general finite-horizon bargaining game with simultaneous moves and a disagreement outcome that need not be the worst possible result for the agents. Conditions are identified under which the game is dominance solvable in the sense that iterative deletion of weakly dominated strategies selects a unique outcome. Our analysis uses a backward induction procedure to pinpoint the latest moment at which a coalition can be found with both an incentive and the authority to force one of the available alternatives. Iterative dominance then implies that the alternative characterized in this way will be agreed upon at the outset—or, if a suitable coalition is never found, that no agreement will be reached.     

On the core and Walrasian expectations equilibrium in infinite dimensional commodity spaces

In this paper, we establish two different characterizations of Walrasian expectations allocations by the veto power of the grand coalition in an asymmetric information economy having finitely many agents and states of nature and whose commodity space is a Banach lattice. The first one deals with Aubin non-dominated allocations, and the other claims that an allocation is a Walrasian expectations allocation if and only if it is not privately dominated by the grand coalition, by considering perturbations of the original initial endowments in precise directions.