The replacement principle for the provision of multiple public goods on tree networks

This article considers the provision of two public goods on tree networks where each agent has a single-peaked preference. We show that if there are at least four agents, then no social choice rule exists that satisfies efficiency and replacement-domination. In fact, these properties are incompatible, even if agents’ preferences are restricted to a smaller domain of symmetric single-peaked preferences. However, for rules on an interval, we prove that Miyagawa’s (Soc Choice Welf 18:527–541, 2001) characterization that only the left-peaks rule and the right-peaks rule satisfy both of these properties also holds on the domain of symmetric single-peaked preferences. Moreover, if agents’ peak locations are restricted to either the nodes or the endpoints of trees, rules exist on a subclass of trees. We provide a characterization of a family of such rules for this tree subclass.     

Solidarity in choosing a location on a cycle

We study the implications of two solidarity conditions on the efficient location of a public good on a cycle, when agents have single-peaked, symmetric preferences. Both conditions require that when circumstances change, the agents not responsible for the change should all be affected in the same direction: either they all gain or they all loose. The first condition, population-monotonicity, applies to arrival or departure of one agent. The second, replacement-domination, applies to changes in the preferences of one agent. Unfortunately, no Pareto-efficient solution satisfies any of these properties. However, if agents’ preferred points are restricted to the vertices of a small regular polygon inscribed in the circle, solutions exist. We characterize them as a class of efficient priority rules.     

A Note on the Separability Principle in Economies with Single-Peaked Preferences

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the analysis of the problem is the so-called uniform rule. Chun (2001) proves that the uniform rule is the only rule satisfying Pareto optimality, no-envy, separability, and Ω-continuity. We obtain an alternative characterization by using a weak replication-invariance condition, called duplication-invariance, instead of Ω-continuity. Furthermore, we prove that the equal division lower bound and separability imply no-envy. Using this result, we strengthen one of Chun’s (2001) characterizations of the uniform rule by showing that the uniform rule is the only rule satisfying Pareto optimality, the equal division lower bound, separability, and either Ω-continuity or duplication-invariance.     

Allocating multiple estates among agents with single-peaked preferences

We consider the problem of allocating multiple social endowments (estates) of a perfectly divisible commodity among a group of agents with single-peaked preferences when each agent’s share can come from at most one estate. We inquire if well-known single-estate rules, such as the Uniform rule, the Proportional rule or the fixed-path rules can be coupled with a matching rule so as to achieve efficiency in the multi-estate level. On the class of problems where all agents have symmetric preferences, any efficient single-estate rule can be extended to an efficient multi-estate rule. If we allow asymmetric preferences however, this is no more the case. For nondictatorial single-estate rules that satisfy efficiency, strategy proofness, consistency, and resource monotonicity, an efficient extension to multiple estates is impossible. A similar impossibility also holds for single-estate rules that satisfy efficiency, peak-only, and a weak fairness property. We would like to express our gratitude to Bhaskar Dutta, Semih Koray, Hervé Moulin, and Yuntong Wang as well as an associate editor and two anonymous referees of this journal for detailed comments and suggestions. We also thank the seminar participants at Bilkent University, Indian Statistical Institute, Bilgi University, University of Warwick, ASSET 2003, and BWED XXVI.     

‘One and a Half Dimensional’ Preferences and Majority Rule

I examine a model of majority rule in which alternatives are described by two characteristics: (1) their position in a standard, left-right dimension, and (2) their position in a good-bad dimension, over which voters have identical preferences. I show that when voters’ preferences are single-peaked and concave over the first dimension, majority rule is transitive, and the majority’s preferences are identical to the median voter’s. Thus, Black’s (The theory of committees and elections, 1958) theorem extends to such a “one and a half” dimensional framework. Meanwhile, another well-known result of majority rule, Downs’ (An economic theory of democracy, 1957) electoral competition model, does not extend to the framework. The condition that preferences can be represented in a one-and-a-half-dimensional framework is strictly weaker than the condition that preferences be single-peaked and symmetric. The condition is strictly stronger than the condition that preferences be order-restricted, as defined by Rothstein (Soc Choice Welf 7:331–342;1990).     

Migration disequilibrium and specific division rules

We examine the extent to which migration equilibria fail to exist in a global economy in which a specific division rule determines the allocation of a perfectly divisible, nondisposable resource among individuals with single-peaked preferences who reside in local economies. In particular, almost without exception, under the egalitarian, proportional, queuing, and uniform division rules, migration equilibria fail to exist for some sets of preferences. Received: 23 May 1995 / Accepted: 1 October 1996     

Strategy-proof division with single-peaked preferences and individual endowments

We consider the problem of (re)allocating the total endowment of an infinitely divisible commodity among agents with single-peaked preferences and individual endowments. We propose an extension of the so-called uniform rule and show that it is the unique rule satisfying Pareto optimality, strategy-proofness, reversibility, and an equal-treatment condition. The resulting rule turns out to be peaks-only and individually rational: the allocation assigned by the rule depends only on the peaks of the preferences, and no agent is worse off than at his individual endowment. Received: 8 September 1995/Accepted: 30 October 1996     

Resource-monotonic solutions to the problem of fair division when preferences are single-peaked

We consider the problem of fairly allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. We search for solutions satisfying resource-monotonicity, the requirement that all agents be affected in the same direction when the amount to divide changes. Although there are resource-monotonic selections from the Pareto solution, there are none satisfying the distributional requirements of no-envy or individual rationality from equal division. We then consider the weakening of resource-monotonicity obtained by allowing only changes in the amount to divide that do not reverse the direction of the inequality between the amount to divide and the sum of the preferred amounts. We show that there is essentially a unique selection from the solution that associates with each economy its set of envy-free and efficient allocations satisfying this property of one-sided resource-monotonicity: it is the uniform rule, a solution that has played a central role in previous analyses of the problem.     

A characterization of the uniform rule with several commodities and agents

We consider a problem of allocating infinitely divisible commodities among a group of agents. More specifically, there are several commodities to be allocated and agents have continuous, strictly convex, and separable preferences. We establish that a rule satisfies strategy-proofness, unanimity, weak symmetry, and nonbossiness if and only if it is the uniform rule. This result extends to the class of continuous, strictly convex, and multidimensional single-peaked preferences.     

A maximal domain of preferences for strategy-proof,efficient, and simple rules in the division problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, tops-onlyness, and continuity. These domains (called partially single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.An earlier version of this paper circulated under the title A maximal domain of preferences for tops-only rules in the division problem. We are grateful to an associate editor of this journal for comments that helped to improve the presentation of the paper and to Matt Jackson for suggesting us the interest of identifying a maximal domain of preferences for tops-only rules. We are also grateful to Dolors Berga, Flip Klijn, Howard Petith, and a referee for helpful comments. The work of Alejandro Neme is partially supported by Research Grant 319502 from the Universidad Nacional de San Luis. The work of Jordi Massó is partially supported by Research Grants BEC2002-02130 from the Spanish Ministerio de Ciencia y Tecnología and 2001SGR-00162 from the Generalitat de Catalunya, and by the Barcelona Economics Program of CREA from the Generalitat de Catalunya. The paper was partially written while Alejandro Neme was visiting the UAB unde r a sabbatical fellowship from the Generalitat de Catalunya.     

Costly voting when both information and preferences differ: is turnout too high or too low?

We study a model of costly voting over two alternatives, where agents’ preferences are determined by both (i) a private preference in favour of one alternative e.g. candidates’ policies, and (ii) heterogeneous information in the form of noisy signals about a commonly valued state of the world e.g. candidate competence. We show that depending on the level of the personal bias (weight on private preference), voting is either according to private preferences or according to signals. When voting takes place according to private preferences, there is an unique equilibrium with inefficiently high turnout. In contrast, when voting takes place according to signals, turnout is locally too low. Multiple Pareto-ranked voting equilibria may exist and in particular, compulsory voting may Pareto dominate voluntary voting. Moreover, an increase in personal bias can cause turnout to rise or fall, and an increase in the accuracy of information may cause a switch to voting on the basis of signals and thus lower turnout, even though it increases welfare. This is a substantially revised version of Department of Economics University of Warwick Working Paper 670, “Information Aggregation, Costly Voting and Common Values”, January 2003. We would like to thank B. Dutta, M. Morelli, C. Perrroni, V. Bhaskar and seminar participants at Warwick, Nottingham and the ESRC Workshop in Game Theory for their comments. We would also like to thank the editor and an anonymous referee for their comments.     

Inefficiencies on linking decisions

It has recently been shown that by linking collective decisions the incentive costs can become negligible and, at the limit, ex ante efficiency can be achieved. In a voting situation this implies that the agents’ intensity of preferences can be taken into account even in the absence of monetary transfers. Rather than considering a limiting result we want to analyse what can be achieved while we consider a finite number of linked decisions. We first characterise the set of implementable mechanisms and show that ex ante efficiency can never be achieved. We then proceed to relax the efficiency requirement and prove that, even when we just require unanimity, the mechanism cannot be sensitive to the agents’ intensity of preference when the domain of preferences is unrestricted.     

Feasible Mechanisms in Economies with Type-Dependent Endowments

We propose two classes of allocation games for N.T.U. and T.U. exchange economies in which initial endowments and preferences depend on the agents’ private information. In both models, agents make non-verifiable claims about their types and effective deposits of consumption goods, which are redistributed by the planner. In a W-allocation game, the agents can withhold part of their endowment, namely consume whatever they do not deposit. In a D-allocation game, the agents can just destroypart of their endowment. W- and D- incentive compatible (I.C.) direct allocation mechanisms ask every agent to reveal his type and to make a deposit consistent with his reported type. The revelation principle holds in full generality for D-I.C. mechanisms but some care is needed for W-I.C. mechanisms. We further investigate the properties of both classes of mechanisms under common assumptions like non-exclusive information and/or constant aggregate endowment. In T.U. economies, W-I.C. and D-I.C. mechanisms are ex ante equivalent.     

A Geometric Study of Shareholders’ Voting in Incomplete Markets: Multivariate Median and Mean Shareholder Theorems

A simple parametric general equilibrium model with S states of nature and K < S firms is considered. Since markets are incomplete, at a (financial) equilibrium shareholders typically disagree on whether to keep or not the status quo production plans. Hence each firm faces a genuine problem of social choice. The setup proposed in the present paper allows to study these problems within a classical (Downsian) spatial voting model. Given the multidimensional nature of the latter, super majority rules with rate are needed to guarantee existence of politically stable production plans. A simple geometric argument is proposed showing why a 50%-majority stable production equilibrium exists when K=S−1. When the degree of incompleteness is more severe, under more restrictive assumptions on agents’ preferences and the distribution of agents’ types, equilibria are shown to exist for rates ρ smaller than Caplin and Nalebuff (Econometrica 59: 1–23, 1991) bound of 0.64: they obtain for production plans whose span contains the ‘ideal securities’ of all K mean shareholders.Hervé Crès is a member of the GREGHEC, unité CNRS, UMR 2959.     

Voting rules and efficiency in one-dimensional bargaining games with endogenous protocol

We analyze a rent-seeking contest that determines the bargaining protocol in a one-dimensional bargaining game, where agents preferences over social outcomes are single-peaked. We relate the incentives of agents to make unproductive and costly efforts/investments to the quota rules that are required to implement agreements. When the contest assigns persistent recognition probabilities, we find that simple majority minimizes the total investments and, hence, inefficiency. In case that the contest recurs each period, multiple equilibria exist with the particularity that in each equilibrium only one agent controls the agenda of the bargaining process.     

Strategy-proof rules for two public goods: double median rules

We consider the problem of selecting the locations of two (identical) public goods on an interval. Each agent has preferences over pairs of locations, which are induced from single-peaked rankings over single locations: each agent compares pairs of locations by comparing the location he ranks higher in each pair. We introduce a class of “double median rules” and characterize it by means of continuity, anonymity, strategy-proofness, and users only. To each pair of parameter sets, each set in the pair consisting of $(n+1)$ parameters, is associated a rule in the class. It is the rule that selects, for each preference profile, the medians of the peaks and the parameters belonging to each set in the pair. We identify the subclasses of the double median rules satisfying group strategy-proofness, weak efficiency, and double unanimity (or efficiency), respectively. We also discuss the classes of “multiple median rules” and “non-anonymous double median rules”.     

Linear cost sharing in economies with non-Samuelsonian public goods: Core equivalence

 We consider an economy with non-Samuelsonian public goods and we focus on linear cost sharing. In a linear cost sharing equilibrium all agents in the economy optimize given a certain fixed cost share to be contributed towards the provision of public goods in the economy. Hence, each agent pays a certain fraction of the total establishment costs of public goods and these cost shares are common knowledge. We show that for a certain fixed contribution scheme the resulting linear cost share equilibria are equivalent to corresponding core allocations, in which the core is based on the integral of the individual cost shares. We also show that there is no equivalence of the Foley core with cost share equilibria, even in well-behaved large economies. Received: 16 August 1995/Accepted: 29 July 1996     

An extension of Bowen’s dynamic voting rule to many dimensions

 We ask in this paper about the effect on social decisions of limiting the size of changes that voters may propose each time in an otherwise standard dynamic social choice model. The voting rule we study can be seen as an extension of Bowen’s dynamic “majority voting” rule, and is closely related to the dynamic procedures for public good allocation in the literature (Drèze and de la Vallée Poussin 1971; Malinvaud 1971; Laffont and Maskin 1983; Chander 1993). Under general assumptions we prove existence and Pareto efficiency of equilibrium, and show that our rule motivates voters not to misrepresent preferences (more precisely, the rule is Strongly Locally Individually Incentive Compatible). Under Euclidean preferences we find that electoral cycles do not arise (i.e., the rule is convergent), that there is a unique equilibrium, and that the equilibrium coincides with the solution to an old problem of geometry, first addressed by Fermat, Torricelli, and Cavallieri. Received: 20 September 1994/Accepted: 6 August 1996     

Equal factor equivalence in economies with multiple public goods

We reconsider the problem of provision and cost-sharing of multiple public goods. The efficient equal factor equivalent allocation rule makes every agent indifferent between what he receives and the opportunity of choosing the bundle of public goods subject to the constraint of paying r times its cost, where r is set as low as possible. We show that this rule is characterized in economies with a continuum of agents by efficiency, a natural upper bound on everyone's welfare, and a property of solidarity with respect to changes in population and preferences. Received: 3 August 1995 / Accepted : 29 April 1997     

Choice rules with fuzzy preferences: Some characterizations

Consider an agent with fuzzy preferences. This agent, however, has to make exact choices when faced with different feasible sets of alternatives. What rule does he follow in making such choices? This paper provides an axiomatic characterization of a class of binary choice rules called the α satisfying rule. When α=1, this rule is the Orlovsky choice rule. On the other hand, for α≤1/2, the rule coincides with the M _α rule that has been extensively analyzed in the literature on fuzzy preferences. Received: 3 August 1995/Accepted: 19 November 1997