Consistent representative democracy

We study axioms which define “representative democracy” in an environment in which agents vote over a finite set of alternatives. We focus on a property that states that whether votes are aggregated directly or indirectly makes no difference. We call this property representative consistency. Representative consistency formalizes the idea that a voting rule should be immune to gerrymandering. We characterize the class of rules satisfying unanimity, anonymity, and representative consistency. We call these rules “partial priority rules.” A partial priority rule can be interpreted as a rule in which each agent can “veto” certain alternatives. We investigate the implications of imposing other axioms to the list specified above. We also study the partial priority rules in the context of specific economic models.     

Asymmetric rules for claims problems without homogeneity

We introduce a general class of rules for claims problems, called the difference rules, and demonstrate that a rule satisfies composition down and composition up if and only if it is a difference rule. We show that these rules are very simple to describe when there are two agents. In a variable population framework, we introduce a family of rules satisfying consistency, composition down, and composition up, which we term the logarithmic-proportional rules. These rules satisfy neither symmetry nor homogeneity.     

The communication requirements of social choice rules and supporting budget sets

The paper examines the communication requirements of social choice rules when the (sincere) agents privately know their preferences. It shows that for a large class of choice rules, any minimally informative way to verify that a given alternative is in the choice rule is by verifying a “budget equilibrium”, i.e., that the alternative is optimal to each agent within a “budget set” given to him. Therefore, any communication mechanism realizing the choice rule must find a supporting budget equilibrium. We characterize the class of choice rules that have this property. Furthermore, for any rule from the class, we characterize the minimally informative messages (budget equilibria) verifying it. This characterization is used to identify the amount of communication needed to realize a choice rule, measured with the number of transmitted bits or real variables. Applications include efficiency in convex economies, exact or approximate surplus maximization in combinatorial auctions, the core in indivisible-good economies, and stable many-to-one matchings.     

Efficient priority rules

We study the assignment of indivisible objects with quotas (universities, jobs, or offices) to a set of agents (students, job applicants, or professors). Each agent receives at most one object and monetary compensations are not possible. We characterize efficient priority rules by efficiency, strategy-proofness, and reallocation-consistency. Such a rule respects an acyclic priority structure and the allocations are determined using the deferred acceptance algorithm.     

Bribe-proof rules in the division problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents with single-peaked preferences. A rule maps preference profiles into n shares of the amount to be allocated. A rule is bribe-proof if no group of agents can compensate one of its subgroups to misrepresent their preferences and, after an appropriate redistribution of their shares, each obtains a weakly preferred share and all agents in the misrepresenting subgroup obtain a strictly preferred share. We characterize all bribe-proof rules as the class of Pareto efficient, strategy-proof, and weakly replacement monotonic rules. This class is larger than the set of sequential allotment rules identified in Barberà et al. [Barberà, S., Jackson, M., Neme, A., 1997. Strategy-proof allotment rules. Games Econ. Behav. 18, 1–21].     

On two competing mechanisms for priority-based allocation problems

We consider the priority-based allocation problem: there is a set of indivisible objects with multiple supplies (e.g., schools with seats) and a set of agents (e.g., students) with priorities over objects (e.g., proximity of residence area). We study two well-known and competing mechanisms. The agent-optimal stable mechanism (AOSM) allots objects via the deferred acceptance algorithm. The top trading cycles mechanism (TTCM) allots objects via Gale's top trading cycles algorithm. We show that the two mechanisms are equivalent, or TTCM is fair (i.e., respects agents’ priorities), or resource monotonic, or population monotonic, if and only if the priority structure is acyclic. Furthermore, if AOSM fails to be efficient (consistent) for a problem, TTCM also fails to be fair (consistent) for it. However, the converse is not necessarily true.     

Bribe-proof rules in the division problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents with single-peaked preferences. A rule maps preference profiles into n shares of the amount to be allocated. A rule is bribe-proof if no group of agents can compensate one of its subgroups to misrepresent their preferences and, after an appropriate redistribution of their shares, each obtains a weakly preferred share and all agents in the misrepresenting subgroup obtain a strictly preferred share. We characterize all bribe-proof rules as the class of Pareto efficient, strategy-proof, and weakly replacement monotonic rules. This class is larger than the set of sequential allotment rules identified in Barberà et al. [Barberà, S., Jackson, M., Neme, A., 1997. Strategy-proof allotment rules. Games Econ. Behav. 18, 1–21].     

Strategy-proof Location on a Network

We consider rules that choose a location on a graph (e.g. a road network) based on agents' single-peaked preferences. First, we characterize the class of strategy-proof, onto rules when the graph is a tree. Such a rule is based on a collection of generalized median voter rules (Moulin, 1980) satisfying a consistency condition. Second, we characterize such rules for graphs containing cycles. We show that while such a rule is not necessarily dictatorial, the existence of a cycle grants some agent an amount of decisive power, unlike the case of trees. Rules for this case can be described in terms of a subclass of such rules for trees. Journal of Economic Literature Classification Numbers: C72, D78.     

Population-monotonicity and separability for economies with single-dipped preferences and the assignment of an indivisible object

We study two allocation models. In the first model, we consider the problem of allocating an infinitely divisible commodity among agents with single-dipped preferences. In the second model, a degenerate case of the first one, we study the allocation of an indivisible object to a group of agents. We consider rules that satisfy Pareto efficiency, strategy-proofness, and in addition either the consistency property separability or the solidarity property population-monotonicity. We show that the class of rules that satisfy Pareto efficiency, strategy-proofness, and separability equals the class of rules that satisfy Pareto efficiency, strategy-proofness, and non-bossiness. We also provide characterizations of all rules satisfying Pareto efficiency, strategy-proofness, and either separability or population-monotonicity. Since any such rule consists for the largest part of serial-dictatorship components, we can interpret the characterizations as impossibility results. Received: September 29, 1999; revised version: March 22, 2000     

Unmediated communication in games with complete and incomplete information

We study the effects of adding unmediated communication to static, finite games of complete and incomplete information. We characterize S^U(G), the set of outcomes of a game G, that are induced by sequential equilibria of cheap talk extensions. A cheap talk extension of G is an extensive-form game in which players communicate before playing G. A reliable mediator is not available and players exchange private or public messages that do not affect directly their payoffs. We first show that if G is a game of complete information with five or more players and rational parameters, then S^U(G) coincides with the set of correlated equilibria of G. Next, we demonstrate that if G is a game of incomplete information with at least five players, rational parameters and full support (i.e., all profiles of types have positive probability), then S^U(G) is equal to the set of communication equilibria of G.     

Recursive preferences and balanced growth

We study a class of utility functions that are defined recursively by an aggregator W(x,y) where u_t=W(c_t,u_t+1). In single-agent economies it is known that a sufficient condition for the existence of a balanced growth path is that utility should be homogenous of degree γ. In the context of a multi-agent economy we show that this restriction implies that either a balanced growth equilibrium fails to exist or all agents have the same constant discount factor. We suggest a generalization of recursive preferences wherein the intertemporal utility function is time dependent. Within this class we establish that there may exist a balanced growth equilibrium even if agents are different.     

Dynamic stability and reform of political institutions

This paper examines endogenous institutional change in a class of dynamic political games. The political aggregation rules used at date t+1 are instrumental choices under rules at date t. Effectively, rules are “players” who can strategically delegate future policy-making authority to different rules. A political rule is stable if it selects itself. A reform occurs when an alternative rule is selected. The stability of a political rule is shown to depend on whether its choices are dynamically consistent. For instance, simple majority rules can be shown to be dynamically consistent in many common environments where wealth-weighted voting rules are not. The result extends to political rules that incorporate private activities such as extra-legal protests, threats, or private investment. The approach is one way of understanding various explanations of institutional change proposed in the literature. A parametric model of public goods provision gives an illustration.     

A characterization of consistent collective choice rules

We characterize a class of collective choice rules such that collective preference relations are consistent. Consistency is a weakening of transitivity and a strengthening of acyclicity requiring that there be no cycles with at least one strict preference, which excludes the possibility of a “money pump.” The properties of collective choice rules used in our characterization are unrestricted domain, strong Pareto, anonymity and neutrality. If there are at most as many individuals as there are alternatives, the axioms provide an alternative characterization of the Pareto rule. If there are more individuals than alternatives, however, further rules become available.     

“Almost” subsidy-free spatial pricing in a multi-dimensional setting

Consider a population of citizens uniformly spread over the entire plane. The population faces a problem of locating public facilities financed by its users, who face an idiosyncratic private access cost to the facility. We show that, under mild assumptions, an external intervention that covers a tiny portion of the facility cost is sufficient to guarantee secession-proofness or no cross-subsidization, where no group of individuals is charged more than the cost incurred if it had acted on its own. Moreover, we demonstrate that in this case the Rawlsian access pricing is the only mechanism that rules out secession threats.     

PARETO EFFICIENCY AND WEIGHTED MAJORITY RULES

We consider the design of decision rules in an environment with two alternatives, independent private values and no monetary transfers. The utilitarian rule subject to incentive compatibility constraints is a weighted majority rule, where agents' weights correspond to expected gains given that their favorite alternative is chosen. It is shown that a rule is interim incentive efficient if and only if it is a weighted majority rule, and we characterize those weighted majority rules that are ex ante incentive efficient. We also discuss efficiency in the class of anonymous mechanisms and the stability of weighted majority rules.     

Joint misrepresentation with bribes

We study the problem of assigning objects to buyers. Monetary transfers are allowed. Each buyer’s preference space contains, but is not limited to, the linear additively separable preferences. A rule maps each preference profile to an allocation. We are concerned about the possibility that a group of buyers may engage in the following kind of manipulation: They make side payments internally and then carry out a joint misrepresentation. A rule is strongly group strategy-proof if no group can gain by engaging in such operations. We also consider several other appealing requirements. We find that the posted-price rules are the only one that satisfies non-triviality, non-imposition, envy-freeness, and strong group strategy-proofness.     

Coalitional Strategy-Proofness in Economies with Single-Dipped Preferences and the Assignment of an Indivisible Object

We study two allocation models. In the first model, we consider the problem of allocating an infinitely divisible commodity among agents with single-dipped preferences. In the second model, a degenerate case of the first one, we study the allocation of an indivisible object to a group of agents. Our main result is the characterization of the class of Pareto optimal and coalitionally strategy-proof allocation rules. Alternatively, this class of rules, which largely consists of serially dictatorial components, can be characterized by Pareto optimality, strategy-proofness, and weak non-bossiness (in terms of welfare). Furthermore, we study properties of fairness such as anonymity and no-envy. Journal of Economic Literature Classification Numbers: D63, D71.     

When too little is as good as nothing at all: Rationing a disposable good among satiable people with acceptance thresholds

We study the problem of rationing a divisible good among a group of people. Each person?s preferences are characterized by an ideal amount that he would prefer to receive and a minimum quantity that he will accept: any amount less than this threshold is just as good as receiving nothing at all. Any amount beyond his ideal quantity has no effect on his welfare.We search for Pareto-efficient, strategy-proof, and envy-free rules. The definitions of these axioms carry through from the more commonly studied problem without disposability or acceptance thresholds. However, these are not compatible in the model that we study. We adapt the equal-division lower bound axiom and propose another fairness axiom called awardee-envy-freeness. Unfortunately, these are also incompatible with strategy-proofness. We characterize all of the Pareto-efficient rules that satisfy these two properties. We also characterize all Pareto-efficient, strategy-proof, and non-bossy rules.     

Justifiable preferences

We characterize preferences over acts that can be represented by a utility function and a multiple-prior, such that an act f is preferred to act g if there is a prior under which the expected utility induced by f is higher than that induced by g. These preferences are referred to as justifiable preferences. We further introduce a generalized model of ambiguity that involves a collection of multiple-priors, namely, multiple multiple-priors and incorporate Bewley?s Knightian model in justifiability: f is preferred to g if, according to at least one set of priors, f is unanimously preferred to g.     

Efficiency and consistency for locating multiple public facilities

In the problem of locating multiple public facilities studied by Barberà and Beviá [Self-selection consistent functions, J. Econ. Theory 105 (2002) 263-277; Locating public facilities by majority: stability, consistency and group formation, Games Econ. Behav. 56 (2006) 185-200], we offer simple necessary and sufficient conditions for efficiency, decentralizability of efficient decisions in a game of community division and local public goods provision, and a constructive algorithm for efficient and consistent decisions.