The equity-efficiency trade-off reconsidered

Envy-free and Pareto optimal allocations never exist in large economies with production, if there is enough variation with respect to preferences and innate abilities of the agents. If distributional equity is given priority only second best envy-free allocations may be considered. Those allocations are characterised in finite and continuum economies. In continuum economies envy-free allocations are type-egalitarian, i.e. agents with the same preferences but different abilities obtain the same consumption-labour bundle. Regarding implementation envy-free allocations can only be implemented by a tax depending on labour and income.I would like to thank two anonymous referees and the editor in charge of this paper for very helpful comments.     

Fair allocation of indivisible goods: the two-agent case

One must allocate a finite set of indivisible goods among two agents without monetary compensation. We impose Pareto-efficiency, anonymity, a weak notion of no-envy, a welfare lower bound based on each agent’s ranking of the subsets of goods, and a monotonicity property w.r.t. changes in preferences. We prove that there is a rule satisfying these axioms. If there are three goods, it is the only rule, together with one of its subcorrespondences, satisfying each fairness axiom and not discriminating between goods.     

On monotonicity in economies with indivisible goods

We consider the problem of fair allocation in economies with indivisible objects that may or may not be desirable (for instance, activities that may or may not be pleasurable but have to be carried out unless there are not enough agents for that). We search for efficient solutions satisfying two additional properties. First, each agent should find his bundle at least as desirable as the bundle that would be assigned to him in the hypothetical economy in which all agents have preferences identical to his, under equal treatment of equals and efficiency. In a preliminary step, we show that there is no logical relation between this requirement and no-envy, and between it and egalitarian-equivalence. We also establish the existence of efficient allocations satisfying it. The second property, object monotonicity, says that the availability of additional objects either has a negative impact on everyone's welfare, or it has a positive impact on everyone's welfare. We show that there is no object-monotonic selection from the correspondence that associates with each economy its set of efficient allocations meeting an even weaker version of the bound.I am grateful to Atila Abdulkadiroglu, Koichi Tadenuma, and a referee for their very helpful comments.     

Characterizations of the cycle-complete and folk solutions for minimum cost spanning tree problems

Minimum cost spanning tree problems connect agents efficiently to a source when agents are located at different points and the cost of using an edge is fixed. The folk and cycle-complete cost sharing solutions always offer core allocations. We provide similar characterizations for both. A new property is based on the following observation: when all agents have the same cost to connect to the source, we can connect one of them to the source then connect all other agents to him, as if he was the source. Cost sharing should also be done in these two steps. We also use some common properties: core selection, piecewise linearity and an independence property. The solutions are differentiated by properties that apply when the cheapest edge to the source gets cheaper. Either the savings are equally distributed among all agents (folk) or the agent on that edge gets all of the savings (cycle-complete).     

Double implementation of Lindahl allocations by a pure mechanism

This paper considers the issue of designing mechanisms whose Nash allocations and strong Nash allocations coincide with Lindahl allocations for public goods economies when coalition patterns, preferences, and endowments are unknown to the designer. It will be noted that the mechanism presented here is feasible and continuous, and the implementation result is obtained without defining an artificial preference profile on prices announced by individuals. In addition, unlike most existing Nash-implementing mechanisms which need to distinguish the case of two agents from that of three or more agents, this paper provides a unified mechanism which is irrespective of the number of agents. Received: 19 August 1997/Accepted: 16 November 1998     

Voting rules as statistical estimators

We adopt an ‘epistemic’ interpretation of social decisions: there is an objectively correct choice, each voter receives a ‘noisy signal’ of the correct choice, and the social objective is to aggregate these signals to make the best possible guess about the correct choice. One epistemic method is to fix a probability model and compute the maximum likelihood estimator (MLE), maximum a posteriori (MAP) estimator or expected utility maximizer (EUM), given the data provided by the voters. We first show that an abstract voting rule can be interpreted as MLE or MAP if and only if it is a scoring rule. We then specialize to the case of distance-based voting rules, in particular, the use of the median rule in judgement aggregation. Finally, we show how several common ‘quasiutilitarian’ voting rules can be interpreted as EUM.     

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.     

Nash implementation of Lindahl allocations

We define a class of Nash based mechanisms that implement Lindahl allocations in standard public good economies. As those that first proved Nash implementation of Lindahl allocations, defined by Hurwicz (1979) and Walker (1981), the mechanisms provided here are continuous, feasible, and independent of agents' characteristics. In economies with two agents (e.g., bilateral monopolies, duopolies, principal-agent models), our mechanisms are also applicable, in contrast to the well-behaved mechanisms in the literature, and they satisfy favourable stability properties.     

Trade-off between equity and efficiency in a general economy with indivisible goods

In most of the recent literature on fair allocation in economies with indivisible goods and a single infinitely divisible good, it is assumed that each agent can consume at most one indivisible good. In this paper, we show that if this assumption is dropped, there do not necessarily exist envy-free and Pareto efficient allocations. However, envy-free allocations still exist and so do Pareto efficient allocations. Hence, a trade-off between equity and efficiency arises.     

WHO IS AFRAID OF THE FRIEDMAN RULE?

We explore the connection between optimal monetary policy and heterogeneity among agents in a standard monetary economy with two types of agents where the stationary distribution of money holdings is nondegenerate. Sans type-specific fiscal policy, we show that the zero-nominal-interest rate policy (the Friedman rule) does not maximize type-specific welfare; it may not maximize aggregate ex ante social welfare either. Indeed, one or, more surprisingly, both types may benefit if the central bank deviates from the Friedman rule. ( JEL E31, E51, E58)     

Generic efficiency and collusion-proofness in exchange economies

The purpose of this paper is to study the kind of efficient allocations that can be achieved in exchange economies with asymmetric information, by means of a decentralized mechanism robust to coalitional, strategic deviations. To this end, we define a new strategic equilibrium concept – called strong collusion-proof contract – designed to characterize stable communication agreements in games with differential information against non-binding, self-enforcing and incentive compatible deviations by coalitions. We then construct a strategic market mechanism which, for quasi-linear economies, is such that its strong collusion-proof contracts generically induce the incentive compatible interim efficient allocations. Moreover, we show that these allocations can be achieved by strong collusion-proof contracts. We show that the internally consistent extension of the strong collusion-proof contracts generically yields the same set of efficient allocations. Received: 22 January 2001/Accepted: 15 April 2002 RID="*" ID="*"  This author was working at CORE when this paper was written. We wish to thank Claude d'Aspremont, David Martimort, Jean-Fran?ois Mertens and Heracles Polemarchakis for helpful comments on an earlier version. The usual disclaimer applies.     

Characteristic properties of list proportional representation systems

In this paper, three characterizations are given of a rule that models list systems of proportional representation the plurality ranking rule. It is shown that a social preference rule is the plurality ranking rule if and only if it satisfies three independent conditions: consistency, faithfulness, and first score cancellation. It is also shown that first score cancellation is implied by neutrality, anonymity, and topsonlyness. This means a second characterization is found, containing deeper axioms than the previous one. A third characterization contains the notion of top monotonicity. In order to motivate topsonlyness, we show that a scoring seat allocation rule is proof against party fragmentation if and only if it is topsonly. Various other properties of the plurality ranking rule are related to its characterist properties.     

INFORMATIONAL IMPLICATIONS OF MONEY, INTEREST RATE, and PRICE RULES

The information available to private agents determines the effectiveness of various types of monetary policy. In an economy in which private agents have differential information sets, the ranking of three classes of monetary policy rules critically depends on the specification of agents' information sets. A price rule, for example, minimizes the variance of output around its full information level when agents observe both the interest rate and money stock. More generally, if all three monetary policy variables (the money stock, the price level and the interest rate) are contemporaneously observed, the policy ranking is indeterminate.     

Maximum likelihood approach to vote aggregation with variable probabilities

The Condorcet-Kemeny-Young statistical approach to vote aggregation is based on the assumption that voters have the same probability of comparing correctly two alternatives and that this probability is the same for any pair of alternatives. We relax the second part of this assumption by letting the probability of comparing correctly two alternatives be increasing with the distance between two alternatives in the allegedly true ranking. This leads to a rule in which the majority in favor of one alternative against another one is given a larger weight the larger the distance between the two alternatives in the true ranking, i.e., the larger the probability that the voters compare them correctly. This rule is not Condorcet consistent and does not satisfy local independence of irrelevant alternatives. Yet, it is anonymous, neutral, and paretian. It also appears that its performance in selecting the alternative most likely to be the best improves with the rate at which the probability increases.We would like to thank Michel Le Breton for his encouragement to examine this question and for his comments, as well as Philippe De Donder, Jean-Yves Duclos, Stephen Gordon, Cyril Téjédo and an anonymous referee for their comments.     

Collusion, renegotiation and implementation

We study the implementation problem for exchange economies when agents can renegotiate the outcome assigned by the planner and can collude. We focus on the use of sequential mechanisms and present a simple sufficient condition for implementation with renegotiation in strong perfect equilibrium. We present an application to optimal risk sharing, showing that the possibility of collusion and renegotiation does not in general prevent the implementation of efficient allocations. Received: 27 August 1997/Accepted: 29 October 1998     

Markovian assignment rules

We analyze dynamic assignment problems where agents successively receive different objects (positions, offices, etc.). A finite set of n vertically differentiated indivisible objects are assigned to n agents who live n periods. At each period, a new agent enters society, and the oldest agent retires, leaving his object to be reassigned. We define independent assignment rules (where the assignment of an object to an agent is independent of the way other objects are allocated to other agents), efficient assignment rules (where there does not exist another assignment rule with larger expected surplus), and fair assignment rules (where agents experiencing the same circumstances have identical histories in the long run). When agents are homogenous, we characterize efficient, independent and fair rules as generalizations of the seniority rule. When agents draw their types at random, we prove that independence and efficiency are incompatible, and that efficient and fair rules only exist when there are two types of agents. We characterize two simple rules (type-rank and type-seniority) which satisfy both efficiency and fairness criteria in dichotomous settings.     

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.     

Probabilistic allocation rules and single-dipped preferences

We consider the problem of allocating an infinitely divisible endowment among a group of agents with single-dipped preferences. A probabilistic allocation rule assigns a probability distribution over the set of possible allocations to every preference profile. We discuss characterizations of the classes of Pareto-optimal and strategy-proof probabilistic rules which satisfy in addition replacement-domination or no-envy. Interestingly, these results also apply to problems of allocating finitely many identical indivisible objects – to probabilistic and to deterministic allocation. Received: 23 November 1998/Accepted: 20 October 2000     

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.