Neutrality in arrow and other impossibility theorems

Summary. Although not assumed explicitly, we show that neutrality plays an important role in Arrow and other impossibility theorems. Applying it to pivotal voters we produce direct proofs of classical impossibility theorems, including Arrow's, as well as extend some of these theorems. We further explore the role of neutrality showing that it is equivalent to Pareto or reverse Pareto, and to effective dictatorship for non-null social welfare functions satisfying the principle of independence of irrelevant alternatives. It is also equivalent to Wilson's Citizens' Sovereignty--which is related to the intuition that symmetry over alternatives makes social preference depend only on citizens' preferences. We show that some of these results are more fundamental than others in that they extend both to infinite societies and to considerably smaller domains of preferences. Finally, as an application of Arrow's theorem, we provide a simple proof of the Gibbard-Satterthwaite theorem.Received: 13 April 2000, Revised: 6 December 2002, JEL Classification Numbers: D71, C70.I thank Salvador Barberá, Luis Corchón, Cesar Martinelli, Eric Maskin, Tomas Sjöström, Ricard Torres, José Pedro Ubeda, and an anonymous referee for feedback. The proofs of Arrow's theorem and two Wilson's theorems come from a note I wrote in 1987 at Universitat Autónoma de Barcelona (Ubeda [16]). In 1996 Geanakoplos [7] wrote a proof of Arrow's theorem similar but not identical to mine. All work in this paper is independent of his.     

A one-sided many-to-many matching problem

This study discusses a one-sided many-to-many matching model wherein agents may not be divided into two disjoint sets. Moreover, each agent is allowed to have multiple partnerships in our model. We restrict our attention to the case where the preference of each agent is single-peaked over: (i) the total number of partnerships with all other agents, and (ii) the number of partnerships that the agent has with each of the other agents. We represent a matching as a multigraph, and characterize a matching that is stable and constrained efficient. Finally, we show that any direct mechanism for selecting a stable and constrained efficient matching is not strategy-proof.     

Probabilistic strategy-proof rules over single-peaked domains

It is proved that every strategy-proof, peaks-only or unanimous, probabilistic rule defined over a minimally rich domain of single-peaked preferences is a probability mixture of strategy-proof, peaks-only or unanimous, deterministic rules over the same domain. The proof employs Farkas’ Lemma and the max-flow min-cut theorem for capacitated networks.     

Strategy-proof and nonbossy allocation of indivisible goods and money

Summary. Which strategy-proof nonbossy mechanisms exist in a model with a finite number of indivisible goods (houses, jobs, positions) and a perfectly divisible good (money)? The main finding is that only a finite number of distributions of the divisible good is consistent with strategy-proofness and nonbossiness. Under various additional assumptions - neutrality, individual rationality, object efficiency, weak decentralization - the distribution of the divisible good is further restricted. For instance, under neutrality the outcome of the mechanism can have only one distribution, which is hence independent of individual preferences. In this case the mechanism becomes serially dictatorial. On the other hand, individual rationality leads to a fixed price equilibrium with a well-defined rationing method (Gale's top-trading cycle procedure). Received: October 3, 2000; revised version: August 10, 2001     

Strategy-proofness, core, and sequential trade

We extend the Shapley-Scarf (1974) model - where a finite number of indivisible objects is to be allocated among a finite number of individuals - to the case where the primary endowment set of an individual may contain none, one, or several objects and where property rights may be transferred (objects inherited) as the allocation process unfolds, under the retained assumption that an individual consumes at most one object. In this environment we analyze the core of the economy and characterize the set of strategy-proof and Pareto efficient mechanisms. As an alternative approach, we consider property rights implicitly defined by a strategy-proof and Pareto efficient mechanism and show a core property for the mechanism-induced endowment rule.Received: 19 February 2004, Accepted: 14 April 2005, JEL Classification: C71, C78, D71, D78We would like to thank two anonymous referees for valuable comments. Financial support from The Swedish Council for Research in the Humanities and Social Sciences is gratefully acknowledged by Lars-Gunnar Svensson. Financial support from The Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged by Bo Larsson.     

Efficiency and truthfulness with Leontief preferences. A note on two-agent,two-good economies

In exchange economies where agents have private information about their preferences, strategy-proof and individually rational social choice functions are in general not efficient. We provide a restricted domain, namely the set of preferences representable by Leontief utility functions, where there exist mechanisms which are strategy-proof, efficient and individually rational. In two-agent, two-good economies we are able to provide an even stronger result. We characterize the class of efficient and individually rational social choice functions, which are fully implementable in truthful strategies.Received: 28 April 2003, Accepted: 23 June 2003, JEL Classification: D51, D71The author thanks Matthew Jackson, Jordi Massó and James Schummer for fruitful discussions, William Thomson for many valuable comments on an earlier version. A particular thank to Salvador Barberá for his fundamental help.     

A leximin characterization of strategy-proof and non-resolute social choice procedures

Summary. We characterize strategy-proof social choice procedures when choice sets need not be singletons. Sets are compared by leximin. For a strategy-proof rule g, there is a positive integer k such that either (i) the choice sets g(r) for all profiles r have the same cardinality k and there is an individual i such that g(r) is the set of alternatives that are the k highest ranking in i's preference ordering, or (ii) all sets of cardinality 1 to k are chosen and there is a coalition L of cardinality k such that g(r) is the union of the tops for the individuals in L. There do not exist any strategy-proof rules such that the choice sets are all of cardinality to k where . Received: November 8, 1999; revised version: September 18, 2001     

Another direct proof of the Gibbard–Satterthwaite Theorem

This paper provides a new and direct proof of the Gibbard–Satterthwaite Theorem based on induction on the number of individuals.     

Dynamic provision of public goods

Summary. This paper deals with implementing the efficient level of public good provision in a dynamic setting. First, we prove that when the good is provided in several stages, no sequence of Groves' mechanisms guarantees that agents will reveal their true valuations as a dominant strategy. The contribution of this paper is the characterization of those mechanisms which guarantee truthful revelation in this environment.Received: 30 December 2001, Revised: 27 March 2003, JEL Classification Numbers: D61, D78, D82, H41.This paper has greatly benefited from the ideas and comments of Sandro Brusco, Luis Corchón and Roberto Burguet. I would also like to thank José Alcalde, Luis J. Alías, Javier López-Cuñat, Juan Vicente Llinares, Ashley Piggins, Juan Perote and Antonio Quesada for very helpful suggestions. I am also grateful to an anonymous referee whose suggestions aided the quality of exposition in the paper and led me to Proposition 4.     

A strategy-proofness characterization of majority rule

Summary. A feasible alternative x is a strong Condorcet winner if for every other feasible alternative y there is some majority coalition that prefers x to y. Let (resp., denote the set of all profiles of linear (resp., merely asymmetric) individual preference relations for which a strong Condorcet winner exists. Majority rule is the only non-dictatorial and strategy-proof social choice rule with domain , and majority rule is the only strategy-proof rule with domain . Received: August 29, 2000; revised version: November 13, 2002 RID="*" ID="*"We are grateful to Wulf Gaertner and our two referees for insightful comments on a previous draft. Correspondence to: D. E. Campbell