Efficient strategy-proof exchange and minimum consumption guarantees

For exchange economies with classical economic preferences, it is shown that any strategy-proof social choice function that selects Pareto optimal outcomes cannot guarantee everyone a consumption bundle bounded away from the origin. This result demonstrates that there is a fundamental conflict between efficiency and distributional goals in exchange economies if the social choice rule is required to be strategy-proof.     

An extreme point characterization of random strategy-proof social choice functions: The two alternative case

We show that every strategy-proof random social choice function is a convex combination of strategy-proof deterministic social choice functions in a two-alternative voting model. This completely characterizes all strategy-proof random social choice functions in this setting.     

Subgame-perfect implementation of bargaining solutions

We study house allocation problems introduced by L. Shapley and H. Scarf (1974, J. Math. Econ.1, 23–28). We prove that a mechanism (a social choice function) is individually rational, anonymous, strategy-proof, and nonbossy (but not necessarily Pareto efficient) if and only if it is either the core mechanism or the no-trade mechanism, where the no-trade mechanism is the one that selects the initial allocation for each profile of preferences. This result confirms the intuition that even if we are willing to accept inefficiency, there exists no interesting strategy-proof mechanism other than the core mechanism. Journal of Economic Literature Classification Numbers: C71, C78, D71, D78, D89.     

On strategy-proofness and symmetric single-peakedness

We characterize the class of strategy-proof social choice functions on the domain of symmetric single-peaked preferences. This class is strictly larger than the set of generalized median voter schemes (the class of strategy-proof and tops-only social choice functions on the domain of single-peaked preferences characterized by Moulin, 1980) since, under the domain of symmetric single-peaked preferences, generalized median voter schemes can be disturbed by discontinuity points and remain strategy-proof on the smaller domain. Our result identifies the specific nature of these discontinuities which allow to design non-onto social choice functions to deal with feasibility constraints.     

Strategy-proof and individually rational social choice functions for public good economies: A note

Summary. Serizawa [3] characterized the set of strategy-proof, individually rational, no exploitative, and non-bossy social choice functions in economies with pure public goods. He left an open question whether non-bossiness is necessary for his characterization. We will prove that non-bossiness is implied by the other three axioms in his characterization. Received: October 17, 1997; revised version: January 19, 1998     

Strategy-proof contract auctions and the role of ties

A contract auction establishes a contract between a center and one of the bidders. As contracts may describe many terms, preferences over contracts typically display indifferences. The Qualitative Vickrey Auction (QVA) selects the best contract for the winner that is at least as good for the center as any of the contracts offered by the non-winning players. When each bidder can always offer a contract with higher utility for the center at an arbitrarily small loss of her own utility, the QVA is the only mechanism that is individually rational, strategy-proof, selects stable outcomes, and is Pareto efficient. For general continuous utility functions, a variant of the QVA involving fixed tie-breaking is strategy-proof and also selects stable outcomes. However, there is no mechanism in this setting that in addition also selects Pareto efficient outcomes.     

Second-best efficiency of allocation rules: strategy-proofness and single-peaked preferences with multiple commodities

We study strategy-proof allocation rules in economies with perfectly divisible multiple commodities and single-peaked preferences. In this setup, it is known that the incompatibility among strategy-proofness, Pareto efficiency and non-dictatorship arises in contrast with the Sprumont (Econometrica 59:509–519, 1991) one commodity model. We first investigate the existence problem of strategy-proof and second-best efficient rules, where a strategy-proof rule is second-best efficient if it is not Pareto-dominated by any other strategy-proof rules. We show that there exists an egalitarian rational (consequently, non-dictatorial) strategy-proof rule satisfying second-best efficiency. Second, we give a new characterization of the generalized uniform rule with the second-best efficiency in two-agent case.     

A Democracy Principle and Strategy-Proofness

In some social choice applications we want more than one alternative to be selected in some situations. This allows the construction of strategy-proof social choice rules that are not dictatorial. But if we also require x alone to be selected if it is at the top of some ordering that is submitted by more than half of the individuals then the rule cannot be strategy-proof. We prove this for rules that sometimes select one alternative, and sometimes two, but never more than two.     

Strategy-proof and individually rational social choice functions for public good economies

Summary This note is to inform about a mistake in my paper (Serizawa, 1996). In that paper, I characterized strategy-proof, individually rational, budget-balancing, non-exploitative and non-bossy social choice functions for economies with one public good and one private good. I established as Theorem 3 (page 507) that a social choice function is strategy-proof, individually rational with respect to endowment, budget-balancing, non-exploitative and non-bossy if and only if it is a scheme of semi-convex cost sharing determined by the minimum demand principle. I also exposed one example (Example 2, page 507) in order to emphasize that non-bossiness is indispensable for this characterization. I claimed that the social choice function in that example satisfies the above axioms except for non-bossiness, and is not a scheme of semi-convex cost sharing. However, the social choice function in the example is actually not strategy-proof, as shown in the simple discussion below. Therefore it is an open question whether or not a similar characterization theorem holds without non-bossiness.I thank Professor Rajat Deb, who kindly pointed out my mistake.     

How competition affects schools' performances: Does specification matter?

If the number of individuals is odd, majority rule is the only non-dictatorial strategy-proof social choice rule on the domain of linear orders that admit a Condorcet winner (Campbell and Kelly, 2003). This paper shows that the claim is false when the number of individuals is even, and provides a counterpart to the theorem for the even case.     

On the generic impossibility of truthful behavior: A simple approach

Summary We provide an elementary proof showing how in economies with an arbitrary number of agents an arbitrary number of public goods and utility functions quasi-linear in money, any efficient and individually rational mechanism is not strategy-proof for any economy satisfying a mild regularity requirement.The authors wish to thank William Thomson, Salvadpr Barberá, José Angel Silva and an anonymous referee for helpful comments. The remaining errors are our exclusive responsibility. Financial support from DGICYT under project PB 91-0756 and the Instituto Valenciano de Investigaciones Económicas is gratefully acknowledged.     

A geometric proof of Gibbard's random dictatorship theorem

Summary Gibbard has shown that a social choice function is strategy-proof if and only if it is a convex combination of dictatorships and pair-wise social choice functions. I use geometric techniques to prove the corollary that every strategy-proof and sovereign social choice function is a random dictatorship.I thank Kim Border for several useful discussions and many insightful comments.     

Voting by committees under constraints

We consider social choice problems where a society must choose a subset from a set of objects. Specifically, we characterize the families of strategy-proof voting procedures when not all possible subsets of objects are feasible, and voters’ preferences are separable or additively representable.     

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     

Decomposable Strategy-Proof Social Choice Functions

This article shows that a social choice function defined on a domain of separable preferences which satisfies a relatively weak domain-richness condition on a product set of alternatives is (i) strategy-proof and only depends on the tops of the individual preferences if and only if (ii) the range of the social choice function is a product set and the social choice function can be decomposed into the product of one-dimensional, strategy-proof, nontop-insensitive social choice functions.
JEL Classification Number: D71.     

Random dictatorship domains

A domain of preference orderings is a random dictatorship domain if every strategy-proof random social choice function satisfying unanimity defined on the domain is a random dictatorship. Gibbard (1977) showed that the universal domain is a random dictatorship domain. We ask whether an arbitrary dictatorial domain is a random dictatorship domain and show that the answer is negative by constructing dictatorial domains that admit anonymous, unanimous, strategy-proof random social choice functions which are not random dictatorships. Our result applies to the constrained voting model. Lastly, we show that substantial strengthenings of linked domains (a class of dictatorial domains introduced in Aswal et al., 2003) are needed to restore random dictatorship and such strengthenings are “almost necessary”.     

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     

Strategy-proof preference aggregation: Possibilities and characterizations

An aggregation rule maps each profile of individual strict preference orderings over a set of alternatives into a social ordering over that set. We call such a rule strategy-proof if misreporting one's preference never produces a different social ordering that is between the original ordering and one's own preference. After describing two examples of manipulable rules, we study in some detail three classes of strategy-proof rules: (i) rules based on a monotonic alteration of the majority relation generated by the preference profile; (ii) rules improving upon a fixed status-quo; and (iii) rules generalizing the Condorcet–Kemeny aggregation method.     

Representative consumer's risk aversion and efficient risk-sharing rules

We study the representative consumer's risk attitude and efficient risk-sharing rules in a single-period, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must the representative consumer. We also identify a relationship between the curvature of an individual consumer's individual risk sharing rule and his absolute cautiousness, the first derivative of absolute risk-tolerance. Furthermore, we discuss some consequences of these results and refinements of these results for the class of HARA utility functions.     

Extraneous Alternatives And Strategy-Proofness

It is well known that the Gibbard–Satterthwaite theorem cannot be circumvented by adding extraneous alternatives that are included in the individual preference information but are never selected. We generalize this by proving that, for any domain on which every strategy-proof rule is dictatorial, the addition of extraneous alternatives will not permit the construction of a non-dictatorial and strategy-proof rule if the new domain is a product set. We show how this result, and our other theorem, can be applied to seven families of social choice situations, including those in which more than one alternative is selected.