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.     

ON STRATEGY‐PROOFNESS AND THE SALIENCE OF SINGLE‐PEAKEDNESS

We consider strategy‐proof rules operating on a rich domain of preference profiles. We show that if the rule satisfies in addition tops‐onlyness, anonymity, and unanimity, then the preferences in the domain have to satisfy a variant of single‐peakedness (referred to as semilattice single‐peakedness). We do so by deriving from the rule an endogenous partial order (a semilattice) from which the concept of a semilattice single‐peaked preference can be defined. We also provide a converse of this main finding. Finally, we show how well‐known restricted domains under which nontrivial strategy‐proof rules are admissible are semilattice single‐peaked domains.     

A Strategy‐Proofness Characterization of Plurality Rule

Assuming at least four individuals and at least four alternatives, a social choice function on the domain of profiles at which there is an alternative ranked first by more individuals than any other alternative is nondictatorial, strategy‐proof, and has full range if and only if it is plurality rule.     

On the inconsistency of a weak version of the libertarian principle

It is shown that even granting weak group rights will sometimes result in a conflict with such a widely acceptable efficiency criterion as the Pareto principle. On the other hand, if we strengthen the decesive power of groups, this may lead to a conflict even with the weak non-imposition condition, provided that a social choice function satisfies a rather mild choice-consistency property.     

SOCIAL CHOICE FROM AN n‐DIMENSIONAL EUCLIDEAN SPACE: A SHORT IMPOSSIBILITY PROOF

Most presentations of social choice theory are difficult for a non‐specialist to follow. This paper attempts to provide some feel for what is going on by providing a short proof of an impossibility theorem in terms of the techniques that are familiar to political‐economists. We illustrate the advantages of this approach with a short proof of an impossibility theorem.     

Nash Equilibrium and Welfare Optimality

If A is a set of social alternatives, a social choice rule (SCR) assigns a subset of A to each potential profile of individuals' preferences over A , where the subset is interpreted as the set of "welfare optima". A game form (or "mechanism") implements the social choice rule if, for any potential profile of preferences, (i) any welfare optimum can arise as a Nash equilibrium of the game form (implying, in particular, that a Nash equilibrium exists) and, (ii) all Nash equilibria are welfare optimal. The main result of this paper establishes that any SCR that satisfies two properties—monotonicity and no veto power—can be implemented by a game form if there are three or more individuals. The proof is constructive.     

STRATEGY‐PROOF ALLOCATION OF INDIVISIBLE GOODS AMONG COUPLES

We consider the problem of allocating indivisible goods among couples. Agents in a couple share the indivisible good assigned to them. The main result is that an allocation rule is strategy‐proof, neutral and non‐bossy if and only if it is serially dictatorial. An allocation rule is serially dictatorial if there is a priority order of couples and a function that identifies who chooses in each couple, such that for all preference profiles, a good assigned to couple i is the best element according to the preference of the identified agent in couple i among the remaining goods when the couples with higher priorities have made their choice.     

Mechanism design with side payments: Individual rationality and iterative dominance

We investigate the collective decision with incomplete information and side payments. We show that a direct mechanism associated with the social choice function that satisfies budget balancing, incentive compatibility, and interim individual rationality exists for generic prior distributions. We consider the possibility that a risk-averse principal extracts full surplus in agency problems with adverse selection. With regard to generic prior distributions, we show that there exists a modified direct mechanism associated with the virtual social choice function, which satisfies budget balancing and interim individual rationality, such that truth telling is the unique three times iteratively undominated message rule profile.     

An experimental comparison of collective choice procedures for excludable public goods

This paper compares three collective choice procedures for the provision of excludable public goods under incomplete information. One, serial cost sharing (SCS), is budget balanced, individually rational, anonymous and strategy proof. The other two are “hybrid” procedures: voluntary cost sharing with proportional rebates (PCS) and with no rebates (NR). PCS satisfies all these properties except strategy proofness, and NR satisfies all the properties except for strategy proofness and budget balance. However, PCS and NR do not exclude any potential users, and they do not require equal cost shares, thereby overcoming the two main sources of inefficiency with SCS. We characterize the Bayesian Nash equilibria (BNE) of the hybrid mechanisms and conduct laboratory experiments to compare the performance of the three mechanisms. We find that PCS produces significantly more efficient allocations than either SCS or NR.     

Stable Assignment of Public Facilities under Congestion

We study the problem of locating multiple public facilities when each member of society has to be assigned to exactly one of these facilities. Individuals' preferences are assumed to be single‐peaked over the interval of possible locations and negatively affected by congestion. We characterize strategy‐proof, efficient, and stable allocation rules when agents have to be partitioned between two groups of users and discuss the normative content of the stability property. Finally we prove that when more than two groups have to be formed, even with common information on the distribution of the peaks, there is no strategy‐proof, efficient, and stable allocation rule.     

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.     

利益分配、战略行动与集体选择的不确定性

爱因斯坦说,时间是一种错觉;普利高津则说,确定性是一种错觉。而文章认为,均衡也是一种错觉:集体选择的结果存在内生的不确定性。基于个体战略行动的多样性,文章从利益分配的角度对集体选择的不确定性作出了理论上的证明。认识到集体选择的不确定性特征对于理解社会的运行以及设计与社会控制相关的制度规章都具有重要的意义。     

Robust Implementation in Direct Mechanisms

A social choice function is robustly implementable if there is a mechanism under which the process of iteratively eliminating strictly dominated messages lead to outcomes that agree with the social choice function for all beliefs at every type profile. In an interdependent-value environment with single-crossing preferences, we identify a contraction property on the preferences which together with strict ex post incentive compatibility is sufficient to guarantee robust implementation in the direct mechanism. Strict ex post incentive compatibility and the contraction property are also necessary for robust implementation in any mechanism, including indirect ones. The contraction property requires that the interdependence is not too high. In a linear signal model, the contraction property is equivalent to an interdependence matrix having all eigenvalues smaller than one.     

A Class of Social Welfare Functions That Depend on Mean Income and Income Polarization

A well‐established strategy for evaluating alternative income distributions is based on the use of an abbreviated social welfare function that depends only on mean income and an inequality index. In keeping with this literature, we study the existence of social welfare functions that can be written as a trade‐off between efficiency and income polarization. This paper proposes a class of social welfare functions consistent with the Esteban and Ray, and Duclos, Esteban and Ray income polarization indices. For this result, we expand the domain for personal preferences to incorporate not only own income but also the well‐being of others. In addition, we link our proposal to the literature on relative satisfaction. The approach is illustrated by an empirical application using the CPS database for the United States in the period 1991–2010.     

A characterization of virtual Bayesian implementation

We provide a characterization of virtual Bayesian implementation in pure strategies for environments satisfying no-total-indifference. A social choice function in such environments is virtually Bayesian implementable if and only if it satisfies incentive compatibility and a condition we term virtual monotonicity. The latter is weaker than Bayesian monotonicity—known to be necessary for Bayesian implementation. Virtual monotonicity is weak in the sense that it is generically satisfied in environments with at least three alternatives. This implies that in most environments virtual Bayesian implementation is as successful as it can be (incentive compatibility is the only condition needed).     

Undominated Nash Implementation with Collusion and Renegotiation

This article looks at implementation in economic environments when agents have perfect information about the state of the world, but cannot commit not to renegotiate bad outcomes or to collude against each other. If renegotiation satisfies a weak condition of disagreement point monotonicity, then any Pareto-efficient social choice function can be implemented if there are at least three agents who play undominated Nash equilibria. The mechanism does not use modulo or integer games, has no bad mixed strategy equilibria, and is “bounded.”Journal of Economic LiteratureClassification Number: D71.     

Learning buyers' valuation distribution in posted-price selling

Summary. For his proof of the existence of a general competitive equilibrium Abraham Wald assumed a strictly pseudomonotone inverse market demand function or, equivalently, that market demand satisfies the Weak Axiom of Revealed Preference. It is well known that more recent existence theorems do not need this assumption. In order to clarify its role in Wald's proof, the question of existence of an equilibrium for a modified version of the Walras-Cassel model is reduced to the solvability of a related variational inequality problem. In general, the existence of a solution to such a problem can only be proved by advanced mathematical methods. We provide an elementary induction proof which demonstrates the essence of Abraham Wald's famous contribution. Received: July 22, 1997; revised version: December 11, 1997     

Lexical Measures of Social Inequality: From Pigou‐Dalton to Hammond

A measure of social inequality is essentially a rational ordering over a space of social distributions. However, different measures, including the most popular ones, may provide very different rankings over the same set of typical distributions. We thus propose an axiomatic approach to inequality measurement mainly based on the Hammond principle, a natural generalization of the Pigou‐Dalton principle, attempting to clarify the true nature of social inequality: the rich get richer and the poor get poorer. Under the standard assumptions of anonymity and scale independence, we show that a social inequality ordering is the leximinimax measure if and only if it satisfies the first Hammond principle, and it is the leximaximin measure if and only if it satisfies the second Hammond principle.     

Coalitional Bayesian Nash implementation in differential information economies

Summary. A mechanism coalitionally implements a social choice set if any outcome of the social choice set can be achieved as a coalitional Bayesian Nash equilibrium of a mechanism and vice versa. We say that a social choice set is coalitionally implementable if there is a mechanism which coalitionally implements it. Our main theorem proves that a social choice set is coalitionally implementable if and only if it is interim individually rational, interim efficient, coalitional B ayesian incentive compatible, and satisfies a coalitional Bayesian monotonicity condition as well as a closure condition. As an application of our main result, we show that the private core and the private Shapley value of an economy with differential information are coalitionally implementable. Received: January 12, 1998; revised version: March 30, 2000     

Securing basic well-being for all

The purpose of this article is to examine the possibility of a social choice rule to implement a social policy for “securing basic well-being for all.” The article introduces a new scheme of social choice, called a social relation function (SRF), which associates a reflexive and transitive binary relation over a set of social policies to each profile of individual well-being appraisals and each profile of group evaluations. As part of the domains of SRFs, the available class of group evaluations is constrained by three conditions. Furthermore, the non-negative response (NR) and the weak Pareto condition (WP) are introduced. NR demands giving priority to group evaluation, while treating the groups as formally equal relative to each other. WP requires treating impartially the well-being appraisals of all individuals. In conclusion, this article shows that under some reasonable assumptions, there exists an SRF that satisfies NR and WP.