Non-Dummy Agents in Pure Exchange Economies

We introduce a very fundamental and important axiom of the non-dummy. This states that each agent can change the outcome of the mechanism at some preference profile, thus guaranteeing every agent the minimum right to affect the social decision. We study the possibility of strategy-proof, efficient and non-dummy mechanisms in pure exchange economies. We provide two new interesting classes of such mechanisms. The results shed light on the structure of strategy-proof and efficient mechanisms, and should promote a complete characterization of those mechanisms in pure exchange economies with three or more agents.     

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.     

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.     

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     

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.     

Inefficiency of Strategy-Proof Rules for Pure Exchange Economies

In his pioneering article, (in “Decision and Organization” (C. B. McGuire and R. Radner, Eds.), pp. 297-336, North-Holland, Amsterdam, 1972) Hurwicz establishes that there is no strategy-proof, Pareto-efficient, and individually rational rule for pure exchange economies with two agents and two goods, provided that the domain includes a sufficiently wide class of classical preferences. In this article, we extend his result to pure exchange economies with any finite number of agents and goods. We establish that (i) there is no strategy-proof, Pareto-efficient, and individually rational rule on the class of classical, homothetic, and smooth preferences; and (ii) there is no strategy-proof, Pareto-efficient, and symmetric rule on the same class of preferences. Journal of Economic Literature Classification Numbers: D78, D71, C72.     

Dominant strategy implementation in economic environments

We study dominant strategy implementation especially in economic environments. We first show that in general environments, strategy-proofness and quasi-strong-non-bossiness together are necessary and sufficient for dominant strategy implementation via the associated direct revelation mechanism. We next prove that in weak separable environments, strategy-proofness is sufficient for dominant strategy implementation, by using an augmented revelation mechanism similar to the one devised by Jackson, Palfrey, and Srivastava [Jackson, M.O., Palfrey, T.R., Srivastava, S., 1994. Undominated Nash implementation in bounded mechanisms. Games Econ. Behav. 6, 474–501]. Moreover, we focus on pure exchange economies without free disposal, and try to construct another augmented revelation mechanism that satisfies balancedness in and out of equilibrium, and which implements all strategy-proof social choice functions in dominant strategy equilibria.     

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 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.     

The strategy-proof provision of public goods under congestion and crowding preferences

We examine the strategy-proof provision of excludable public goods when agents care about the number of other consumers. We show that strategy-proof and efficient social choice functions satisfying an outsider independence condition must always assign a fixed number of consumers, regardless of individual desires to participate. A hierarchical rule selects participants and a generalized median rule selects the level of the public good. Under heterogeneity in agents’ views on the optimal number of consumers, strategy-proof, efficient, and outsider independent social choice functions are much more limited and in an important case must be dictatorial.     

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.     

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”.     

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 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     

Secure implementation experiments: Do strategy-proof mechanisms really work?

Strategy-proofness, requiring that truth-telling is a dominant strategy, is a standard concept used in social choice theory. Saijo, Sjöström and Yamato [Saijo, T., Sjöström, T., Yamato, T., 2003. Secure implementation: Strategy-proof mechanisms reconsidered. Working paper 4-03-1. Department of Economics, Pennsylvania State University] argue that this concept has serious drawbacks. In particular, many strategy-proof mechanisms have a continuum of Nash equilibria, including equilibria other than dominant strategy equilibria. For only a subset of strategy-proof mechanisms do the set of Nash equilibria and the set of dominant strategy equilibria coincide. For example, this double coincidence occurs in the Groves mechanism when preferences are single-peaked. We report experiments using two strategy-proof mechanisms. One of them has a large number of Nash equilibria, but the other has a unique Nash equilibrium. We found clear differences in the rate of dominant strategy play between the two.     

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.     

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.     

Preference revelation with a limited number of indifference classes

Suppose that g is a strategy-proof social choice rule on the domain of all profiles of complete and transitive binary relations that have exactly m indifference classes. If and the range of g has three or more members, then g is dictatorial. If m = 2, then for any set X of feasible alternatives, there exist non-dictatorial and strategy-proof rules that are sensitive to the preferences of every individual and which have X as range.     

Secure implementation experiments: Do strategy-proof mechanisms really work?

Strategy-proofness, requiring that truth-telling is a dominant strategy, is a standard concept used in social choice theory. Saijo, Sjöström and Yamato [Saijo, T., Sjöström, T., Yamato, T., 2003. Secure implementation: Strategy-proof mechanisms reconsidered. Working paper 4-03-1. Department of Economics, Pennsylvania State University] argue that this concept has serious drawbacks. In particular, many strategy-proof mechanisms have a continuum of Nash equilibria, including equilibria other than dominant strategy equilibria. For only a subset of strategy-proof mechanisms do the set of Nash equilibria and the set of dominant strategy equilibria coincide. For example, this double coincidence occurs in the Groves mechanism when preferences are single-peaked. We report experiments using two strategy-proof mechanisms. One of them has a large number of Nash equilibria, but the other has a unique Nash equilibrium. We found clear differences in the rate of dominant strategy play between the two.     

The structure of strategy-proof social choice — Part I: General characterization and possibility results on median spaces

We define a general notion of single-peaked preferences based on abstract betweenness relations. Special cases are the classical example of single-peaked preferences on a line, the separable preferences on the hypercube, the “multi-dimensionally single-peaked” preferences on the product of lines, but also the unrestricted preference domain. Generalizing and unifying the existing literature, we show that a social choice function is strategy-proof on a sufficiently rich domain of generalized single-peaked preferences if and only if it takes the form of voting by issues (“voting by committees”) satisfying a simple condition called the “Intersection Property.”Based on the Intersection Property, we show that the class of preference domains associated with “median spaces” gives rise to the strongest possibility results; in particular, we show that the existence of strategy-proof social choice rules that are non-dictatorial and neutral requires an underlying median space. A space is a median space if, for every triple of elements, there is a fourth element that is between each pair of the triple; numerous examples are given (some well-known, some novel), and the structure of median spaces and the associated preference domains is analysed.