Subgame perfect implementation of voting rules via randomized mechanisms

We characterize completely ordinal and onto choice rules that are subgame perfect of Nash equilibrium (SPE) implementable via randomized mechanisms under strict preferences. The characterization is very operationalizable, and allows us to analyse SPE implementability of voting rules. We show that no scoring rule is SPE implementable. However, the top-cycle and the uncovered correspondences as well as plurality with runoff and any strongly Condorcet consistent voting rule can be SPE implemented. Therefore our results are favourable to majority based voting rules over scoring rules. Nevertheless, we show that many interesting Condorcet consistent but not strongly Condorcet consistent rules, such as the Copeland rule, the Kramer rule and the Simpson rule, cannot be SPE implemented.     

Strongly implementable social choice correspondences and the supernucleus

In this paper, we present a characterization of social choice correspondences which can be implemented in strong Nash equilibrium, stated in terms of the power structure implicit in the social choice rule. We extend the notion of an effectivity function to allow for simultaneous vetoing by several coalitions. This leads to the concept of a domination structure as a generalized effectivity function.  Using this concept and a solution known from the theory of effectivity functions, the supernucleus, we give a characterization of strongly implementable social choice correspondences as supernucleus correspondence relative to an appropriate domination structure. Received: 2 February 1996/Accepted: 2 February 1998     

Implementation in perfect equilibria

This paper considers implementation when the feasible outcomes are lotteries over a finite set of alternatives. The following weak condition is sufficient for implementation in trembling hand perfect equilibria (with three or more players): if all but one player agree on which alternative is the best, this alternative is (among those that are) chosen by the social choice rule, and if all but one player agree on which alternative is the worst, this alternative is not chosen. Many interesting social choice rules that are not Nash implementable satisfy this condition. On the other hand, there are social choice rules that are implementable in Nash equilibria but not in perfect equilibria.I am grateful to Luis Corchón, Eric Maskin, William Thomson, seminar participants at Harvard and Rochester, and two anonymous referees for helpful comments and suggestions. This research was supported by grants from the Royal Swedish Academy of Sciences and the Bank of Sweden Tercentenary Foundation.     

Equivalence of Nash implementability and robust implementability with incomplete information

This paper is concerned with the design of robust mechanisms which are applicable to a wide class of possible information structures of agents. We examine a society consisting of several groups such that (i) there are at least three agents in each group; and (ii) each agent knows the preferences of the agents in his group but has incomplete information about the preferences of the agents outside his group. We show that for a large class of information structures, a social choice set (SCS) is implementable for each possible information structure if and only if it is Nash implementable. In other words, the class of robustly implementable SCS's is identical to the class of implementable SCS's in the complete information setting.This paper is a substantially revised version of a chapter of my dissertation submitted to the University of Rochester (Yamato [25]). I thank Professor William Thomson for his invaluable advice and suggestions. Detailed comments and suggestions of an anonymous referee were very helpful for further revision of the paper. I also acknowledge comments from Professors Randall Calvert, Luis Corchon, Glenn MacDonald, Eric Maskin, Lionel McKenzie, Ryo-Ichi Nagahisa, Koji Okuguchi, Ignacio Ortuño-Ortin, Tatsuyoshi Saijo, Ken-Ichi Shimomura, Tomas Sjöström, Yoshikatsu Tatamitani, and seminar participants at Harvard University, the 1992 Meeting of Kobe Summer Seminar in Economics of Organization and Game Theory, Tokyo Metropolitan University, and Toyama University. This work was supported in part by the Ministry of Education in Japan, the Nomura Foundation for the Social Sciences, and the Tokyo Center for Economic Research.     

A characterization of natural and double implementation in production economies

We define two types of natural mechanisms, quantity and price-quantity types, in convex production economies, and characterize the class of Pareto subsolutions doubly implementable in Nash and strong Nash equilibria by these mechanisms respectively. First, we show that there is a class of Pareto subsolutions doubly implementable by natural quantity mechanisms, as long as production sets have smooth boundaries. We characterize the class of Pareto subsolutions doubly implementable by natural price-quantity mechanisms without assuming differentiability of utility functions. Third, we show that the Walrasian solution is the unique Pareto and fully individually rational solution naturally and doubly implementable in private ownership economies. Received: 4 December 1997/Accepted: 25 August 1999     

Bayesian implementation in exchange economies with state dependent feasible sets and private information

This paper considers the problem of implementation for exchange economies with state dependent feasible sets. Agents are assumed to have private information about their endowments. We provide necessary and sufficient conditions for social choice rules that are Bayesian implementable by feasible mechanisms for such an environment. We compare our main result to the Nash implementation result derived in an environment of complete information.     

Robust normative comparisons of socially risky situations

In this paper, we theoretically characterize robust empirically implementable normative criteria for evaluating socially risky situations. Socially risky situations are modeled as distributions, among individuals, of lotteries on a finite set of state-contingent pecuniary consequences. Individuals are assumed to have selfish Von Neumann–Morgenstern preferences for these socially risky situations. We provide empirically implementable criteria that coincide with the unanimity, over a reasonably large class of such individual preferences, of anonymous and Pareto-inclusive Von Neuman Morgenstern social rankings of risks. The implementable criteria can be interpreted as sequential expected poverty dominance. An illustration of the usefulness of the criteria for comparing the exposure to unemployment risk of different segments of the French and US workforce is also provided.     

The implementation of social choice functions via social choice correspondences: A general formulation and a limit result

A corollary of Maskin's characterization theorem for Nash implementable social choice correspondences is that only trivial social choice functions can be implemented. This paper explores the consequences of implementing non-trivial social choice functions by extending them minimally to social choice correspondences which are implementable. The concept of asymptotic monotonicity is introduced. The main result states that it is not possible to find social choice rules satisfying a mild condition on its range, which is asymptotically monotonic. The implication of this result is that the multiplicity of equilibria problem which is at the heart of Nash implementation theory persists even in the limit as the number of individuals in society tends to infinity. This is true even though the opportunities for an individual to manipulate the outcome disappears in the limit.This paper is an extensively revised version of a chapter of my Ph.D. dissertation submitted to Princeton University in June 1987. I wish to thank my advisor Hugo Sonnenschein for his valuable advice and constant encouragement. I am also grateful to Andrew Caplin, Vijay Krishna, William Thomson, Jean-Luc Vila and two anonymous referees of this journal for their numerous suggestions. All remaining errors are my own responsibility.     

On Individual Difference,Choice, Selection,and Complexity in Adoption Research

Abstract

The silent confounds of the Main Effects Model as used in adoption research are individual difference driven self-selection and choice along with intermediary and birthparent selections. Two Chain-of-Choices Models -one for adoptive parents and one for birthparents and adoptees -are presented as possible frameworks within which to consider the role of individual differences, choices, and selections in understanding both the process of adoption and adoption outcomes. The article concludes with an extensive discussion of the research and practice implications which follow from the Chain-of-Choices Models and the emphasis on pre-existing individual differences.     

Iterative elimination of weakly dominated strategies in binary voting agendas with sequential voting

This paper describes the correspondences between the results given by backward induction (BI) and iterative elimination of weakly dominated strategies (IEWDS) in binary voting agendas with sequential voting. When the voters have strict preferences over all candidates, the strategies that survive IEWDS all select the unique candidate selected by the BI strategy profiles. But if some voters are indifferent, this result no longer holds. However, when there are only two candidates, it is possible to demonstrate strong relationships between the results given by BI and IEWDS, even when some voters have indifferences.     

On removing Condorcet effects from pairwise election tallies

Condorcet profiles are responsible for a number of well known preference aggregation paradoxes. It is reasonable to claim that these profiles represent complete ties between the candidates and should therefore be excluded to determine election outcomes. Established profile decomposition techniques are of limited usefulness in extracting and removing Condorcet effects, because of the computational complexity involved, even if complete knowledge of voters’ rankings of all candidates are available. The paper discusses an easily implementable method of removing or reducing Condorcet effects from pairwise scores. Pairwise scores (and not complete knowledge of voters’ rankings) are often the only available data based on which an election winner has to be determined.     

Natural implementation in public goods economies

In this paper, we identify necessary and sufficient conditions for social choice correspondences to be Nash implemented by “natural” mechanisms in economies with arbitrary numbers of private and public goods. We find that when there exist only one public good and an arbitrary number of private goods, the Lindahl correspondence is implementable by a natural quantity mechanism in which each agent announces his own consumption bundle of private goods and input vectors for public goods. However, regardless of the numbers of private and public goods, the Pareto correspondence is not implementable even by any natural price ⁿ -quantity mechanism in which each agent reports a price vector of private goods and all agents’ personalized price vectors of public goods, in addition to his own consumption bundle of private goods and input vectors for public goods.     

A purely non-cooperative model of divided government

In this paper I describe an institutional structure in which there are two branches of the government: the executive one, elected by plurality rule, and the legislative one elected by proportional rule. The resulting policy outcome is described through a compromise between these two branches. Given the presidential result, legislative elections are characterized by essentially an unique Nash equilibrium such that any voter on the left of the corresponding policy outcome votes for the leftist party and any voter on the right votes for the rightist party. Moreover, this equilibrium can be obtained by a process of iterated elimination of dominated strategies. The whole game is then solved by backward induction and dominance arguments.I thank Francesco De Sinopoli, Jean-Francois Mertens, Howard Rosenthal and Jacques Thisse for very helpful discussions.     

Horizontal inequity comparisons

In this paper, we expound the idea that horizontal inequity (HI) in different tax systems be compared by transplanting the HI from one tax system into the other, as a mapping between its pre- and post-tax living standard distributions, and then applying known results to compare the extent of association present in the two joint distributions. We make this idea operational by means of axioms which, we show, lead to an implementable procedure based on the `copula'. Statistical inference procedures are discussed, and illustrative empirical exercises are undertaken for the UK, Canadian and Israeli tax and benefit systems. Received: 1 March 1999/Accepted: 29 May 2000     

Nash implementation and the bargaining problem

We study Nash implementation of the bargaining solutions in a cake sharing set up. We argue that the minimal Pareto optimal, symmetric and Nash implementable SBS is the one inducing all Pareto optimal and midpoint-dominating utility vectors in each state.     

FIAT EXCHANGE IN FINITE ECONOMIES

The state of the art of rendering fiat money valuable is either to impose a boundary condition or to make the boundary condition unimportant through an infinite sequence of markets so as to circumvent backward induction. We show fiat exchange may nevertheless arise in finite economies if agents have incomplete information about their relative position in the trade cycle or when the barter and autarky equilibria of the one-shot trading round support a monetary equilibrium with repeated trades.     

Hearing the voices of disabled students in higher education

Since the return of the Labour government to power in the UK in 1997 issues of social inclusion have risen up the political and statutory agenda within higher education (HE). This study reports the findings of disabled students lived experiences and views of transition from induction through to employability within one HE institution. The study examined the perspectives of disabled students via a questionnaire and face‐to‐face interviews. It found that there was still much work to be done in levelling HE experiences for disabled students and identified five key issues that should be addressed in order to enable access and entitlement to HE. These are pre‐course induction support, commitment by HE institutions to facilitating barrier free curricula, consultation with disabled students, institutional commitment to develop support services and embedding of personal development planning.     

Monotonicity implies generalized strategy-proofness for correspondences

We show that Maskin monotone social choice correspondences on sufficiently rich domains satisfy a generalized strategy-proofness property, thus generalizing Muller and Satterthwaite’s (1977) theorem to correspondences. The result is interpreted as a possibility theorem on the dominant-strategy implementability of monotone SCCs via set-valued mechanisms for agents who are completely ignorant about the finally selected outcome. Alternatively, the result yields a partial characterization of the restrictions entailed by Nash implementability of correspondences. Received: 3 November 1997/Accepted: 26 April 1999     

DISENTANGLING DEMAND‐ENHANCING AND TRADE‐COST EFFECTS OF MAXIMUM RESIDUE REGULATIONS

Maximum residue level (MRL) regulations in plant products can create unnecessary trade barriers on one hand and enhance demand via risk mitigation or quality assurance on the other. We stipulate a generalized gravity equation model to disentangle the effects of MRLs on the import demand and foreign exporters' supply. Applying the framework to the MRLs on pesticides imposed by high‐income Organization for Economic Co‐operation and Development countries, we find that the MRLs jointly enhance the import demand and hinder foreign exporters' supply. In addition, exporters from the less and least developed countries are more constrained by the MRLs than their competitors from the developed world. (JEL F14, Q17)