The core of social choice problems with monotone preferences and a feasibility constraint

We consider collective choice with agents possessing strictly monotone, strictly convex and continuous preferences over a compact and convex constraint set contained in ₊^k . If it is non-empty the core will lie on the efficient boundary of the constraint set and any policy not in the core is beaten by some policy on the efficient boundary. It is possible to translate the collective choice problem on this efficient boundary to another social choice problem on a compact and convex subset of ₊^c (c<k) with strictly convex and continuous preferences. In this setting the dimensionality results in Banks (1995) and Saari (1997) apply to the dimensionality of the boundary of the constraint set (which is lower than the dimensionality of the choice space by at least one). If the constraint set is not convex then the translated lower dimensional problem does not necessarily involve strict convexity of preferences but the dimensionality of the problem is still lower. Broadly, the results show that the homogeneity afforded by strict monotonicity of preferences and a compact constraint set makes generic core emptyness slightly less common. One example of the results is that if preferences are strictly monotone and convex on ² then choice on a compact and convex constraint exhibits a version of the median voter theorem.I thank Donald Saari for helpful comments on an earlier version of this paper.     

‘One and a Half Dimensional’ Preferences and Majority Rule

I examine a model of majority rule in which alternatives are described by two characteristics: (1) their position in a standard, left-right dimension, and (2) their position in a good-bad dimension, over which voters have identical preferences. I show that when voters’ preferences are single-peaked and concave over the first dimension, majority rule is transitive, and the majority’s preferences are identical to the median voter’s. Thus, Black’s (The theory of committees and elections, 1958) theorem extends to such a “one and a half” dimensional framework. Meanwhile, another well-known result of majority rule, Downs’ (An economic theory of democracy, 1957) electoral competition model, does not extend to the framework. The condition that preferences can be represented in a one-and-a-half-dimensional framework is strictly weaker than the condition that preferences be single-peaked and symmetric. The condition is strictly stronger than the condition that preferences be order-restricted, as defined by Rothstein (Soc Choice Welf 7:331–342;1990).     

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.     

Partially monotonic bargaining solutions

The purpose of the paper is to study partially monotonic solutions for two-person bargaining problems. Partial monotonicity relates to the uncertainty a player has about the solution before bargaining. If the minimum utility a player can expect is greater in game T than in game S, and if T contains more alternatives than S, this may bring him to expect that his utility at the solution is greater in T than in S. Partially monotonic solutions reflect these expectations.One partially monotonic solution is axiomatized. The axioms of symmetry and independence of linear transformations are not explicitly assumed, although the solution has also these properties. The Kalai-Smorodinsky solution is shown to be the only continuous partially monotonic solution.This study was financed by the Yrjö Jahnsson Foundation, which is gratefully acknowledged. I like to thank an associate editor and a referee for their valuable suggestions, and the Yrjö Jahnsson Foundation Study Group on Public Economics for useful discussions     

Banks winners in tournaments are difficult to recognize

Given a tournament T, a Banks winner of T is the top vertex of any maximal (with respect to inclusion) transitive subtournament of T. In this technical note, we show that the problem of deciding whether some fixed vertex v is a Banks winner for T is NP-complete. Received: 22 February 2002/Accepted: 20 June 2002 Supported by the START program Y43-MAT of the Austrian Ministry of Science. I would like to thank two thank the referees for a careful reading of the paper, for helpful remarks, and for many suggestions how to improve the presentation.     

Acyclic and continuous social choice in T 1 connected spaces

In this paper, we prove some versions of the Arrovian impossibility theorem in T ₁ connected alternatives spaces, with the collective rationality condition weakened from transitivity to acyclicity, the Pareto condition replaced by some weaker conditions, and a continuity condition of social preferences imposed. Moreover these impossibility theorems are applied to a distributive problem of private goods in economic environments.This is a revised version of my Working Paper No. 111. I would like to thank two anonymous referees of the journal for their insightful comments. This paper was reported at the Western Meeting of Japan Association of Economics and Econometrics, held at Tezukayama University June 1990, and at Second Annual Southeastern Economic Theory Meetings, held at Florida University October 1990. I am grateful to Professors Tetsuya Kishimoto, Makoto Okamura, Koichi Suga, and Donald Campbell for their insightful comments. This paper is supported in part by the Tokyo Center for Economic Research.     

Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems

We consider the problem of allocating indivisible objects when agents may desire to consume more than one object and monetary transfers are not possible. Each agent receives a set of objects and free disposal is allowed. We are interested in allocation rules that satisfy appealing properties from an economic and social point of view. Our main result shows that sequential dictatorships are the only efficient and coalitional strategy-proof solutions to the multiple assignment problem. Adding resource-monotonicity narrows this class down to serial dictatorships.We thank Francois Maniquet, two anonymous referees, and the participants of the GREBE-FRANCQUI Summer School on Axiomatic Resource Allocation Theory, held in Namur, Belgium, for their comments.     

Incomplete property rights, redistribution, and welfare

In a world where the private protection of property is costly, government redistribution can lead to an increase in aggregate output. This result is not new. The novelty of this paper lies in specifying the conditions under which this efficiency-enhancing redistribution improves everyone’s welfare including the welfare of those whose labor finances the redistributive program (i.e., the rich) and how this is affected by the protection of property rights. The state may directly enhance economic rights through investments in security and the protection of property or it may indirectly do so through the redistribution of income. Under certain conditions, redistribution becomes desirable in situations where the state has exhausted its ability to enhance efficiency through the direct enforcement of property rights. In this case, redistribution can make all members of a society better off. Specifically, this occurs when the cost of predation is sufficiently low and the technology of private protection of property rights is sufficiently weak. The adverse effects of redistribution may be the consequence but not the cause of state failure. The real cause is a corrupt and inept state. My thanks are due to an anonymous referee and Zane Spindler for very helpful and critical comments. I thank SSHRC for financial support     

Vietnam as a class war: Myth or reality?

This article reports an extension of the analyses of the fatalities in the Vietnam War presented by Barnett, Stanley, and Shore (1992) as printed in the September‐October 1992 Operations Research. The additional analyses involved an examination of results by Barnett et al. in numeric as well as percentage form and a consideration of how the revised analyses generalize to the population of all American fatalities in Vietnam. These analyses yielded a different conclusion about the role of economic class in the fatalities in the Vietnam War than those drawn by Barnett et al. They suggested that the term class war was not supported by their data analyses. Our analyses indicate that their conclusion is incorrect. The lower class sacrificed considerably more lives than the upper class.     

The lexicographic egalitarian solution on economic environments

This paper considers solutions to distribution problems defined on economic environments. It shows that there is a unique resource-egalitarian and symmetric solution that proposes always Pareto optimal allocations and satisfies Inidivual Restricted Monotonicity; this property requires the poor people of the society to be strictly better-off when social resources increase and the initial outcome is a welfare unequal position. That unique solution is the lexicographic extension of the maxmin criterion.I wish to express my gratitude to Salvador Barberá. I am also very grateful to Hervé Moulin for his encouragement and to Carmen Herrero, Iñigo Iturbe and an anonymous referee for their suggestions. I thank very specially the valuable reading of John Roemer and illuminating conversations with Serge Christophe Kolm. Financial support from Gobierno de Navarra is gratefully acknowledged     

A characterization of strategy-proof social choice functions for economies with pure public goods

We characterize strategy-proof social choice functions when individuals have strictly quasi-concave, continuous and satiated utility functions on convex subsets of IR ^m , representing preferences for the provision of m pure public goods. When specialized to the case m=1, these assumptions amount to requiring that preferences are single peaked, and for such a domain there exists a wide class of strategy-proof social choice functions. These were studied by Moulin (1980) under strong additional assumptions. Our first results characterize the complete class, after an appropriate extension of the single-peakedness condition. The new characterization retains the flavour of Moulin's elegant representation theorem. For the general m-dimensional case, previous results have shown that there is no efficient, strategy-proof, nondictatorial social choice function, even within the domain restrictions under consideration (Border and Jordan 1983; Zhou 1991). In fact, Zhou's powerful result indicates that nondictatorial strategy-proof s.c.f.'s will have a range of dimension one. This allows us to conclude with a complete characterization of all strategy-proof s.c.f.'s on IR ^m , because restrictions of preferences from our admissible class to one dimensional subsets satisfy the slightly generalized notion of single-peakedness that is used in our characterization for the case m=1. We feel that a complete knowledge of the class of strategy-proof mechanisms, in this as well as in other contexts, is an important step in the analysis of the trade-offs between strategy-proofness and other performance criteria, like efficiency.This paper was written while both authors were visiting GREMAQ, Université des Sciences Sociales de Toulouse. We are thankful for its hospitality and good research atmosphere. Barberà's work is supported by the Instituto de Estudios Fiscales and by research grant PB89-0294 from the Secretaría de Estado de Universidades e Investigación, Spain. Jackson acknowledges the support of NSF grant SES8921409. We thank Jacques Crémer, Beth Allen, John Weymark and two anonymous referees for helpful comments on earlier drafts.     

The selective adaptation of the alcoholics anonymous program by Gamblers Anonymous

This paper is largely based on a year long observation study of Gamblers Anonymous and Alcoholics Anonymous meetings in northern California. The paper argues, contrary to popular assumption, that Gamblers Anonymous is significantly different from Alcoholics Anonymous. Differences, in members' consciousness for example, are discussed. The paper contends that although there is some12 step consciousness in G.A., the dominant consciousness ispage 17 consciousness. The significant differences are attributed to the selective adaptation of the Alcoholics Anonymous program. Several consequences of these differences, such as the central role of a language of the self in A.A. and not in G.A., are highlighted.This research was supported by NIAAA post-doctoral grant, 2 T32 AA07240-11, at the Alcohol Research Group, Berkeley, California. I would like to thank everyone at ARG for the wonderfully supportive and intellectually stimulating atmosphere at ARG. I would like to thank especially Mary Phillips, Ron Roizen, Kim Bloomfield, Robin Room, Mike Hilton, Laura Schmidt, John Rumbarger and David Newmark for listening patiently to the unfolding story. I would also like to thank Rachel Volberg and Richard Rosenthal, M.D. for comments on an earlier draft. Comments from the anonymous reviewers and the editor ofJournal of Gambling Studies were also quite useful. Most of all, though, I would like to thank the anonymous members of A.A. and G.A. I, however, take responsibility for the arguments advanced in the paper. This paper is a revision of one presented at theEighth International Conference on Risk and Gambling in London, England, August, 1990.     

The Real Book of Mormon Musical: Latter-day Saint Family Home Evening as a Weekly Ritual

Abstract

Scholars of religious ritual have noted that inadequate attention has been paid to religious ritual in the social sciences. Based on what has been done, it is apparent that sacred family rituals (when done well and with relational sensitivity) can enhance structure, meaning, and family unity. The present study examines the family-level ritual practice of weekly Family Home Evening among members of 26 Latter-day Saint (LDS) families (N?=?58 individuals). Qualitative analyses found the following three themes: (a) Family Home Evening as a Conversation; (b) Challenges of Family Home Evening; and (c) The Value of Family Home Evening. Primary data that support and illustrate the three themes are presented, along with implications and applications.     

A spatial study of teachers’ salaries in Pennsylvania school districts

I explore the relationship among teacher salaries across Pennsylvania school districts. Using techniques developed in spatial econometrics, I find that the error terms in a salary regression are spatially correlated, suggesting evidence of omitted labor market factors. I also find evidence that salaries in nearby, financially similar districts directly influence teacher salaries in a particular district, which is evidence of pattern bargaining or more informal social comparisons across districts. Econometric specifications that ignore these factors overstate the influence of own-district variables, such as economic indicators, on salary. I thank colleagues Linda Babcock and John Engberg for very valuable contributions and for use of their data. Thanks also to Wil Gorr, who helped with some of the GIS aspects of this research. A National Science Foundation grant supported data collection.     

LEADING PRINCIPAL MINORS AND SEMIDEFINITENESS

Semidefinite matrices often arise in economic models, usually as Hessian matrices of convex or concave functions. Anytime the matrix can be semidefinite, rather than definite, the task of characterizing it is burdensome because extant results require that all principal minors be signed. A theorem is presented that shows it is sufficient to sign only selected principal minors when the matrix has a definite submatrix. This theorem is particularly useful in duality applications. The theorem also provides relatively easy proof of the standard relationship between semidefiniteness and principal minors. (JEL C02)     

Autonomy,Dependence, or Display? The Relationship Between Married Women’s Earnings and Housework

I argue that both the dominant models of the relationship between earnings and housework, economic dependence and gender display, have fundamental defects. They focus on the effect of women’s earnings compared to their husbands’ on their housework and ignore the possibility of an independent relationship between women’s own earnings and their time spent on housework. Using a sample of 914 married women employed full time from the second wave of the National Survey of Families and Households, I show that women’s housework is affected only by their own earnings, not by their husbands’, and not by their earnings compared to their husbands’. Further, I show that findings suggestive of dependence and display in earlier research are more simply explained in terms of women’s absolute rather than relative earnings. These results invalidate the dependence and display models of the relationship between earnings and housework time and suggest that married women have a substantial degree of economic autonomy in the areas of domestic life for which they are normatively responsible.     

On ranking linear budget sets in terms of freedom of choice

This paper examines how freedom of choice as reflected in an agents opportunity sets can be measured in economic environments where opportunity sets are linear budget sets in the non-negative orthant of the n-dimensional real space. Three axioms, Symmetry, Monotonicity and Invariance of Scaling Effects, are proposed for this purpose and the measure based on volumes of budget sets is characterized. I am grateful to Prasanta K. Pattanaik for his encouragement and fruitful discussions over many years on this and related subjects. The first draft of this paper was written while I was visiting the Institute of Economic Research at Hitotsubashi University in Japan. I would like to thank its hospitality. Helpful comments of a referee are gratefully acknowledged.     

An alternative characterization of the uniform rule

We consider the problem of allocating some amount of a commodity among a group of agents with single-peaked preferences. We show that the uniform rule is the only rule satisfying equal treatment of equals, Pareto efficiency, and strategy-proofness. This characterization strengthens two interesting results due to Sprumont (1991). Our method of proof involves only elementary arguments.I wish to thank Professor William Thomson for his enormous efforts in supervision. I am grateful to Professor Marcus Berliant and Hideo Konishi for their useful remarks and especially to an anonymous referee for insightful comments. All remaining errors are my own responsibility.     

Legitimations of class structure inGone With The Wind

The role of popular culture in legitimating the existing social order is examined through an analysis of the film version ofGone With The Wind. This film was selected because, judging from its immense popularity, it has had great potential as a vehicle for legitimation. The analysis reveals several ways in which the audience is brought to identify with the upper class as well as several themes which legitimate class structure. An earlier version of this paper was read at the Popular Culture Association National Meeting, 1978, Cincinnati, Ohio. I wish to thank Ava Baron, Joni Fulton, Jane Rosenbaum, and the reviewers ofQualitative Sociology for their helpful comments in preparing the final draft of this paper.