Domains, ranges and strategy-proofness: the case of single-dipped preferences

We characterize the set of all individual and group strategy-proof rules on the domain of all single-dipped preferences on a line. For rules defined on this domain, and on several of its subdomains, we explore the implications of these strategy-proofness requirements on the maximum size of the rules’ range. We show that when all single-dipped preferences are admissible, the range must contain two alternatives at most. But this bound changes as we consider different subclasses of single-dipped preferences: we provide examples of subdomains admitting strategy-proof rules with larger ranges. We establish exact bounds on the maximal size of strategy-proof functions on each of these domains, and prove that the relationship between the sizes of the subdomains and those of the ranges of strategy-proof functions on them need not be monotonic. Our results exhibit a sharp contrast between the structure of strategy-proof rules defined on subdomains of single-dipped preferences and those defined on subsets of single-peaked ones.     

Intermediate preferences and Rawlsian arbitration rules

Given the preferences of two agents over a finite set of alternatives, an arbitration rule selects some fair compromise. We study the idea that more consensus should not be harmful: the closer your preferences are to mine (in the sense of Grandmont's (1978) intermediate preferences), the better I like the selected alternative. We describe several Pareto optimal rules satisfying this principle. If, in addition, a condition akin to Suppes' (1966) grading principle is imposed, the rule must always choose an alternative maximizing the welfare of the worst-off agent, measured by the number of alternatives that he finds worse than the chosen one.Stimulating discussions with H. Moulin and helpful comments from J. Crémer are gratefully acknowledged. The author also wishes to thank a referee and an associate editor for challenging remarks. This research was partly supported by a CAFIR grant from the Université de Montréal.     

Scoring rules on dichotomous preferences

In this paper, we study individual incentives to report preferences truthfully for the special case when individuals have dichotomous preferences on the set of alternatives and preferences are aggregated in form of scoring rules. In particular, we show that (a) the Borda Count coincides with Approval Voting, (b) the Borda Count is the only strategy-proof scoring rule, and (c) if the size of the electorate is greater than three, then the dichotomous preference domain is the unique maximal rich domain under which the Borda Count is strategy-proof. I thank Jordi Massó for his supervision and his never-ending encouragement. Miguel-ángel Ballester showed me how to improve on earlier drafts of the paper. Salvador Barberà, Carmen Bevía, Bhaskar Dutta, Lars Ehlers, Alejandro Neme, Shmuel Nitzan and Yves Sprumont helped me a lot with their comments. All remaining errors are mine. This research was undertaken with support from the fellowship 2001FI 00451 of the Generalitat de Catalunya and from the research grant BEC2002-02130 of the Ministerio de Ciencia y Tecnología of Spain while I have been a graduate student at Universitat Autònoma de Barcelona.     

Probabilistic assignment of indivisible goods with single-peaked preferences

We consider the problem of assigning indivisible goods among a group of agents with lotteries when the preference profile is single-peaked. Unfortunately, even on this restricted domain of preferences, equal treatment of equals, stochastic dominance efficiency, and stochastic dominance strategy-proofness are incompatible.     

Population monotonic rules for fair allocation problems

We consider the property of population monotonicity in the context of fair allocation problems in private good economies. It is already known that the property is compatible with the equal division lower bound. We show that if the equal division lower bound is replaced with no envy, the compatibility does not hold. We also show that the incompatibility persists even though no envy is weakened to no domination or -no domination. Hence, among the fairness criteria mentioned above, only the equal division lower bound is compatible with population monotonicity.This part of my dissertation thesis. I thank to my advisor William Thomson for many valuable comments. I also thank to Youngsub Chun and Yangkyu Byun for their comments. All remaining errors are, of course, mine.     

Implementation of allocation rules under perfect information

We study subgame perfect implementation through perfect information mechanisms in economic environments. We assume that worst bundles exist for each agent and can be assigned to them independently of the bundle assigned to at least one other agent. We restrict our attention to allocation rules that are anonymous, efficient on their own range, single-valued in welfare, and that induce agents' participation. We define a class of mechanisms, which satisfy properties of minimal path length and finiteness of message dimensions. We characterize the class of allocation rules which can be implemented through those mechanisms.I would like to thank Bhaskar Dutta, Louis Gevers, Matthew Jackson, Ozgur Kibris, Hervé Moulin and Arunava Sen for stimulating discussions, seminar participants at Université de Montréal (the Axiomatic Theory of Resource Allocation meeting, May 1996), Universitat Autonoma de Barcelona, Universitad Carlos III de Madrid and Université de Paris Dauphine for their comments, and Frédéric Gaspart, Tarik Kara, James Schummer, William Thomson and an anonymous referee for extremely useful comments and suggestions on earlier versions.     

Choice rules with fuzzy preferences: Some characterizations

Consider an agent with fuzzy preferences. This agent, however, has to make exact choices when faced with different feasible sets of alternatives. What rule does he follow in making such choices? This paper provides an axiomatic characterization of a class of binary choice rules called the α satisfying rule. When α=1, this rule is the Orlovsky choice rule. On the other hand, for α≤1/2, the rule coincides with the M _α rule that has been extensively analyzed in the literature on fuzzy preferences. Received: 3 August 1995/Accepted: 19 November 1997     

Aggregation of fuzzy preferences: Some rules of the mean

This paper studies by means of reciprocal fuzzy binary relations the aggregation of preferences when individuals show their preferences gradually. We have characterized neutral aggregation rules through functions from powers of the unit interval in the unit interval. Furthermore, we have determined the neutral aggregation rules that are decomposable and anonymous. In this class of rules, the collective intensity of preference is the arithmetic mean of the values assigned by a function to the individual intensities of preference. We have also considered the neutral aggregation rules based on quasiarithmetic means. We have established that this class of rules generalizes the simple majority, when individuals have ordinary preferences and collective preferences are reciprocal. Received: 23 April 1999/Accepted: 25 September 1999     

Constrained allocation problems with single-peaked preferences: An axiomatic analysis

We introduce a new class of problems that contains two existing classes: allocation problems with single-peaked preferences and bankruptcy problems. On this class, we analyze the implications of well-known properties such as Pareto optimality, strategy-proofness, resource-monotonicity, no-envy, equal treatment of equals, and two new properties we introduce, hierarchical no-envy and independence of nonbinding constraints. Unlike earlier literature, we consider rules that allow free-disposability. We present characterizations of a rule we introduce on this domain. We relate this rule to well-known rules on the aforementioned subdomains. Based on this relation, we present a characterization of a well-known bankruptcy rule called the constrained equal awards rule. Received: 22 June 2000/Accepted: 21 March 2002 This paper is based on the first chapter of my Ph.D. thesis submitted to the University of Rochester. I wish to thank my advisor, William Thomson, for helpful comments and suggestions.     

Special majority rules necessary and sufficient condition for quasi-transitivity with quasi-transitive individual preferences

A condition on preferences called strict Latin Square partial agreement is introduced and is shown to be necessary and sufficient for quasi-transitivity of the social weak preference relation generated by any special majority rule, under the assumption that individual preferences themselves are quasi-transitive.     

Use of time and preferences for time allocation among urban,employed, married women

This study examines the relationship between employed wives' preferences for household production time, employment time, leisure, and their actual time use. A random sample of 235 employed, married women estimate their time use on an average weekday and weekend day in 13 activities and indicate their preferences for time in those activities. Hierarchical multiple regression procedures are used to examine the relationships between actual and preferred time use. Weekday employment time is not related to preferences for more or less time in household production but wives allocating more time to employment want to spend less time at that employment and more time in leisure. Weekend employment time is related to preferences for more time in leisure, child care, and other household work. Time spent performing household work is not related to preferences for more or less time in any activity except the desire for more leisure time on weekends.Ann Renigar Hiatt is Assistant Professor in the Department of Human Services, College of Education and Allied Professions at the University of North Carolina at Charlotte, Charlotte, NC 28223. Her research interests include employed women's time allocation, time pressures, and use of time management strategies. She received her Ph.D. from the University of North Carolina at Greensboro.Deborah D. Godwin is Associate Professor in the Department of Housing and Consumer Economics at the University of Georgia, Athens, GA 30602. Her research has focused on husbands' and wives' time allocation to household production, the effects of women's employment on family economic functioning, and family financial management. She received her Ph.D. from the University of North Carolina at Greensbore.     

The sensitivity of weight selection for scoring rules to profile proximity to single-peaked preferences

Niemi (Am Polit Sci Rev 63:488–497, 1969) proposed a simple measure of the cohesiveness of a group of n voters’ preferences that reflects the proximity of their preferences to single-peakedness. For three-candidate elections, this measure, k, reduces to the minimum number of voters who rank one of the candidates as being least preferred. The current study develops closed form representations for the conditional probability, PASW(n,IAC|k), that all weighted scoring rules will elect the Condorcet winner in an election, given a specified value of k. Results show a very strong relationship between PASW(n,IAC|k) and k, such that the determination of the voting rule to be used in an election becomes significantly less critical relative to the likelihood of electing the Condorcet winner as voters in a society have more structured preferences. As voters’ preferences become more unstructured as measured by their distance from single-peakedness, it becomes much more likely that different voting rules will select different winners.A preliminary version of this paper was presented at the European Public Choice Society Conference in Berlin, Germany, April 15–18, 2004.     

A maximal domain of preferences for strategy-proof,efficient, and simple rules in the division problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, tops-onlyness, and continuity. These domains (called partially single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.An earlier version of this paper circulated under the title A maximal domain of preferences for tops-only rules in the division problem. We are grateful to an associate editor of this journal for comments that helped to improve the presentation of the paper and to Matt Jackson for suggesting us the interest of identifying a maximal domain of preferences for tops-only rules. We are also grateful to Dolors Berga, Flip Klijn, Howard Petith, and a referee for helpful comments. The work of Alejandro Neme is partially supported by Research Grant 319502 from the Universidad Nacional de San Luis. The work of Jordi Massó is partially supported by Research Grants BEC2002-02130 from the Spanish Ministerio de Ciencia y Tecnología and 2001SGR-00162 from the Generalitat de Catalunya, and by the Barcelona Economics Program of CREA from the Generalitat de Catalunya. The paper was partially written while Alejandro Neme was visiting the UAB unde r a sabbatical fellowship from the Generalitat de Catalunya.     

Rent-seeking and competitive preferences

In this experiment, I examine the extent to which competitive social preferences can explain over-bidding in rent-seeking contests. The Human treatment is a standard two-player contest. In the Robot treatment, a single player bids against a computerized player, eliminating potential social preference motives. The results show no difference in bids between treatments at the aggregate level. Further analysis shows evidence of heterogeneous treatment effects between impulsive and reflective subjects. Moreover, impulsive subjects are more likely than reflective subjects to deviate qualitatively from the shape of the theoretical best response function.     

Transitivity and fuzzy preferences

The authors would like to thank a referee at Social Choice and Welfare for insightful comments.     

Probabilistic cheap talk

We consider a model in which there is uncertainty over when a one-shot game will be played. We show how a mechanism designer can implement desirable outcomes in certain economic games by manipulating only the probability that the game is played in a given round while leaving all other aspects of the game unchanged. We also show that if there is no discounting, this uncertainty imparts a sequential structure that is almost mathematically equivalent to a repeated version of the game with discounting. In particular, a folk theorem applies to such games. Thus, games of probabilistic cheap provide a third interpretation of the repeated game framework with the additional feature that expected payoff is invariant to the probability of the game ending. Received: 10 May 1999/Accepted: 16 October 2000     

Endogenous preferences and sustainable development

This paper focuses on the relevance of endogenous preferences for the explanation of consumer behavior and its role for sustainable development. The demand side has received far less attention in the sustainability discussion than the production side. There seems, however, little doubt that consumption is equally as important for achieving sustainability (e.g., F. Duchin, G.-M. Lange, The Future of the Environment: Ecological Economics and Technological Change, Oxford University Press, New York, 1994). While the influence of social interaction of preferences has been pointed out by economists for centuries, this link is generally submerged in the standard economic assumption of individual interest maximizing behavior. With reference to a specific type of local food market (community supported agriculture groups, CSA), this paper investigates consumer behavior and its relevance for sustainable development. Several studies have investigated CSAs’ contributions to different aspects of sustainable development and barriers to their expansion. One aspect usually left out is the change in preferences after interaction with the farmer/s and other market participants for several years. This learning aspect may, however, prove crucial to identify paths towards sustainable development.     

Tax rules

Tax schemes are more restricted by constitutional rules than subsidies. We introduce a model of public good provision with incentive problems in agenda-setting and identify several advantages of restrictions on tax schemes. In particular, tax rules may prevent the proposal and adoption of inefficient projects that benefit only a small minority. We also propose “redistribution efficiency” as a socially desirable property of proposals and find that tax rules guarantee this kind of efficiency. Moreover, a constitution that requires certain restrictions on both taxes and subsidies satisfies a criterion we label “robustness against counter-proposals.” We provide an axiomatic characterization of this constitution. Finally, we perform utilitarian welfare comparisons.     

Interpersonal distance preferences

The utility of various curvilinear comfort models of interpersonal distance was examined in a study employing subjects' responses to a broad range of videotaped, seated distances. Results obtained provided considerable support for these models. Intermediate distances were rated as more comfortable, preferable, and appropriate than more extreme close or far distances. This pattern of results was manifested for interaction situations involving both two- and four-person groups.This research was supported by Grants #HD-07045 and HD-8546-01 from the National Institute of Child Health and Human Development and by a NIH Biomedical Research Support grant 5S07 RR07087-12.