Strategic requirements with indifference: single-peaked versus single-plateaued preferences

We concentrate on the problem of the provision of one pure public good whenever agents that form the society have either single-plateaued preferences or single-peaked preferences over the set of alternatives. We are interested in comparing the relationships between different nonmanipulability notions under these two domains. On the single-peaked domain, under strategy-proofness, non-bossiness is equivalent to convexity of the range. Thus, minmax rules are the only strategy-proof non-bossy rules. On the single-plateaued domain, only constant rules are non-bossy or Maskin monotonic; but strategy-proofness and weak non-bossiness are equivalent to weak Maskin monotonicity. Moreover, strategy-proofness and plateau-invariance guarantee convexity of the range. We thank Salvador Barberà, Matthew Jackson, Bettina Klaus, Jordi Massó, John Weymark, and two anonymous referees and the Associate Editor for helpful comments and suggestions. We also thank the participants in the 3rd Workshop on Social Decisions that took place in Málaga in November 2007. Dolors Berga acknowledges the financial support by the Spanish Ministry of Education and Science through Research Grants SEJ2004-03276 and SEJ2007-60671 and also by the Generalitat de Catalunya through Research Grant 2005SGR-213 and the Barcelona Economics Program (CREA). Bernardo Moreno gratefully acknowledges financial support from Junta de Andalucía through grant SEJ522 and the Spanish Ministry of Science and Technology through grant SEC2005-04805.     

Measuring the cohesiveness of preferences: an axiomatic analysis

In this paper, we axiomatically study how to measure the similarity of preferences in a group of individuals. For simplicity, we refer to this as the cohesiveness. First, we provide axioms that characterize a family of linear and additive measures whose intersection is a partial ordinal criterion similar to first order stochastic dominance. The introduction of some additional properties isolates a one-parameter subfamily. This parameter evaluates the effect on the cohesiveness if one individual changes his ranking on a single pair of objects, as a function of how many of the remaining individuals in the group rank the first object over the second and vice versa. Finally, we characterize the focal measures of this subfamily separately showing that they coincide with measures constructed using two, at first sight, totally different approaches suggested in the literature.     

Allocating multiple estates among agents with single-peaked preferences

We consider the problem of allocating multiple social endowments (estates) of a perfectly divisible commodity among a group of agents with single-peaked preferences when each agent’s share can come from at most one estate. We inquire if well-known single-estate rules, such as the Uniform rule, the Proportional rule or the fixed-path rules can be coupled with a matching rule so as to achieve efficiency in the multi-estate level. On the class of problems where all agents have symmetric preferences, any efficient single-estate rule can be extended to an efficient multi-estate rule. If we allow asymmetric preferences however, this is no more the case. For nondictatorial single-estate rules that satisfy efficiency, strategy proofness, consistency, and resource monotonicity, an efficient extension to multiple estates is impossible. A similar impossibility also holds for single-estate rules that satisfy efficiency, peak-only, and a weak fairness property. We would like to express our gratitude to Bhaskar Dutta, Semih Koray, Hervé Moulin, and Yuntong Wang as well as an associate editor and two anonymous referees of this journal for detailed comments and suggestions. We also thank the seminar participants at Bilkent University, Indian Statistical Institute, Bilgi University, University of Warwick, ASSET 2003, and BWED XXVI.     

Strategy-proof division with single-peaked preferences and individual endowments

We consider the problem of (re)allocating the total endowment of an infinitely divisible commodity among agents with single-peaked preferences and individual endowments. We propose an extension of the so-called uniform rule and show that it is the unique rule satisfying Pareto optimality, strategy-proofness, reversibility, and an equal-treatment condition. The resulting rule turns out to be peaks-only and individually rational: the allocation assigned by the rule depends only on the peaks of the preferences, and no agent is worse off than at his individual endowment. Received: 8 September 1995/Accepted: 30 October 1996     

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.     

Balanced allocation methods for claims problems with indivisibilities

We study claims problems in which a certain amount of indivisible units (of an homogeneous good) has to be distributed among a group of agents, when this amount is not enough to fully satisfy agents’ demands. Our aim is to find solutions fulfilling procedural and fairness properties. To do that, we define the M-down methods, which are the unique robust (composition down and consistency) and fair (balancedness and conditional full compensation) rules. Besides, we also establish the relationship between these M-down methods and the constrained equal awards rule.     

Paired comparisons analysis: an axiomatic approach to ranking methods

In this paper we present an axiomatic analysis of several ranking methods for general tournaments. We find that the ranking method obtained by applying maximum likelihood to the (Zermelo-)Bradley-Terry model, the most common method in statistics and psychology, is one of the ranking methods that perform best with respect to the set of properties under consideration. A less known ranking method, generalised row sum, performs well too. We also study, among others, the fair bets ranking method, widely studied in social choice, and the least squares method.     

Multidimensional inequality and multidimensional generalized entropy measures: An axiomatic derivation

This paper generalizes the axiomatic approach to the design of income inequality measures to the multiattribute context. While the extension of most axioms considered desirable for inequality indices is straightforward, it is not entirely clear when a situation is more unequal than another when each person is characterised by a vector of attributes of well-being. We explore two majorization criteria which are partial orders ranking distributions of attributes by their degree of inequality. The two criteria are motivated by the Pigou-Dalton Transfer Principle in the unidimensional context and its equivalent formulation. These criteria gauge inequality loosely speaking with respect to the dispersion of the multidimensional distribution of the attributes. They, however, fail to address a different dimension of multivariate inequality pertaining to an increase in the correlation of the attributes. In this connection, this paper introduces a correlation-increasing majorization criterion proposed by Boland and Proschan (1988). Finally, in conjunction with other axioms commonly invoked in the literature on inequality, the majorization criteria lead inexorably to the class of multidimensional generalized entropy measures. Received: 15 June 1995 / Accepted: 30 September 1997     

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.     

Advocacy and the SSSP: An analysis of research articles in social problems

This study examines the extent of advocacy in the research articles appearing in the journalSocial Problems from 1953–1992. The Society for the Study of Social Problems (SSSP) was founded in order to counter the mainstream scientism of the American Sociological Society. Becker’s presidential address to the SSSP in 1966 confronted the issue of advocacy and the consequences associated with research that does not explicitly “take sides.” The present study investigates advocacy inSocial Problems by means of a typology drawn from Becker’s address. The findings indicate that political advocacy has increased sharply over the duration ofSocial Problems. Implications of the findings are discussed in the context of value-neutrality and its relation to social problems research.     

The construction of fear: Americans' preferences for social distance from children and adolescents with mental health problems

Debates about children's mental health problems have raised questions about the reliability and validity of diagnosis and treatment. However, little research has focused on social reactions to children with mental health problems. This gap in research raises questions about competing theories of stigma, as well as specific factors shaping prejudice and discrimination toward those children. Here, we organize a general model of stigma that synthesizes previous research. We apply a reduced version of this model to data from a nationally representative sample responding to vignettes depicting several stigmatizing scenarios, including attention-deficit/hyperactivity disorder (ADHD), depression, asthma, or "normal troubles." Results from the National Stigma Study-Children suggest a gradient of rejection from highest to lowest, as follows: ADHD, depression, "normal troubles," and physical illness. Stigmatizing reactions are highest toward adolescents. Importantly, respondents who label the vignette child's situation as a mental illness compared to those who label the problem as a physical illness or a "normal" situation report greater preferences for social distance, a pattern that appears to result from perceptions that the child is dangerous.     

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     

Social preferences for public intervention: An empirical investigation based on French data

In this paper we examine the support given by French households to public intervention aimed at reducing inequalities and improving the well-being of low-income classes. We first discuss to what extent the model of self-interest could be relied upon when one wants to take into account social norms to explain the individual demand for redistribution. We find that social beliefs play an important role in explaining individual attitudes towards public intervention. We also find that the support given to redistribution can increase or decrease depending on the interaction between reciprocity norms and beliefs regarding the causes of poverty.     

The Paretian liberal with intuitionistic fuzzy preferences: A result

In the present paper we consider a situation in which the individual preferences and the social preference relation are intuitionistic fuzzy and study the compatibility between the Pareto principle and Sens minimal liberalism condition. A possible factorization of the intuitionistic fuzzy weak preference relation allows us to prove a possibility result for the case of max-min transitive social preference.I am extremely grateful to the Coordinating Editor and an anonymous referee of this journal for their detailed comments and suggestions. The paper was written while I was a Post-doc fellow at the Graduiertenkolleg Allocationstheorie, Wirtschaftspolitik und kollektive Entscheidungen, Ruhr-University Bochum. Thanks are due to Krassimir Atanassov, Luis G. Gonzalez-Morales and Gergana Dimitrova for helpful comments, and to the Deutsche Forschungsgemeinschaft for financial support.     

Placement preferences among children living in foster or kinship care: A cluster analysis

This research provides a longitudinal assessment regarding children's placement preferences, distinguishing between what children prefer to be permanent home situations and what children expect will be permanent situations. Cluster analysis was used in an effort to classify the responses of 1313 children, ages 6–14, in foster or kinship care, over a three year period, regarding placement preferences. Results of the cluster analyses indicate classification in the following four groups of permanency preferences: 1) I don't want to be here/going home; 2) I can stay here, but I don't want to/going home; 3) I can stay here and I want to, but no adoption; and 4) I can stay here and I want to, with adoption. Findings indicate that across waves of data collection, children express a sense of belonging in their foster homes. Older children were more agreeable to their current placements as long as there was no option of permanency/adoption. Also, White children were more likely to prefer and expect to go home. This research provides great utility in evaluative efforts that include listening to the voices of the children by encouraging their participation in case planning and service evaluation.