How to cut a pizza fairly: Fair division with decreasing marginal evaluations

Existential and constructive solutions to the classic problems of fair division are known for individuals with constant marginal evaluations. By considering nonatomic concave capacities instead of nonatomic probability measures, we extend some of these results to the case of individuals with decreasing marginal evaluations. Received: 12 June 2001/Accepted: 23 May 2002 An earlier version of this paper, Caltech Social Science Working Paper # 1126, was titled “How to cut a cake healthily”. We wish to thank Maristella Botticini, Erio Castagnoli, Marco Dall'Aglio, Paolo Ghirardato, Luigi Montrucchio, Marco Scarsini, Marciano Siniscalchi, as well as Maurice Salles (the Editor), an Associate Editor, and four anonymous Referees for helpful suggestions. The financial support of MIUR, CNR, and Università Bocconi is gratefully acknowledged. Part of this research was done while the first author was visiting Boston University and the California Institute of Technology, which he thanks for their hospitality.     

Fair and efficient division through unanimity bargaining when claims are subjective

In a subjective claims problem several partners have conflicting perceptions on how a jointly produced surplus should be divided fairly amongst them. In a large-scale experiment, we compare the fairness and efficiency of three unanimity bargaining procedures used to reach a consensus in a three-partner subjective claims problem. Under each procedure partners move sequentially, making alternating proposals. The procedures differ in whether they ask for a complete division proposal (Offer and Exit rule) or only for a proposal regarding the partner’s own fair share (Demand rule); and in whether partners have to accept the entire division proposal (Offer and Demand rule) or only their own share (Exit rule). For the fairness assessment partial and impartial fairness views are used and we find that the Offer rule performs best in terms of allocative fairness and no worse in terms of efficiency.     

Fair division under joint ownership: Recent results and open problems

Two microeconomic models of joint ownership are discussed: the division of unproduced commodities and the joint production of a single output by a single input. In both models the two principal interpretations of fairness are Equal Split Guarantee (ESG) and No Envy (NE). When combined with Pareto optimality these axioms are however not compatible with some appealing monotonicity properties. Resource monotonicity (more cake to share makes everyone happy) is incompatible with either ESG or NE, and Population Monotonicity (one more mouth to feed makes everyone unhappy) is incompatible with NE. This in turn suggests three disjoint classes of fair solutions. This paper contains very few new results, it is mostly a survey of recent literature.A first version of this paper was delivered in June 1989 at the University of Alicante, for the third German Bernacer Lectures. The hospitality of this institution is gratefully acknowledged. I am also thankful to Claude d'Aspremont, Louis Gevers and William Thomson for stimulating discussions and to an anonymous referee for helpful criticisms.     

Fair division of indivisible items between two people with identical preferences: Envy-freeness, Pareto-optimality, and equity

This paper focuses on the fair division of a set of indivisible items between two people when both have the same linear preference order on the items but may have different preferences over subsets of items. Surprisingly, divisions that are envy-free, Pareto-optimal, and ensure that the less well-off person does as well as possible (i.e., are equitable) can often be achieved. Preferences between subsets are assumed to satisfy axioms of qualitative probability without implying the existence of additive utilities, which is treated as a special case. Algorithms that render fair division practicable are proposed, and their vulnerability to strategic manipulation is investigated. Received: 18 May 1998/Accepted: 2 March 1999     

Consistency between tastes and values: A universalization approach

The object of this paper is to propose a consistency test for an individual involved in collective choice process. Collective choice processes considered in the paper are those that transform individuals ‘tastes’– which reflect the self-interested view point of the individuals – into (social) ranking of alternatives. In addition to her tastes, an individual has values about the way by which collective decision should be made. We distinguish two categories of such values. First, there are end-values that restrict the class of social rankings that the individual considers ethically acceptable. Second there are aggregation-values that specify the way by which the social ranking should depend upon the individuals tastes. The consistency test stands on an hypothetical operation of universalization of the individual tastes to everyone. Five illustrations of the potential usefulness of our approach for interpreting social choice theory and welfare economics are proposed. These illustrations deal with utilitarian aggregation in the presence of income inequality aversion, the so-called ‘ethics of responsibility’ and the aggregation of individual ranking of opportunity sets based on their freedom of choice. A discussion of the relevance of the consistency test for addressing the problem of ‘laundering’ individual preferences is also provided. Received: 25 June 1998/Accepted: 16 March 1999     

Fair and group strategy-proof good allocation with money

We completely characterize the class of fair and group strategy-proof mechanisms. We consider two notions of fairness, anonymity in welfare and no-envy. Both fairness axioms, when applied with strategy-proofness, imply decision efficiency, and lead to the same class of group strategy-proof mechanisms (where the group size is restricted to two). We find that the only feasible mechanism satisfying a mild zero transfer axiom, in this class, is the Pivotal mechanism.     

Infants Associate Praise and Admonishment with Fair and Unfair Individuals

Recent evidence suggests that infants possess a rudimentary sensitivity to fairness: Infants expect resources to be distributed fairly and equally, and prefer individuals that distribute resources fairly over those that do so unfairly. The goal of this work was to determine whether infants' evaluations of fair and unfair individuals also includes an understanding that fair individuals are worthy of praise and unfair individuals are worthy of admonishment. After watching individuals distribute goods fairly or unfairly to recipients, 15‐month‐old (Experiments 1 and 2) and 13‐month‐old (Experiment 3) infants took part in a test phase in which they saw only the distributors' faces accompanied by praise or admonishment. Across all experiments, infants differentially shifted their visual attention to images of the fair and unfair distributors as a function of the accompanying praise or admonishment, although the direction in which they did so varied by age. Thus, by the start of the second year of life, infants appear to perceive fair individuals as morally praiseworthy and unfair individuals as morally blameworthy.     

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     

The division problem with voluntary participation

The division problem consists of allocating a given amount of a homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this article we consider the division problem when agents’ participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents’ shares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents’ voluntary participation.     

The wasted vote phenomenon with uncertain voter population

Palfrey (A mathematical proof of Duvergers law, 1989) shows that in large electorates with deterministic voter population, the expected equilibrium vote share of the weakest party tends to zero asymptotically. We extend this result to the uncertain case where the number of valid votes is a random variable satisfying a mild condition. Special cases include the degenerate, Poisson, binomial, and negative binomial distributions. In particular, we demonstrate that no matter how the number of valid votes fluctuates, as the probability of having a large number of valid votes approaches one, the expected equilibrium vote shares of the weak parties are asymptotically negligible.     

Analyzing consumers heterogeneity and self-reported tastes: An approach consistent with the consumer’s decision making process

This paper analyses whether self-reported valuation of goods is an adequate proxy for underlying tastes. In this case, different self-reported appraisals, which we can associate with different utility functions, would imply different demand curves. To estimate these kinds of relationships we have used data on reported tastes on new film releases and cinema attendance. We have used a latent class approach in order to imitate the data generating process underlying the demand functions, where consumer’s preferences are determined before consumers purchase. With this procedure we can reject the hypothesis of a unique demand function for all consumers. As expected, moreover, prices have a different influence depending on individuals’ self-reported tastes and specific market policies for each consumer group could therefore be designed.     

Individual and couple tastes for children: Theoretical,methodological, and empirical issues

A comparison is made between two alternatives for explaining family size decisions: a psychological model based on the individual needs of the spouses and a social psychological model based on the husband-wife relationship. By use of higher order factors within the context of structural equation models, it is shown that the two approaches can be derived as special cases of a single, integrative framework. In this way, a theory is developed and tested which explicitly represents the family-size decision process as both an individual and joint experience of the spouses.     

Fertility, labor force participation, and tastes: An economic psychology perspective

Economic and economic psychology models of wife's labor force participation and family size decisions are examined within the context of a marriage cohort. Among other results, it was found that tastes influence the demand for work and number of children, along with traditional economic determinants such as opportunity costs and income. Tastes have an especially strong impact when modeled as unobservables, in order to correct for measurement error. Further, the often observed empirical association between labor force participation and fertility is found to be spurious and not necessarily causal in nature. That is, labor force participation and fertility negatively covary largely as a consequence of common economic and taste antecedents and not due to reciprocal interactions. Hypotheses were tested using a new structural equation methodology.     

Efficient solutions to bargaining problems with uncertain disagreement points

We consider a cooperative model of bargaining where the location of the disagreement point may be uncertain. Based on the maximin criterion, we formulate an ex ante efficiency condition and characterize the class of bargaining solutions satisfying this axiom. These solutions are generalizations of the monotone path solutions. Adding individual rationality yields a subclass of these solutions. By employing maximin efficiency and an invariance property that implies individual rationality, a new axiomatization of the monotone path solutions is obtained. Furthermore, we examine the consequences of employing efficiency axioms based on alternative decision criteria. Received: 17 March 2000/Accepted: 15 January 2001     

Children with epilepsy who have special needs

SUMMARY. About five percent of children with epilepsy are severely or multiply handicapped. Many of these probably did not go to school before the 1970 Education Act, although epilepsy had been a named category for special education from the earliest provision. This paper describes two studies of the characteristics of children attending the residential special schools for epilepsy in England and Wales before the 1981 Education Act, and discusses the provision of local services for severely handicapped children with epilepsy as a consequence of the Act and the possible continuing role for residential schools for this group.     

Families who adopt children with special needs

This study explores the type of family who adopts children with special needs. Fifty-six families who adopted special needs children were interviewed. Many of the interview questions were based upon a cognitive social learning framework. These questions assessed such areas as parent expectations, competencies, and sense of responsibility and attachment. This framework, along with demographic characteristics and an assessment of parents' discretionary and support resources, resulted in a profile of adoptive parents. Implications are discussed for recruitment of adoptive parents for children with special needs and suggestions are given for future research.     

Met needs and unmet needs, and satisfaction among Social HMO members

This article reports on a survey of 800 members of four Social HMO demonstration sites, who were receiving home-based, community-based, and short-term institutional services under the demonstration's expanded community care benefits. The survey asked whether members needed help in 11 areas, whether they received help in each area from an informal caregiver, whether they wanted more help from the Social HMO, and whether help provided by both was adequate. Satisfaction with the program and with service coordination was also assessed. The adequacy of informal care differed by problem area, as did the help desired from the Social HMO and its responsiveness. Members were less satisfied when they had weaker informal care, were African American, and when they received inadequate help from the plan with ADLs, transportation, medical access, and managing money. Members were more satisfied when they were professionals, home owners, knew their service coordinator's name (or how to contact her), and received help with their problems. The findings point to the importance of clarifying divisions of labor with informal caregivers, as well as possible expansions in responsibilities for service coordinators and benefits beyond traditional boundaries.