Strategy-proof allocation of indivisible goods

Strategy-proof allocation of a finite number of indivisible goods among a finite number of individuals is considered. The main result is that in a pure distributional case, a mechanism is strategy-proof, nonbossy and neutral if and only if it is serially dictatorial. If the indivisible goods are initially owned by the individuals, a mechanism is strategy-proof, individually rational and Pareto consistent if and only if it is the core mechanism. Received: 15 September 1997/Accepted: 12 May 1998     

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.     

Preverbal Infants' Ability to Encode the Outcome of Distributive Actions

This research examined whether 10‐month‐old infants expect agents to perform equal distribution of resources. In Experiment 1, infants saw a distributor performing either an equal distribution where one strawberry was given to each of two recipients, or an unequal distribution that favored one of the recipients. Infants looked longer at the unequal test event, suggesting that they expected the strawberries to be distributed equally. In Experiment 2, the potential recipients were replaced with inanimate objects to rule out a lower‐level alternative explanation of the results in Experiment 1 based on symmetric movement of the distributor. Infants' looking times did not reveal a preference for one of the two outcomes of the test events (i.e., symmetric or asymmetric movement). Experiment 3 controlled for the role of the distributive action, that is, here the distributors only removed barriers revealing strawberries that the recipients already had. No preference was observed when an equal or unequal initial allocation of resources was revealed. Experiment 4 assessed whether infants relied on affiliative information provided by the distributor's movements. The distributor made the same movements as in Experiment 1, but without distributing any strawberries, and no difference in looking times was observed. These findings support the view that preverbal infants expect agents to behave according to a simple principle: Resources are to be distributed equally among equivalent recipients. We discuss the possible links between such reactions and the emergence of an early sense of fairness.     

The division of domestic work among dual-career and other dual-earner couples in Finland

This study compares the division of domestic work among dual-career and other dual-earner couples. We examine whether gender attitudes, relative resources and working time explain the differences between dual-career and other dual-earner couples. We define dual-career couples as those in which both spouses are professionals and/or managers. The division of housework is important for these couples because of the intense pressures of work. We hypothesise that domestic work is more equally shared among dual-career couples than among other dual-earner couples. The quantitative analyses are based on the Finnish data from the 2010 European Social Survey (N?=?493). The qualitative data consist of 20 Finnish career spouses interviewed in 2005. The quantitative analysis indicates that domestic work is shared the most equally among couples where the woman or both spouses have a career status. Attitudes, resources or working time do not explain this difference entirely. The results support the class culture hypothesis: The division of housework is most equal in homogeneous dual-career couples and least equal in homogeneous no-career couples.     

Queue allocation of indivisible goods

A model with a finite number of indivisible goods (houses) and the same number of individuals is considered. The allocation of houses among the individuals according to a queue order is analysed. First an allocation mechanism is constructed where it is a dominant strategy for the individuals to truthfully report their preferences. Second it is demonstrated that in order to obtain the desired allocation, the individuals must not in general report their complete ranking of the houses, but only their maximal elements in recursively defined choice sets.Financial support from Jan Wallander's Foundation for Research in the Social Sciences is gratefully acknowledged.A first version of this paper was presented at ESEM in Cambridge 1991.     

The impossibility of a Paretian egalitarian

In a one-good world, there is a nice correspondence between the Pigou-Dalton principle of transfer and social welfare dominance. In this paper we study the case of multiple goods (without using prices as a means to come back to one dimension), and show that many results of the one-dimensional setting carry over to the multidimensional case when individuals are assumed to have identical preferences. But the nice correspondence breaks down as soon as individual preferences display minimal differences, and multidimensional versions of the transfer principle clash with the Pareto principle. This analysis reveals an interesting connection with the theory of fair allocation, since multidimensional transfer principles are closely related to the no-domination criterion, a weak version of the no-envy criterion.For helpful comments, we thank J. L. Castillo, M. Le Breton, Y. Sprumont, K. Suzumura and participants at a workshop in Osnabrück, a LivinTax conference in Bordeaux and a seminar in Hitotsubashi University, as well as two referees. Financial support from TMR project Living Standards, Inequality and Taxation Contract no ERBFMXCT 980248 of the European Commission is gratefully acknowledged. We thank Michel Le Breton for giving us the permission to state a result contained in his unpublished Ph D thesis.     

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.     

The replacement principle in economies with indivisible goods

 We consider the problem of allocating a list of indivisible goods and some amount of an infinitely divisible good among agents with equal rights on these resources, and investigate the implications of the following requirement on allocation rules: when the preferences of some of the agents change, all agents whose preferences are fixed should (weakly) gain, or they should all (weakly) lose. This condition is an application of a general principle of solidarity discussed in Thomson (1990b) under the name “replacement principle”. We look for selections from the no-envy solution satisfying this property. We show that in the general case, when the number of objects is arbitrary, there is no such selection. However, in the one-object case (a single prize), up to Pareto-indifference, there is only one selection from the no-envy solution satisfying the property. Such a solution always selects an envy-free allocation at which the winner of the prize is indifferent between his bundle and the losers’ common bundle. Received: 15 May 1995 / Accepted: 5 June 1996     

Allocational and distributional aspects of future immigration to Western Europe

"This article shows that an analysis of the impacts of immigration [in Western Europe] has to be divided into allocational and distributional aspects. From an allocational point of view, like free trade in goods, services and capital, migration is welfare-improving as long as marginal productivities of labor are not equalized worldwide. From a distributional point of view, however, the immigration society has to bear the effects of sharing its common public goods and its social values with the new immigrants. Free immigration will only be allowed if the allocational welfare gains exceed the distributional welfare losses. According to this rule of thumb, a guideline for an efficient migration policy is sketched."     

Distributive justice: an ordering of priorities. A comparative analysis of European opinions

As far as distributive justice is concerned, an important issue is to know whether the different principles by which a given distribution of goods is judged fair or unfair are exclusive or complementary. The European Values Survey carried out in 1999 shows clearly the priorities of Europeans in this matter. The first concerns the guarantee that ‘basic needs are met for all’, then comes ‘recognizing people on their merits’ and finally ‘eliminating big inequalities in income’. The consensus on this hierarchy is not altered by national, demographical, social, economic or political divisions. These different divisions do indeed influence opinions on each criterion, but, with very few exceptions, they are not sufficient to upset this order of priorities. Thus, the usual applied principles of distributive justice do not define competing spheres. Their nested (or ‘lexical’) order is compatible with the purely procedural condition of ‘equal liberty’.     

Shipping the Good Apples Out: A New Perspective

An alternative explanation is provided for the Alchian and Allen substitution theorem, which posits that a per unit tax or shipping fee applied to similar goods will increase the relative consumption of the higher-quality good. The usual explanation is that consumers substitute out of "bad apples" and into "good apples." This article generalizes the Alchian and Allen result in an n -good world, providing an alternative explanation that is more cogent in situations where the two goods (for example $500 and $5 wines) are not close substitutes.     

Thresholds, productivity, and context: an experimental study on determinants of distributive behaviour

In our questionnaire experiment we confronted students of economics, law and medicine with distributive situations in different contexts characterised by two features inspired by medical decision problems: First, individual threshold values indicate minimal amounts needed by potential recipients of the given resource to obtain positive benefits. Second, recipients differ with respect to their ability to benefit from the given quantity, which indicates the productivity of the resource. Allocations offered in the questionnaire are theoretically grounded. However, respondents were also able to make their own proposals. Well-known allocation rules, but also new procedures, were witnessed. Two multistage principles were most prominent: After distributing all minimal amounts, in a second step one aims for resource-equality while the other principle in the second step demands the maximisation of the sum of payoffs. Besides threshold values and productivity, the acceptance of different principles also depended on the field of study, the degree of scarcity of the resources and the sequential order of situations.     

A comparison of pricing rules for auctions and fair division games

Consider an auction or fair division game where every bidder knows his true value of the single object but is only incompletely informed about the true values of his competitors. By imposing the axiom of envy freeness with respect to stated preferences the set of pricing rules is restricted to the prices between the highest and second highest bid. Whereas for auctions one also can satisfy incentive compatibility, the same is not true for fair division games. We analyse and compare the different pricing rules, partly incentive compatible and partly not, by deriving the optimal bidding strategies. By comparing the payoff expectations induced by the various pricing rules we can prove directly a special equivalence statement saying that expected payoffs do not depend on the pricing rule. It is interesting that in fair division games equivalence of pricing rules is only valid if information is sufficiently incomplete.The authors gratefully acknowledge the helpful comments of an anonymous referee     

Perceived Fairness and Satisfaction with the Division of Housework Among Dual-Earner Couples in Italy

A well-documented paradox in family literature is that most married women and men consider the division of household labor to be fair, although its distribution is quite uneven. In this article I report results from a survey on 404 dual-earner couples with young children living in Torino, Italy. A small proportion of wives and husbands (13.6% and 5.7%, respectively) reported both unfairness and dissatisfaction with the division of housework. The absolute majority (55%) of both wives and husbands perceived fairness and satisfaction, even if most of the chores (about two-thirds) fell on wives’ shoulders. To explain these judgments, elements of Thompson's distributive justice theoretical framework were operationalized and tested. A critical reassessment of these elements is provided, based on empirical findings.     

Resource-monotonic solutions to the problem of fair division when preferences are single-peaked

We consider the problem of fairly allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. We search for solutions satisfying resource-monotonicity, the requirement that all agents be affected in the same direction when the amount to divide changes. Although there are resource-monotonic selections from the Pareto solution, there are none satisfying the distributional requirements of no-envy or individual rationality from equal division. We then consider the weakening of resource-monotonicity obtained by allowing only changes in the amount to divide that do not reverse the direction of the inequality between the amount to divide and the sum of the preferred amounts. We show that there is essentially a unique selection from the solution that associates with each economy its set of envy-free and efficient allocations satisfying this property of one-sided resource-monotonicity: it is the uniform rule, a solution that has played a central role in previous analyses of the problem.     

The Role of the Housing Allowance for the Elderly in Norway: Views of Recipients

This article concerns the housing allowance, an economic benefit provided to low-income households and the elderly in Norway. Ensuring a high quality of housing for the elderly has been a priority in the development of the Norwegian welfare state. This article is based on results from a qualitative study among elderly recipients of a housing allowance. The study shows that while these recipients viewed the financial support the allowance offered as crucial, they still felt impoverished. The study raises some questions about whether the housing allowance scheme encourages high-quality housing.     

Faire Formeln

The literature on fair division has experienced a renaissance recently. Novel mathematical procedures promising an envy-free, socially efficient solution to conflicts over nearly indivisible goods play a particularly prominent role. This article presents a comparative experimental evaluation of three procedures. We examine to what extent features of the subjects of the procedures influence the choice in favor of one of the three negotiation protocols and the results of the division. Our analysis of the behavior of 119 subjects shows that psychological factors only affect the procedural choice. Dominance-seeking individuals tend to opt for those procedures that promise a fairer outcome than the relatively crude divide-and-choose-mechanism. In contrast, the outcome of the bilateral negotiations is determined by the attributes of the procedures. The strong influence of psychological factors at the initial stage of the bargaining process nevertheless casts strong doubts on the practicability of the procedures, recommended by the normative strand of game-theoretic negotiation analysis. The further development of ”fair formulas” for the resolution of redistributive conflicts should not neglect that the warring parties have to agree with the philosophy of the proposed bargaining protocol.     

Gender, household labor, and psychological distress: the impact of the amount and division of housework.

Using a national longitudinal survey of a representative sample of 1,256 adults, I assess the impact of the amount of household labor performed and its division within the household on men's and women's depression levels, adjusting for prior mental health status. I test two alternative explanations of the contributions of household labor and the division of household labor to gender differences in depression: differential exposure and differential vulnerability. The results indicate that men's lower contributions to household labor explain part of the gender difference in depression. Inequity in the division of household labor has a greater impact on distress than does the amount of household labor. Employment status moderates the effect of the division of labor on depression. Among those who describe themselves as keeping house, depression was lowest for those who performed 79.8 percent of housework. In contrast, for those employed full-time the minimum level of depression occurs at 45.8 percent of the household labor. Men report performing 42.3 percent of the housework in their homes compared to 68.1 percent reported by women. Thus, on average women are performing household labor beyond the point of maximum psychological benefit, whereas men are not. Social support mediates the effects of the division of household labor. The only gender difference in effects occurred among those who are married, for whom social support was associated with lower levels of depression for women than men.     

Size and distributional uncertainty, public information and the information paradox

In this paper we examine the strategic implications of collective acquisition of information in a committee or in a legislature. We show that the prospect of acquiring information can harm a majority even if information is only available by the support of a majority. Moreover, the model provides two results about incentives to acquire information. First, for policies with high distributional uncertainties, we expect that less information is acquired collectively by a committee than for other policies. Second, for policies that show only size uncertainty, our model predicts intense efforts to acquire information collectively. Received: 20 January 1997/Accepted: 15 February 1999     

The priority of justice: a framework approach to ethics in program evaluation

The situations of evaluation are inevitably complex and various, often involving conflicts between ethical principles as well as among aims or stakeholders. To meet this challenge, evaluators and stakeholders need an interpretive framework to clarify the issues at hand and open the way to workable solutions. This paper provides a three-part framework of justice to guide practitioners in this interpretive task.First, evaluation is instituted to serve the public with fidelity to the values, standards, and ideals that characterize it as a profession and as an office deserving the public trust, here called public justice. Second, these requirements evoke and entail the more general demands of fair process, mutual respect, and right action known as procedural justice. Third, the operations of office and just process must serve the public good, meeting the demands of distributive justice that govern the allocation of goods and benefits.This framework takes as a starting point the priority of justice as articulated by John Rawls: “Justice is the first virtue of social institutions, as truth is to thought. A theory however elegant and economical must be rejected or revised if it is untrue; likewise laws and institutions no matter how efficient and well-arranged must be reformed or abolished if they are unjust” (1971, p. 3).