Envy-free Allocations Research Articles

The positive consequence of strategic manipulation in indivisible good allocation

It is well known that any decision efficient, budget balanced, and envy-free mechanism for allocating a single object with transfers is vulnerable to manipulation. In this paper we examine whether the possible manipulations can have a serious impact on the outcome. Specifically, we examine which allocations are realized in the direct revelation game of any rule satisfying certain normative properties. For this class of rules we show that decision efficient, budget balanced, and envy-free allocations are the only ones realized through an ɛ-Nash equilibrium for any sufficiently small ɛ > 0.

Double implementation in a market for indivisible goods with a price constraint

I consider the problem of assigning indivisible objects to agents, in which each agent pays a price for his object and all prices sum to a given constant. The objective is to select an assignment–price pair that is envy-free with respect to the agents' true preferences. I propose a simple mechanism whereby agents announce valuations for all objects and an envy-free allocation is selected with respect to these announced preferences. I prove that the proposed mechanism implements both in Nash and strong Nash equilibrium the set of true envy-free allocations.

An Algorithm for Stable and Equitable Coalition Structures with Public Goods

We study the formation of coalitions that provide public goods to members. Individuals are linked on a tree graph and those with similar preferences are connected on the tree. We present a well-defined solution that selects envy-free allocations from the core.

An Algorithm for Stable and Equitable Coalition Structures with Public Goods

We study the formation of coalitions that provide public goods to members. Individuals are linked on a tree graph and those with similar preferences are connected on the tree. We present a well-defined solution that selects envy-free allocations from the core.

The equity-efficiency trade-off reconsidered

Envy-free and Pareto optimal allocations never exist in large economies with production, if there is enough variation with respect to preferences and innate abilities of the agents. If distributional equity is given priority only second best envy-free allocations may be considered. Those allocations are characterised in finite and continuum economies. In continuum economies envy-free allocations are “type-egalitarian”, i.e. agents with the same preferences but different abilities obtain the same consumption-labour bundle. Regarding implementation envy-free allocations can only be implemented by a tax depending on labour and income.

Dividing resources by flexible majority rules

We examine the division of resources among individuals by flexible majority rules where the majority necessary to adopt a proposal depends on the proposal itself. For instance, the size of the majority may increase with the maximal difference between the shares individuals receive. For large discount factors such rules imply an efficient and even distribution of resources. For low discount factors flexible majority rules supplemented by specific agenda-planning rules such as agenda rights for the opposition guarantee envy-free distribution. Uncertainty about discount rates can make it easier to achieve efficient and envy-free allocations.

Money-egalitarian-equivalent and gain-maximin allocations of indivisible items with monetary compensation

Suppose that a certain quantity M of money and a finite number of indivisible items are to be distributed among n people, all of whom have equal claims on the whole. Different allocations are presented using various criteria of fairness in the special case where each player's utility function is additively separable. An allocation is “money-egalitarian-equivalent” (MEE) if each player's monetary valuation of his or her bundle is a fixed constant. We show that there is an essentially unique allocation that is MEE and Pareto-optimal; it is also envy-free. Alternatively, the “gain” of a player may be defined as the difference between how the player evaluates his bundle and an exact nth part of the whole according to his numerical evaluation of the whole. A “gain-maximin” criterion would maximize the minimum gain obtained by any player. We show that Knaster's procedure finds an allocation which is optimal under the gain-maximin criterion. That allocation is not necessarily envy-free, so we also find the envy-free allocation that is optimal under the gain-maximin criterion among all envy-free allocations. It turns out that, even though there exist allocations that are simultaneously envy-free and Pareto-optimal, this optimal allocation may fail to be Pareto-optimal, and it may also violate monotonicity criteria.

Envy-free and Pareto efficient allocations in economies with indivisible goods and money

This paper investigates the existence of envy-free and Pareto efficient allocations in economies with finitely many indivisible goods and one divisible good (money). The existence of envy-free allocations is proved under very weak conditions, but the paper contains an example of an economy in which the set of envy-free allocations and the set of Pareto efficient allocations are disjoint. It contains moreover sufficient conditions for an economy in which the existence of an envy-free and Pareto efficient allocation is assured.

A simple procedure for finding equitable allocations of indivisible goods

The paper investigates how far a particular procedure, called the “descending demand procedure,” can take us in finding equitable allocations of indivisible goods. Both interpersonal and intrapersonal criteria of equitability are considered. It is shown that the procedure generally fares well on an interpersonal criterion of “balancedness”; specifically, the resulting allocations are Pareto-optimal and maximize the well-being of the worst-off individual. As a criterion of intrapersonal equitability, the property of envy-freeness is considered. To accommodate envy-freeness, a modification of the basic procedure is suggested. With two individuals, the modified procedure is shown to select the envy-free allocations that are balanced, i.e. the allocations that maximize the well-being of the worse-off individual among all envy-free allocations.

Dividing Resources by Flexible Majority Rules

We examine the division of resources among individuals by flexible majority rules where the majority necessary to adopt a proposal depends on the proposal itself. For instance, the size of the majority may increase with the maximal difference between the shares individuals receive. For large discount factors such rules imply an efficient and even distribution of resources. For low discount factors flexible majority rules supplemented by specific agenda-setting rules such as agenda rights for the opposition guarantee envy-free distribution. Uncertainty about discount rates can make it easier to achieve efficient and envy-free allocations.

Balancedness of permutation games and envy-free allocations in indivisible good economies

We present a simple proof of the balancedness of permutation games. In the proof we use the existence of envy-free allocations in economies with indivisible objects, quasi-linear utility functions, and an amount of money.

An algorithm for envy-free allocations in an economy with indivisible objects and money

This paper studies envy-free allocations for economies with indivisible objects, quasi-linear utility functions, and an amount of money. We give a polynomially bounded algorithm for finding envy-free allocations. Connectedness of envy-graphs, which are used in the algorithm, characterizes the extreme points of the polytopes of sidepayments corresponding with envy-free allocations.

Welfarism and rationalizability in allocation problems with indivisibilities

This paper characterizes solutions for allocation problems with indivisibilities that can be rationalized by social-welfare orderings on the agents' utility vectors. Unlike most earlier contributions (which mainly focus on the existence of envy-free allocations), the approach chosen in this paper is welfarist in the sense that allocations are compared solely on the basis of the utilities experienced by the individuals involved in the problem. The presence of an indivisible commodity leads to a framework where the domain of the choice correspondence that selects allocations differs from the standard domains that are usually analyzed in the theory of rational choice.

Implementability and Horizontal Equity Imply No-Envy

THE REQUIREMENT OF NO-ENVY is at the heart of recent equity theory. An allocation is free from envy if no agent strictly prefers the bundle of goods which is assigned to another agent to the one she/he gets. An allocation rule satisfies No-Envy if it only selects envy-free allocations. In this paper, we examine the relationship between No-Envy and implementability in a general model. Our main result is that in monotonically closed domains the No-Envy property is satisfied by any allocation rule which is both horizontally equitable and Nash Implementable. The requirement of horizontal equity, called Equal Treatment of Equals, simply states that two agents having the same preferences should be treated equally, i.e., should be assigned the same welfare level. The monotonic closedness condition on the domain of admissible preferences is satisfied in many private and/or public good environments, as discussed below. Quasi-linear domains, however, are examples of nonmonotonically closed domains. Our result confirms the widespread intuition that the No-Envy requirement is justified not only from an equity point of view but also from an implementation standpoint (see Hammond (1979) and Champsaur and Laroque (1981)). Moreover, it throws some light on several previous results where specific allocation rules defined over monotonically closed domains are characterized by Nash Implementability among other axioms. As a consequence of our analysis, No-Envy can be weakened into Equal Treatment of Equals in these characterizations (see, e.g., Thomson (1990) and Nagahisa and Suh (1995)). Similar arguments apply to decentralization problems where informational efficiency is the primary concern. For instance, Calsamiglia and Kirman (1993) characterized the Equal Income Walrasian rule on the basis of informational efficiency, Pareto Optimality, and No-Envy. Again, No-Envy can be replaced by Equal Treatment of Equals in this result.2 On the other hand, our result also explains why Nash Implementable allocation rules violating No-Envy over monotonically closed domains all fail to satisfy Equal Treatment of Equals. Examples include the Lindahl solution, the ratio equilibrium solution (Kaneko (1977)) and the balanced linear cost share solution (Mas-Colell and Silvestre (1989)); see Corchon (1989) and Wilkie (1990). At the end of the paper, we show that if we restrict ourselves to allocation functions (that is, allocation rules selecting one and only one allocation per economy), then a similar result holds for Strategy-Proofness, provided the Satterthwaite-Sonnenschein (1981) property of Non-Bossiness is also imposed. That is, in monotonically closed

Self-Ownership and Equality: Brute Luck, Gifts, Universal Dominance, and LeximinReal Freedom for All. Philippe Van Parijs's

Previous articleNext article No AccessReview EssaySelf-Ownership and Equality: Brute Luck, Gifts, Universal Dominance, and Leximin Real Freedom for All. Philippe Van Parijs'sPeter VallentynePeter Vallentyne Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Ethics Volume 107, Number 2Jan., 1997 Article DOIhttps://doi.org/10.1086/233723 Views: 20Total views on this site Citations: 23Citations are reported from Crossref Copyright 1997 The University of ChicagoPDF download Crossref reports the following articles citing this article:Giacomo Pisani A justification of basic income beyond a theory of justice, Oñati Socio-Legal Series 12, no.44 (Aug 2022): 737–761.https://doi.org/10.35295/osls.iisl/0000-0000-0000-1265M. Niaz Asadullah, Alain Trannoy, Sandy Tubeuf, Gaston Yalonetzky Measuring educational inequality of opportunity: pupil’s effort matters, World Development 138 (Feb 2021): 105262.https://doi.org/10.1016/j.worlddev.2020.105262Roberto Fumagalli Buyer Beware: A Critique of Leading Virtue Ethics Defenses of Markets, Journal of Social Philosophy 51, no.33 (Mar 2020): 457–482.https://doi.org/10.1111/josp.12336Sang Yoon (Tim) Lee, Ananth Seshadri Economic Policy and Equality of Opportunity, The Economic Journal 128, no.612612 (Jan 2018): F114–F151.https://doi.org/10.1111/ecoj.12480Jørgen Pedersen Just inheritance taxation, Philosophy Compass 13, no.44 (Feb 2018): e12491.https://doi.org/10.1111/phc3.12491Arnaud Lefranc, Alain Trannoy Equality of opportunity, moral hazard and the timing of luck, Social Choice and Welfare 49, no.3-43-4 (May 2017): 469–497.https://doi.org/10.1007/s00355-017-1054-8Anna-Karin Andersson, Frode Lindemark, Kjell Arne Johansson Priority rules as solutions to conflicting health care rights, Medicine, Health Care and Philosophy 20, no.11 (Sep 2016): 67–76.https://doi.org/10.1007/s11019-016-9728-zMaximilian Sommer The Normative Argument for an Unconditional Basic Income, (Mar 2016): 7–49.https://doi.org/10.1007/978-3-319-24064-0_2Christopher Freiman, Adam Lerner Self-ownership and disgust: why compulsory body part redistribution gets under our skin, Philosophical Studies 172, no.1212 (Mar 2015): 3167–3190.https://doi.org/10.1007/s11098-015-0463-8Cornelius Cappelen, Jørgen Pedersen Borgerlønn: en rettferdig reform?, Tidsskrift for samfunnsforskning 56, no.33 (Sep 2015): 354–371.https://doi.org/10.18261/ISSN1504-291X-2015-03-06Hugh Lazenby Luck, Risk and the Market, Ethical Theory and Moral Practice 17, no.44 (Sep 2013): 667–680.https://doi.org/10.1007/s10677-013-9454-zSerena Olsaretti RESCUING JUSTICE AND EQUALITY FROM LIBERTARIANISM, Economics and Philosophy 29, no.11 (Apr 2013): 43–63.https://doi.org/10.1017/S0266267113000072Gideon Elford Equality of Opportunity and Other-Affecting Choice: Why Luck Egalitarianism Does Not Require Brute Luck Equality, Ethical Theory and Moral Practice 16, no.11 (Dec 2011): 139–149.https://doi.org/10.1007/s10677-011-9331-6Jean-Sébastien Gharbi, Cléa Sambuc Propriété de soi et justice sociale chez les libertariens, Cahiers d'économie Politique n° 62, no.11 (Sep 2012): 187–222.https://doi.org/10.3917/cep.062.0187Lloyd P. Gerson WHO OWNS WHAT? SOME REFLECTIONS ON THE FOUNDATION OF POLITICAL PHILOSOPHY, Social Philosophy and Policy 29, no.11 (Dec 2011): 81–105.https://doi.org/10.1017/S0265052511000069Arnaud Lefranc, Nicolas Pistolesi, Alain Trannoy Equality of opportunity and luck: Definitions and testable conditions, with an application to income in France, Journal of Public Economics 93, no.11-1211-12 (Dec 2009): 1189–1207.https://doi.org/10.1016/j.jpubeco.2009.07.008Davide Tondani Universal Basic Income and Negative Income Tax: Two different ways of thinking redistribution, The Journal of Socio-Economics 38, no.22 (Mar 2009): 246–255.https://doi.org/10.1016/j.socec.2008.10.006Arnaud Lefranc, Nicolas Pistolesi, Alain Trannoy INEQUALITY OF OPPORTUNITIES VS. INEQUALITY OF OUTCOMES: ARE WESTERN SOCIETIES ALL ALIKE?, Review of Income and Wealth 54, no.44 (Dec 2008): 513–546.https://doi.org/10.1111/j.1475-4991.2008.00289.xKASPER LIPPERT-RASMUSSEN Against Self-Ownership: There Are No Fact-Insensitive Ownership Rights over One's Body, Philosophy & Public Affairs 36, no.11 (Jan 2008): 86–118.https://doi.org/10.1111/j.1088-4963.2008.00125.xJean-Fabien Spitz Le libertarisme de gauche : l'égalité sous condition de la propriété de soi, Raisons politiques 23, no.33 (Jan 2006): 23.https://doi.org/10.3917/rai.023.0023Serena Olsaretti Liberty, Desert and the Market, 48 (Sep 2009).https://doi.org/10.1017/CBO9780511487422Richard Sturn, Rudi Dujmovits Basic Income in Complex Worlds, Analyse & Kritik 22, no.22 (Jan 2000).https://doi.org/10.1515/auk-2000-0203Daniel Shapiro Why Even Egalitarians Should Favor Market Health Insurance, Social Philosophy and Policy 15, no.22 (Jan 2009): 84–132.https://doi.org/10.1017/S0265052500001965

Trade-off between equity and efficiency in a general economy with indivisible goods

In most of the recent literature on fair allocation in economies with indivisible goods and a single infinitely divisible good, it is assumed that each agent can consume at most one indivisible good. In this paper, we show that if this assumption is dropped, there do not necessarily exist envy-free and Pareto efficient allocations. However, envy-free allocations still exist and so do Pareto efficient allocations. Hence, a trade-off between equity and efficiency arises.

Old and new moving-knife schemes

In general, moving-knife schemes seem to be easier to come by than pure existence results (like Neyman’s [N] theorem) but harder to come by than discrete algorithms (like the Dubins-Spanier [DS] last-diminisher method). For envy-free allocations for four or more people, however, the order of difficulty might actually be reversed. Neyman’s existence proof (for anyn) goes back to 1946, the discovery of a discrete algorithm for alln ≥ 4 is quite recent [BT1, BT2, BT3], and a moving-knife solution forn = 4 was found only as this article was being prepared (see [BTZ]). We are left with this unanswered question: Is there a moving-knife scheme that yields an envyfree division for five (or more) players?

A derivation of the money Rawlsian solution

We study the set of envy-free allocations for economies with indivisible objects and quasi-linear utility functions. We characterize the minimal amount of money necessary for its nonemptiness when negative distributions of money are not allowed. We also find that, when this is precisely the available amount of money, there is a unique way to combine objects and money such that these bundles may form an envy-free allocation. Based on this property, we describe a solution to the envy-free selection problem following a pseudo-egalitarian criterion. This solution coincides with the “Money Rawlsian Solution” proposed by Alkan et al. (1991).

Games of Fair Division

We consider the problem of fairly allocating an indivisible good to one of several agents equally entitled to it when monetary compensations to the others are possible. Our primary normative concept is no-envy. First, we show that there is no non-manipulable selection from the no-envy solution. Then we study the direct revelation games associated with subsolutions of the no-envy solution. The set of equilibrium allocations of any one of them coincides with the set of envy-free allocations for the true preferences. Journal of Economic Literature Classification Numbers: C72, D63, D7l, D82.

An Envy-Free Cake Division Protocol

(1995). An Envy-Free Cake Division Protocol. The American Mathematical Monthly: Vol. 102, No. 1, pp. 9-18.