Fair division of indivisible items

Steven J. Brams; Paul H. Edelman; Peter C. Fishburn

doi:10.1023/B:THEO.0000024421.85722.0a

Fair division of indivisible items

Steven J. Brams, Paul H. Edelman, Peter C. Fishburn

Research output: Contribution to journal › Article › peer-review

Abstract

This paper analyzes criteria of fair division of a set of indivisible items among people whose revealed preferences are limited to rankings of the items and for whom no side payments are allowed. The criteria include refinements of Pareto optimality and envy-freeness as well as dominance-freeness, evenness of shares, and two criteria based on equally-spaced surrogate utilities, referred to as maxsum and equimax. Maxsum maximizes a measure of aggregate utility or welfare, whereas equimax lexicographically maximizes persons' utilities from smallest to largest. The paper analyzes conflicts among the criteria along with possibilities and pitfalls of achieving fair division in a variety of circumstances.

Original language	English (US)
Pages (from-to)	147-180
Number of pages	34
Journal	Theory and Decision
Volume	55
Issue number	2
DOIs	https://doi.org/10.1023/B:THEO.0000024421.85722.0a
State	Published - Sep 2003

Keywords

Allocation of indivisible items
Envy-freeness
Fair division
Lexicographic maximin
Pareto optimality

ASJC Scopus subject areas

General Decision Sciences
Developmental and Educational Psychology
Arts and Humanities (miscellaneous)
Applied Psychology
General Social Sciences
Economics, Econometrics and Finance(all)
Computer Science Applications

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10.1023/B:THEO.0000024421.85722.0a

Cite this

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title = "Fair division of indivisible items",

abstract = "This paper analyzes criteria of fair division of a set of indivisible items among people whose revealed preferences are limited to rankings of the items and for whom no side payments are allowed. The criteria include refinements of Pareto optimality and envy-freeness as well as dominance-freeness, evenness of shares, and two criteria based on equally-spaced surrogate utilities, referred to as maxsum and equimax. Maxsum maximizes a measure of aggregate utility or welfare, whereas equimax lexicographically maximizes persons' utilities from smallest to largest. The paper analyzes conflicts among the criteria along with possibilities and pitfalls of achieving fair division in a variety of circumstances.",

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author = "Brams, {Steven J.} and Edelman, {Paul H.} and Fishburn, {Peter C.}",

note = "Funding Information: Steven J. Brams acknowledges the support of the C. V. Starr Center for Applied Economics at New York University. Research by Paul H. Edelman was done while he was in the School of Mathematics, University of Minnesota.",

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AU - Edelman, Paul H.

AU - Fishburn, Peter C.

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N2 - This paper analyzes criteria of fair division of a set of indivisible items among people whose revealed preferences are limited to rankings of the items and for whom no side payments are allowed. The criteria include refinements of Pareto optimality and envy-freeness as well as dominance-freeness, evenness of shares, and two criteria based on equally-spaced surrogate utilities, referred to as maxsum and equimax. Maxsum maximizes a measure of aggregate utility or welfare, whereas equimax lexicographically maximizes persons' utilities from smallest to largest. The paper analyzes conflicts among the criteria along with possibilities and pitfalls of achieving fair division in a variety of circumstances.

AB - This paper analyzes criteria of fair division of a set of indivisible items among people whose revealed preferences are limited to rankings of the items and for whom no side payments are allowed. The criteria include refinements of Pareto optimality and envy-freeness as well as dominance-freeness, evenness of shares, and two criteria based on equally-spaced surrogate utilities, referred to as maxsum and equimax. Maxsum maximizes a measure of aggregate utility or welfare, whereas equimax lexicographically maximizes persons' utilities from smallest to largest. The paper analyzes conflicts among the criteria along with possibilities and pitfalls of achieving fair division in a variety of circumstances.

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KW - Lexicographic maximin

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Fair division of indivisible items

Abstract

Keywords

ASJC Scopus subject areas

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