On Maxsum Fair Cake Divisions

Steven J. Brams; Michal Feldman; John K. Lai; Jamie Morgenstern; Ariel D. Procaccia

On Maxsum Fair Cake Divisions

Steven J. Brams, Michal Feldman, John K. Lai, Jamie Morgenstern, Ariel D. Procaccia

Research output: Contribution to conference › Paper › peer-review

6 Scopus citations

Abstract

We consider the problem of selecting fair divisions of a heterogeneous divisible good among a set of agents. Recent work (Cohler et al., AAAI 2011) focused on designing algorithms for computing maxsum-social welfare maximizing-allocations under the fairness notion of envy-freeness. Maxsum allocations can also be found under alternative notions such as equitability. In this paper, we examine the properties of these allocations. In particular, we provide conditions for when maxsum envy-free or equitable allocations are Pareto optimal and give examples where fairness with Pareto optimality is not possible. We also prove that maxsum envy-free allocations have weakly greater welfare than maxsum equitable allocations when agents have structured valuations, and we derive an approximate version of this inequality for general valuations.

Original language	English
Pages	1285-1291
Number of pages	7
State	Published - 2012
Externally published	Yes
Event	26th AAAI Conference on Artificial Intelligence, AAAI 2012 - Toronto, Canada Duration: 22 Jul 2012 → 26 Jul 2012

Conference

Conference	26th AAAI Conference on Artificial Intelligence, AAAI 2012
Country/Territory	Canada
City	Toronto
Period	22/07/12 → 26/07/12

Funding

Funders	Funder number
Google Inter-university center for Electronic Markets and Auctions
Microsoft Research Graduate Women's Scholarship
Microsoft Research Graduate Women’s Scholarship
National Science Foundation
Seventh Framework Programme	274919
FP7 People: Marie-Curie Actions
Israel Science Foundation	1219/09
Seventh Framework Programme
Business School, Hebrew University of Jerusalem

Cite this

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title = "On Maxsum Fair Cake Divisions",

abstract = "We consider the problem of selecting fair divisions of a heterogeneous divisible good among a set of agents. Recent work (Cohler et al., AAAI 2011) focused on designing algorithms for computing maxsum-social welfare maximizing-allocations under the fairness notion of envy-freeness. Maxsum allocations can also be found under alternative notions such as equitability. In this paper, we examine the properties of these allocations. In particular, we provide conditions for when maxsum envy-free or equitable allocations are Pareto optimal and give examples where fairness with Pareto optimality is not possible. We also prove that maxsum envy-free allocations have weakly greater welfare than maxsum equitable allocations when agents have structured valuations, and we derive an approximate version of this inequality for general valuations.",

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AU - Brams, Steven J.

AU - Feldman, Michal

AU - Lai, John K.

AU - Morgenstern, Jamie

AU - Procaccia, Ariel D.

PY - 2012

Y1 - 2012

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On Maxsum Fair Cake Divisions

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