TY - GEN
T1 - On maxsum fair cake divisions
AU - Brams, Steven J.
AU - Feldman, Michal
AU - Lai, John K.
AU - Morgenstern, Jamie
AU - Procaccia, Ariel D.
PY - 2012
Y1 - 2012
N2 - 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 envyfreeness. 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.
AB - 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 envyfreeness. 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.
UR - http://www.scopus.com/inward/record.url?scp=84868279692&partnerID=8YFLogxK
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AN - SCOPUS:84868279692
SN - 9781577355687
T3 - Proceedings of the National Conference on Artificial Intelligence
SP - 1285
EP - 1291
BT - AAAI-12 / IAAI-12 - Proceedings of the 26th AAAI Conference on Artificial Intelligence and the 24th Innovative Applications of Artificial Intelligence Conference
T2 - 26th AAAI Conference on Artificial Intelligence and the 24th Innovative Applications of Artificial Intelligence Conference, AAAI-12 / IAAI-12
Y2 - 22 July 2012 through 26 July 2012
ER -