Democratic fair allocation of indivisible goods

Abstract We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unanimous fairness, in which all agents in each group must agree that their group's share is fair. Under this strict requirement, fair allocations exist only for small groups. We introduce the concept of democratic fairness, which aims to satisfy a certain fraction of the agents in each group. This concept is better suited to large groups such as cities or countries. We present protocols for democratic fair allocation among two or more arbitrarily large groups of agents with monotonic, additive, or binary valuations. For two groups with arbitrary monotonic valuations, we give an efficient protocol that guarantees envy-freeness up to one good for at least 1/2 of the agents in each group, and prove that the 1/2 fraction is optimal. We also present other protocols that make weaker fairness guarantees to more agents in each group, or to more groups. Our protocols combine techniques from different fields, including combinatorial game theory, cake cutting, and voting.

[1]  Warut Suksompong,et al.  Democratic Fair Allocation of Indivisible Goods , 2017, IJCAI.

[2]  Yair Zick,et al.  Diversity Constraints in Public Housing Allocation , 2017, AAMAS.

[3]  Pasin Manurangsi,et al.  Computing an Approximately Optimal Agreeable Set of Items , 2016, IJCAI.

[4]  Elchanan Mossel,et al.  On approximately fair allocations of indivisible goods , 2004, EC '04.

[5]  Erel Segal-Halevi,et al.  Fair and Efficient Division among Families , 2018 .

[6]  Amey Bhangale,et al.  Simultaneous Approximation of Constraint Satisfaction Problems , 2014, ICALP.

[7]  H. Varian.  Equity, Envy and Efficiency , 1974 .

[8]  Moshe Babaioff,et al.  Fair Allocation through Competitive Equilibrium from Generic Incomes , 2019, FAT.

[9]  Farhad Hüsseinov,et al.  A theory of a heterogeneous divisible commodity exchange economy , 2011 .

[10]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[11]  Josue Ortega,et al.  Social Integration in Two-Sided Matching Markets , 2018, Journal of Mathematical Economics.

[12]  Warut Suksompong,et al.  Approximate maximin shares for groups of agents , 2017, Math. Soc. Sci..

[13]  Edith Elkind,et al.  Fair Division of a Graph , 2017, IJCAI.

[14]  Pasin Manurangsi,et al.  Asymptotic existence of fair divisions for groups , 2017, Math. Soc. Sci..

[15]  Erel Segal-Halevi,et al.  Redividing the cake , 2016, Autonomous Agents and Multi-Agent Systems.

[16]  Parag A. Pathak,et al.  Matching with Couples: Stability and Incentives in Large Markets , 2010 .

[17]  Erel Segal-Halevi,et al.  Proportional Cake-Cutting among Families , 2015, 1510.03903.

[18]  R. B. Bapat,et al.  A constructive proof of a permutation-based generalization of Sperner's lemma , 1989, Math. Program..

[19]  Bettina Klaus,et al.  Stable matchings and preferences of couples , 2005, J. Econ. Theory.

[20]  Steven J. Brams,et al.  Multiwinner approval voting: an apportionment approach , 2017 .

[21]  Michael Krivelevich,et al.  Positional Games , 2014, 1404.2731.

[22]  Kathryn L. Nyman,et al.  Discrete Envy-free Division of Necklaces and Maps , 2015, 1510.02132.

[23]  Yann Chevaleyre,et al.  Fair Allocation of Indivisible Goods , 2016, Handbook of Computational Social Choice.

[24]  Warut Suksompong,et al.  Almost Envy-Freeness in Group Resource Allocation , 2019, IJCAI.

[25]  Walter Stromquist,et al.  Envy-Free Cake Divisions Cannot be Found by Finite Protocols , 2008, Electron. J. Comb..

[26]  Vittorio Bilò,et al.  Almost Envy-Free Allocations with Connected Bundles , 2018, ITCS.

[27]  Makoto Yokoo,et al.  Generalizing Envy-Freeness toward Group of Agents , 2011, IJCAI.

[28]  Vincent Conitzer,et al.  Group Fairness for Indivisible Goods Allocation , 2019 .

[29]  Steven J. Brams,et al.  A Procedure for Divorce Settlements , 1996 .

[30]  William Thomson,et al.  Introduction to the Theory of Fair Allocation , 2016, Handbook of Computational Social Choice.

[31]  Ariel D. Procaccia,et al.  The Unreasonable Fairness of Maximum Nash Welfare , 2016, EC.

[32]  Evangelos Markakis,et al.  Comparing Approximate Relaxations of Envy-Freeness , 2018, IJCAI.

[33]  Vincent Conitzer,et al.  Fair Public Decision Making , 2016, EC.

[34]  F. Su.  Rental Harmony: Sperner's Lemma in Fair Division , 1999 .

[35]  Warut Suksompong,et al.  Fairly Allocating Contiguous Blocks of Indivisible Items , 2017, SAGT.

[36]  Paul Erdös,et al.  On a Combinatorial Game , 1973, J. Comb. Theory, Ser. A.

[37]  Edith Elkind,et al.  Fairness Towards Groups of Agents in the Allocation of Indivisible Items , 2019, IJCAI.

[38]  H. Moulin.  Uniform externalities: Two axioms for fair allocation , 1990 .

[39]  Mohammad Ghodsi,et al.  Rent Division Among Groups , 2018, COCOA.

[40]  W. Thomson,et al.  On the fair division of a heterogeneous commodity , 1992 .

[41]  W. Stromquist.  How to Cut a Cake Fairly , 1980 .

[42]  Ariel D. Procaccia,et al.  Leximin Allocations in the Real World , 2015, EC.

[43]  Ioannis Caragiannis,et al.  Fair allocation of combinations of indivisible goods and chores , 2018, ArXiv.

[44]  Moshe Babaioff,et al.  Competitive Equilibria with Indivisible Goods and Generic Budgets , 2017, Math. Oper. Res..

[45]  Ulrich Endriss,et al.  Lecture Notes on Fair Division , 2018, ArXiv.

[46]  Erel Segal-Halevi,et al.  Competitive Equilibrium For almost All Incomes , 2017, AAMAS.

[47]  H. Moulin.  Fair Division in the Internet Age , 2019, Annual Review of Economics.

[48]  Ariel D. Procaccia,et al.  Spliddit: unleashing fair division algorithms , 2015, SECO.

[49]  Bettina Klaus,et al.  Paths to stability for matching markets with couples , 2007, Games Econ. Behav..

[50]  Eric Budish.  The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes , 2011, Journal of Political Economy.

[51]  Richard Stong,et al.  Collective choice under dichotomous preferences , 2005, J. Econ. Theory.