Fairness and externalities

We study equitable allocation of indivisible goods and money among agents with other-regarding preferences. First, we argue that Foley's (1967) equity test, i.e., the requirement that no agent prefer the allocation obtained by swapping her consumption with another agent, is suitable for our environment. Then, we establish the existence of allocations passing this test for a general domain of preferences that accommodates prominent other-regarding preferences. Our results are relevant for equitable allocation among inequity-averse agents and in a domain with linear externalities that we introduce. Finally, we present conditions guaranteeing that these allocations are efficient.

[1]  E. Fehr.  A Theory of Fairness, Competition and Cooperation , 1998 .

[2]  Efe A. Ok,et al.  Negatively interdependent preferences , 2000, Soc. Choice Welf..

[3]  James Andreoni,et al.  Giving according to GARP: an experimental test of the rationality of altruism , 1999 .

[4]  John H. Miller,et al.  NOTES AND COMMENTS GIVING ACCORDING TO GARP: AN EXPERIMENTAL TEST OF THE CONSISTENCY OF PREFERENCES FOR ALTRUISM , 2002 .

[5]  W. Thomson,et al.  Games of Fair Division , 1995 .

[6]  D. Gale,et al.  Fair Allocation of Indivisible Goods and Criteria of Justice , 1991 .

[7]  R. Vohra.  Equity and efficiency in non-convex economies , 1992 .

[8]  Tommy Andersson,et al.  Budget-Balance, Fairness and Minimal Manipulability , 2014 .

[9]  D. Foley.  Resource allocation and the public sector , 1967 .

[10]  Lars-Gunnar Svensson.  Large Indivisibles: An analysis with respect to price equilibrium and fairness , 1983 .

[11]  Eran Shmaya,et al.  Rental harmony with roommates , 2014, J. Econ. Theory.

[12]  Charles R. Skinner.  Now , 1927 .

[13]  Dan W. Brockt,et al.  The Theory of Justice , 2017 .

[14]  Martin Eiliv Sandbu,et al.  Axiomatic foundations for fairness-motivated preferences , 2008, Soc. Choice Welf..

[15]  Kim C. Border,et al.  Fixed point theorems with applications to economics and game theory: Fixed point theorems for correspondences , 1985 .

[16]  James R. Munkres,et al.  Elements of algebraic topology , 1984 .

[17]  W. Zame,et al.  Competitive markets with externalities , 2006 .

[18]  Rodrigo A. Velez,et al.  Sharing an increase of the rent fairly , 2017, Soc. Choice Welf..

[19]  Daniel Friedman,et al.  Revealed Altruism , 2005 .

[20]  James W. Vick,et al.  Homology Theory: An Introduction to Algebraic Topology , 1973 .

[21]  Kotaro Suzumura,et al.  Introduction, Handbook of Social Choice and Welfare, Edited by Kenneth Arrow, Amartya Sen and Kotaro Suzumura, Amsterdam: Elsevier/North-Holland , 2001 .

[22]  Luis C. Corchón,et al.  A Proposal to Unify Some Concepts in the Theory of Fairness , 2001, J. Econ. Theory.

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

[24]  Andrew McLennan,et al.  Using volume to prove Sperner’s Lemma , 2008 .

[25]  Kirsten I. M. Rohde,et al.  A preference foundation for Fehr and Schmidt’s model of inequity aversion , 2010, Soc. Choice Welf..

[26]  W. Thomson.  Fair Allocation Rules , 2011 .

[27]  Edi Karni,et al.  Individual Sense of Justice: A Utility Representation , 2002 .

[28]  Flip Klijn,et al.  An algorithm for envy-free allocations in an economy with indivisible objects and money , 2000, Soc. Choice Welf..

[29]  K. Arrow,et al.  Handbook of Social Choice and Welfare , 2011 .

[30]  William Thomson,et al.  Refinements of the no-envy solution in economies with indivisible goods , 1995 .

[31]  J. Horowitz,et al.  Fairness in Simple Bargaining Experiments , 1994 .

[32]  Eric Maskin.  On the Fair Allocation of Indivisible Goods , 1987 .

[33]  Ernst Fehr,et al.  Theories of Fairness and Reciprocity , 2001 .

[34]  H. Varian.  Two Problems in the Theory of Fairness , 1976 .

[35]  D. Gale.  Equilibrium in a discrete exchange economy with money , 1984 .

[36]  Douglas R. Woodall,et al.  Dividing a cake fairly , 1980 .

[37]  Enriqueta Aragones,et al.  A derivation of the money Rawlsian solution , 1995 .

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

[39]  Serge-Christophe Kolm,et al.  The Economics Of Social Sentiments: The Case Of Envy , 1995 .

[40]  Lester E. Dubins,et al.  How to Cut a Cake Fairly , 1961 .

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

[42]  D. Kahneman,et al.  Experimental Tests of the Endowment Effect and the Coase Theorem , 1990, Journal of Political Economy.

[43]  David Schmeidler,et al.  A Difficulty in the Concept of Fairness , 1974 .

[44]  Hervé Moulin,et al.  Fair division and collective welfare , 2003 .

[45]  M. Dufwenberg,et al.  Other-Regarding Preferences in General Equilibrium ∗ , 2009 .

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

[47]  William S. Neilson.  Axiomatic reference-dependence in behavior toward others and toward risk , 2006 .

[48]  Simina Brânzei,et al.  Externalities in Cake Cutting , 2013, IJCAI.

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