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Balanced House Allocation

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  • Xinghua Long
  • Rodrigo A. Velez

Abstract

We introduce balancedness a fairness axiom in house allocation problems. It requires a mechanism to assign the top choice, the second top choice, and so on, on the same number of profiles for each agent. This axiom guarantees equal treatment of all agents at the stage in which the mechanism is announced when all preference profiles are equally likely. We show that, with an interesting exception for the three-agent case, Top Trading Cycles from individual endowments is the only mechanism that is balanced, efficient, and group strategy-proof.

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  • Xinghua Long & Rodrigo A. Velez, 2021. "Balanced House Allocation," Papers 2109.01992, arXiv.org.
    • Handle: RePEc:arx:papers:2109.01992
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    References listed on IDEAS

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    1. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
    2. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
    3. Bird, Charles G., 1984. "Group incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 14(4), pages 309-313.
    4. Pycia, Marek & Unver, Utku, 2017. "Incentive compatible allocation and exchange of discrete resources," Theoretical Economics, Econometric Society, vol. 12(1), January.
    5. , A. & ,, 2011. "Lotteries in student assignment: An equivalence result," Theoretical Economics, Econometric Society, vol. 6(1), January.
    6. Lars-Gunnar Svensson, 1999. "Strategy-proof allocation of indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 557-567.
    7. Freeman, Rupert & Pritchard, Geoffrey & Wilson, Mark, 2021. "Order Symmetry: A New Fairness Criterion for Assignment Mechanisms," SocArXiv xt37c, Center for Open Science.
    8. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    9. Carroll, Gabriel, 2014. "A general equivalence theorem for allocation of indivisible objects," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 163-177.
    10. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
    11. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
    12. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
    13. Sophie Bade, 2020. "Random Serial Dictatorship: The One and Only," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 353-368, February.
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