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Population monotonic rules for fair allocation problems

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  • Hyungjun Kim

Abstract

We consider the property of population monotonicity in the context of fair allocation problems in private good economies. It is already known that the property is compatible with the equal division lower bound. We show that if the equal division lower bound is replaced with no envy, the compatibility does not hold. We also show that the incompatibility persists even though no envy is weakened to no domination or ε-no domination. Hence, among the fairness criteria mentioned above, only the equal division lower bound is compatible with population monotonicity. Copyright Springer-Verlag 2004

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  • Hyungjun Kim, 2004. "Population monotonic rules for fair allocation problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(1), pages 59-70, August.
    • Handle: RePEc:spr:sochwe:v:23:y:2004:i:1:p:59-70
    DOI: 10.1007/s00355-003-0236-8
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    Cited by:

    1. Duygu Yengin, 2017. "No-envy and egalitarian-equivalence under multi-object-demand for heterogeneous objects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 81-108, January.
    2. Thomson, William, 2024. "On the manipulability of allocation rules through endowment augmentation," Games and Economic Behavior, Elsevier, vol. 146(C), pages 91-104.
    3. William Thomson, 2009. "Borrowing-proofness," RCER Working Papers 545, University of Rochester - Center for Economic Research (RCER).
    4. Duygu Yengin, 2011. "Population Monotonic and Strategy-Proof Mechanisms Respecting Welfare Lower Bounds," School of Economics and Public Policy Working Papers 2011-34, University of Adelaide, School of Economics and Public Policy.
    5. Christopher P. Chambers & Takashi Hayashi, 2020. "Can everyone benefit from economic integration?," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(3), pages 821-833, June.
    6. Chambers, Christopher P. & Hayashi, Takashi, 2020. "Can everyone benefit from innovation?," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 187-191.
    7. Yengin, Duygu, 2013. "Population monotonic and strategy-proof mechanisms respecting welfare lower bounds," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 389-397.
    8. Emre Doğan, 2021. "Population monotonicity in fair division of multiple indivisible goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 361-376, June.

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