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Population Monotonic and Strategy-Proof Mechanisms Respecting Welfare Lower Bounds

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  • Duygu Yengin

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    (School of Economics, University of Adelaide)

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    Abstract

    The significance of population monotonicity and welfare bounds is well-recognized in the fair division literature. We characterize population monotonic and incentive compatible mechanisms which allocate the goods efficiently and respect a welfare lower bound chosen in the fair allocation problem of allocating collectively owned indivisible goods or bads when monetary transfers are possible and preferences are private information. We consider the welfare bounds that are central to the fair allocation literature, namely, the identical-preferences lower-bound, individual rationality, the stand-alone lower-bound, and k-fairness. We also compare the strength and associated budget deficits of and the logical relations between the aforementioned lower bounds.

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    File URL: http://www.economics.adelaide.edu.au/research/papers/doc/wp2011-34.pdf
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    Bibliographic Info

    Paper provided by University of Adelaide, School of Economics in its series School of Economics Working Papers with number 2011-34.

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    Length: 28 pages
    Date of creation: Dec 2011
    Date of revision:
    Handle: RePEc:adl:wpaper:2011-34

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    Web page: http://www.economics.adelaide.edu.au/
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    Keywords: welfare bounds; the identical-preferences lower-bound; individual rationality; the stand-alone lower-bound; k-fairness; population monotonicity; collective ownership; allocation of indivisible goods and money; NIMBY problems; imposition of tasks; Groves mechanisms; strategy-proofness;

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    1. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    2. Roemer, John E, 1986. "Equality of Resources Implies Equality of Welfare," The Quarterly Journal of Economics, MIT Press, vol. 101(4), pages 751-84, November.
    3. Duygu Yengin, 2011. "Identical Preferences Lower Bound for Allocation of Heterogeneous Tasks and NIMBY Problems," School of Economics Working Papers 2011-27, University of Adelaide, School of Economics.
    4. Pazner, Elisha A & Schmeidler, David, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, MIT Press, vol. 92(4), pages 671-87, November.
    5. Duygu Yengin, 2012. "Egalitarian-equivalent Groves mechanisms in the allocation of heterogenous objects," Social Choice and Welfare, Springer, vol. 38(1), pages 137-160, January.
    6. Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, vol. 45(2), pages 427-38, March.
    7. Hyungjun Kim, 2004. "Population monotonic rules for fair allocation problems," Social Choice and Welfare, Springer, vol. 23(1), pages 59-70, 08.
    8. Murat Atlamaz & Duygu Yengin, 2008. "Fair Groves mechanisms," Social Choice and Welfare, Springer, vol. 31(4), pages 573-587, December.
    9. Duygu Yengin, 2011. "Characterizing Welfare-egalitarian Mechanisms with Solidarity When Valuations are Private Information," School of Economics Working Papers 2011-20, University of Adelaide, School of Economics.
    10. Moulin, Herve, 1991. "Welfare bounds in the fair division problem," Journal of Economic Theory, Elsevier, vol. 54(2), pages 321-337, August.
    11. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
    12. Thomson, W., 1991. "Population-Monotonic Solutions to the Problem of Fair Division when Preferences are Single-Peaked," RCER Working Papers 302, University of Rochester - Center for Economic Research (RCER).
    13. Fleurbaey, Marc, 1995. "Equality and responsibility," European Economic Review, Elsevier, vol. 39(3-4), pages 683-689, April.
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    15. Shinji Ohseto, 2006. "Characterizations of strategy-proof and fair mechanisms for allocating indivisible goods," Economic Theory, Springer, vol. 29(1), pages 111-121, September.
    16. Duygu Yengin, 2011. "Axiomatizing Political Philosophy of Distributive Justice: Equivalence of No-envy and Egalitarian-equivalence with Welfare-egalitarianism," School of Economics Working Papers 2011-19, University of Adelaide, School of Economics.
    17. Bevia, Carmen, 1996. "Population monotonicity in economies with one indivisible good," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 125-137, October.
    18. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    19. Holmstrom, Bengt, 1979. "Groves' Scheme on Restricted Domains," Econometrica, Econometric Society, vol. 47(5), pages 1137-44, September.
    20. Szilvia Pápai, 2003. "Groves sealed bid auctions of heterogeneous objects with fair prices," Social Choice and Welfare, Springer, vol. 20(3), pages 371-385, 06.
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