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Population Monotonic and Strategy-Proof Mechanisms Respecting Welfare Lower Bounds

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  • Duygu Yengin

    ()
    (School of Economics, University of Adelaide)

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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Bibliographic Info

Paper provided by University of Adelaide, School of Economics in its series School of Economics Working Papers with number 2012-05.

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Length: 28 pages
Date of creation: Aug 2012
Date of revision:
Handle: RePEc:adl:wpaper:2012-05

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Phone: (618) 8303 5540
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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References

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  1. Moulin, H., 1988. "Welfare Bounds In The Fair Division Problem," UFAE and IAE Working Papers 106-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Yengin Duygu, 2012. "Characterizing Welfare-egalitarian Mechanisms with Solidarity When Valuations are Private Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-35, April.
  3. Hervé Moulin, 2010. "Auctioning or assigning an object: some remarkable VCG mechanisms," Social Choice and Welfare, Springer, vol. 34(2), pages 193-216, February.
  4. Bevia, Carmen, 1996. "Population monotonicity in economies with one indivisible good," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 125-137, October.
  5. 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).
  6. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  7. 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.
  8. Duygu Yengin, 2010. "Egalitarian-equivalent Groves Mechanisms in the Allocation of Heterogeneous Objects," School of Economics Working Papers 2010-29, University of Adelaide, School of Economics.
  9. Fleurbaey, Marc, 1995. "Equality and responsibility," European Economic Review, Elsevier, vol. 39(3-4), pages 683-689, April.
  10. Shinji Ohseto, 2006. "Characterizations of strategy-proof and fair mechanisms for allocating indivisible goods," Economic Theory, Springer, vol. 29(1), pages 111-121, September.
  11. Murat Atlamaz & Duygu Yengin, 2008. "Fair Groves mechanisms," Social Choice and Welfare, Springer, vol. 31(4), pages 573-587, December.
  12. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
  13. Hyungjun Kim, 2004. "Population monotonic rules for fair allocation problems," Social Choice and Welfare, Springer, vol. 23(1), pages 59-70, 08.
  14. 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.
  15. 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.
  16. Elisha A. Pazner & David Schmeidler, 1975. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," Discussion Papers 174, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  17. Alkan, Ahmet, 1994. "Monotonicity and Envyfree Assignments," Economic Theory, Springer, vol. 4(4), pages 605-16, May.
  18. Yengin, Duygu, 2013. "Population monotonic and strategy-proof mechanisms respecting welfare lower bounds," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 389-397.
  19. Tadenuma, Koichi & Thomson, William, 1993. "The fair allocation of an indivisible good when monetary compensations are possible," Mathematical Social Sciences, Elsevier, vol. 25(2), pages 117-132, February.
  20. Porter, Ryan & Shoham, Yoav & Tennenholtz, Moshe, 2004. "Fair imposition," Journal of Economic Theory, Elsevier, vol. 118(2), pages 209-228, October.
  21. 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.
  22. 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.
  23. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
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Cited by:
  1. Duygu Yengin, 2012. "Population Monotonic and Strategy-Proof Mechanisms Respecting Welfare Lower Bounds," School of Economics Working Papers 2012-05, University of Adelaide, School of Economics.

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