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Filling a multicolor urn: an axiomatic analysis

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  • Moulin, Herve
  • Stong, Richard

Abstract

We study the probabilistic distribution of identical successive units. We represent the allocation process as the filling of an urn with balls of different colors (one color per agent). Applications include the scheduling of homogeneous tasks among workers and allocating new workers between divisions. The fixed chances methods allocate each unit independently of the current distribution of shares. The Polya-Eggenberger methods place in an urn a fixed number of balls and draw from the urn with replacement of two balls of the color drawn. These two families of urn-filling methods emerge uniquely from our axiomatic discussion involving: a version of the familiar Consistency property; Share Monotonicity (my probability of receiving the next ball is non-decreasing in my current share); Independence of Transfers (transferring balls across agents is not profitable), and Order Independence (a sequence of successive allocations is as likely as any permuted sequence). We also explore the impact of Share Monotinicity (my probability of receiving the next ball is non-increasing in my current share), leading to an equalization of individual shares along a fixed standard of comparison.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 45 (2003)
Issue (Month): 1 (October)
Pages: 242-269

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Handle: RePEc:eee:gamebe:v:45:y:2003:i:1:p:242-269

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Web page: http://www.elsevier.com/locate/inca/622836

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  1. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer, vol. 4(3), pages 255-272.
  2. Hervé Moulin, 2002. "The proportional random allocation of indivisible units," Social Choice and Welfare, Springer, vol. 19(2), pages 381-413.
  3. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
  4. Antonio Villar Notario & Carmen Herrero Blanco & Michael Maschler, 1996. "Individual rights and collective responsibility: The rights-egalitarian solution," Working Papers. Serie AD 1996-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
  6. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics.
  7. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  8. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  9. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
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Cited by:
  1. Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.
  2. Chambers, Christopher P., 2004. "Consistency in the probabilistic assignment model," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 953-962, December.

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