Filling a Multicolor Urn: An Axiomatic Analysis
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.
|Date of creation:||Jan 2001|
|Date of revision:|
|Contact details of provider:|| Postal: MS-22, 6100 South Main, Houston, TX 77005-1892|
Phone: (713) 527-4875
Fax: (713) 285-5278
Web page: http://www.ruf.rice.edu/~econ/papers/index.html
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
- Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
- Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics.
- 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).
- Herrero, Carmen & Maschler, Michael & Villar, Antonio, 1999. "Individual rights and collective responsibility: the rights-egalitarian solution," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 59-77, January.
- Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125 Elsevier.
- Hervé Moulin, 2002. "The proportional random allocation of indivisible units," Social Choice and Welfare, Springer, vol. 19(2), pages 381-413.
- 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.
- Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
- O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
- 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.
- M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer, vol. 4(3), pages 255-272.
When requesting a correction, please mention this item's handle: RePEc:ecl:riceco:2001-01. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.