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Seoul Journal of Economics - Vol. 14 , No. 3

[ Article ]
Seoul Journal of Economics - Vol. 14, No. 3, pp. 269-297
Abbreviation: SJE
ISSN: 1225-0279 (Print)
Print publication date 31 Aug 2001
Received 09 Jun 2001 Revised 17 Jan 2002

Constrained Egalitarianism: A New Solution for Claims Problems
Youngsub Chun ; James Schummer ; William Thomson
Professor, School of Economics, Seoul National University, Seoul 151-742, Korea, Tel: +82-2-880-6382 (ychun@plaza.snu.ac.kr)
Professor, MEDS, Kellogg School of Management, Northwestern University, Evanston, IL 60208-2009, USA, Tel: +1-847-491-5151 (schummer@nwu.edu)
Professor, Department of Economics, University of Rochester, NY 14627, USA, Tel: +1-716-275-2236 (WTH2@troi.cc.rochester.edu)

Funding Information ▼

JEL Classification: D63, D7O


Abstract

We propose a new rule to solve claims problems (O'Neill 1982) and show that this rule is best in achieving certain objectives of equality. We present three theorems describing it as the most “egalitarian” among all rules satisfying two minor requirements, “estate-monotonicity” and “the midpoint property.” We refer to it as the “constrained egalitarian” rule. We show that it is consistent and give a parametric representation of it. We also define several other rules and relate all of them to the rules that have been most commonly discussed in the literature.


Keywords: Claims problems, Constrained egalitarian rule, Talmud rule, Consistency

Acknowledgments

We thank Robert Aumann, Bettina Klaus, and Sang-Young Sonn for their comments. Youngsub Chun gratefully acknowledges financial support from the LG Yonam Foundation and William Thomson from NSF under grant SBR-9731431. This is a much revised version of a note by the first and last authors entitled “A consistent solution for claims problems,” September 1990.


References
1. Aadland, D., and Kolpin, V. “Shared Irrigation Costs: An Empirical and Axiomatic Analysis.” Mathematical Social Sciences 35 (1998): 203-18.
2. Aumann, R., and Maschler, M. “Game Theoretic Analysis of a Bankruptcy Problem from the Talmud.” Journal of Economic Theory 36 (1985): 195-213.
3. Benassy, J-P. The Economics of Market Disequilibrium. Academic Press, 1982.
4. Benoît, J-P. “The Nucleolus is Contested-Garment-Consistent: A Direct Proof.” Journal of Economic Theory 77 (1997): 192-6.
5. Chun, Y. “The Proportional Solution for Rights Problems.” Mathematical Social Sciences 15 (1988): 231-46.
6. Chun, Y. “A Noncooperative Justification for Egalitarian Surplus Sharing.” Mathematical Social Sciences 17 (1989): 245-61.
7. Chun, Y. “Equivalence of Axioms for Bankruptcy Problems.” International Journal of Game Theory 28 (1999): 511-20.
8. Chun, Y., and Thomson, W. “Bargaining Problems with Claims.” Mathematical Social Sciences 24 (1992): 19-33.
9. Curiel, I., Maschler, M., and Tijs, S. “Bankruptcy Games.” Zeitschrift für Operations Research 31 (1987): 143-59.
10. Dagan, N. “New Characterizations of Old Bankruptcy Rules.” Social Choice and Welfare 13 (1996): 51-9.
11. Dagan, N., and Volij, O. “The Bankruptcy Problem: A Cooperative Bargaining Approach.” Mathematical Social Sciences 26 (1993): 287-97.
12. de Frutos, M-A., and Massó, J. “More on the Uniform Allocation Rule: Equality and Consistency.” Mimeograph, Universitat Autonoma de Barcelona, 1995.
13. Herrero, C. “A Characterization of the Equal Loss Solution.” Mimeograph, 1998.
14. Herrero, C., Maschler, M., and Villar, A. “Individual Rights and Collective Responsibility: The Rights-Egalitarian Solution.” Mathematical Social Sciences 37 (1999): 59-77.
15. Herrero, C., and Villar, A. “A Characterization of the Constrained Equal-Loss Rule in Bankruptcy.” Mimeograph, 1998.
16. Hokari, T., and Thomson, W. “Weighted Talmud Rules.” Mimeograph, April 2000.
17. Littlechild, S. C., and Owen, G. “A Simple Expression for the Shapley Value in a Special Case.” Management Science 20 (1973): 370-2.
18. O'Neill, B. “A Problem of Rights Arbitration from the Talmud.” Mathematical Social Sciences 2 (1982): 345-71.
19. Otten, G-J., Peters, H., and Volij, O. “Two Characterizations of the Uniform Rule for Division Problems with Single-Peaked Preferences.” Economic Theory 7 (1996): 291-306.
20. Schummer, J., and Thomson, W. “Two Derivations of the Uniform Rule and an Application to Bankruptcy.” Economics Letters 55 (1997): 333-7.
21. Serrano, R. “Strategic Bargaining, Bankruptcy Problems and the Nucleolus.” Mimeograph, Brown University, January 1993.
22. Shapley, L. “A Value for n-Person Games.” In H. W, Kuhn and A. W. Tucker (eds.), Annals of Mathematical Studies; Contributions to the Theory of Games II. New Jersey: Princeton University Press, 28 (1953): 307-14.
23. Sonn, S. “Sequential Bargaining for Bankruptcy Problems.” Mimeograph, University of Rochester, October 1992.
24. Sprumont, Y. “The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule.” Econometrica 59 (1991): 509-19.
25. Thomson, W. “Resource-Monotonic Solutions to the Problem of Fair Division When Preferences are Single-Peaked.” Social Choice and Welfare 11 (1994a): 205-23.
26. Thomson, W. “Consistent Solutions to the Problem of Fair Division When Preferences are Single-Peaked.” Journal of Economic Theory 63 (1994b): 219-45.
27. Thomson, W. “Population-Monotonic Solutions to the Problem of Fair Division When Preferences are Single-Peaked.” Economic Theory 5 (1995): 229-46.
28. Thomson, W. “Consistent Allocation Rules.” Mimeograph, 1997.
29. Thomson, W. “Axiomatic Analyses of Bankruptcy and Taxation Problems: A Survey.” Forthcoming in Mathematical Social Sciences, 1996.
30. Young, P. “On Dividing an Amount According to Individual Claims or Liabilities.” Mathematics of Operations Research 12 (1987): 398-414.