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On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach

  • William Thomson

    ()

For the problem of adjudicating conflicting claims, a rule is consistent if the choice it makes for each problem is always in agreement with the choice it makes for each "reduced problem" obtained by imagining that some claimants leave with their awards and reassessing the situation from the viewpoint of the remaining claimants. We develop a general technique to determine whether a given two-claimant rule admits a consistent extension to general populations, and to identify this extension if it exists. We apply the technique to a succession of examples. One application is to a one-parameter family of rules that offer a compromise between the constrained equal awards and constrained equal losses rules. We show that a consistent extension of such a rule exists only if all the weight is placed on the former or all the weight is placed on the latter. Another application is to a family of rules that provide a compromise between the constrained equal awards and proportional rules, and a dual family that provide a compromise between the constrained equal losses and proportional rules. In each case, we identify the restrictions implied by consistency.

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File URL: http://hdl.handle.net/10.1007/s10058-007-0027-2
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Article provided by Springer in its journal Review of Economic Design.

Volume (Year): 11 (2007)
Issue (Month): 3 (November)
Pages: 225-251

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Handle: RePEc:spr:reecde:v:11:y:2007:i:3:p:225-251
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  1. Volij, Oscar & Dagan, Nir, 1997. "Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems," Staff General Research Papers 5141, Iowa State University, Department of Economics.
  2. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
  3. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
  4. Diego Dominguez & William Thomson, 2006. "A new solution to the problem of adjudicating conflicting claims," Economic Theory, Springer, vol. 28(2), pages 283-307, 06.
  5. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038.
  6. Kaminski, Marek M., 2000. "'Hydraulic' rationing," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 131-155, September.
  7. Schummer, J. & Thomson, W., 1996. "Two Derivations of the Uniform Rule and an Application to Bankruptcy," RCER Working Papers 423, University of Rochester - Center for Economic Research (RCER).
  8. Sasaki, Hiroo & Toda, Manabu, 1992. "Consistency and characterization of the core of two-sided matching problems," Journal of Economic Theory, Elsevier, vol. 56(1), pages 218-227, February.
  9. Toru Hokari & William Thomson, 2007. "On properties of division rules lifted by bilateral consistency," RCER Working Papers 536, University of Rochester - Center for Economic Research (RCER).
  10. Tadenuma, Koichi & Thomson, William, 1991. "No-Envy and Consistency in Economies with Indivisible Goods," Econometrica, Econometric Society, vol. 59(6), pages 1755-67, November.
  11. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer, vol. 28(4), pages 511-520.
  12. Nir Dagan, 1996. "New Characterizations of Old Bankruptcy Rules," Economic theory and game theory 002, Nir Dagan.
  13. Peleg, Bezalel, 1985. "An axiomatization of the core of cooperative games without side payments," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 203-214, April.
  14. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
  15. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  16. Thomson, William, 1988. "A study of choice correspondences in economies with a variable number of agents," Journal of Economic Theory, Elsevier, vol. 46(2), pages 237-254, December.
  17. 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.
  18. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer, vol. 18(4), pages 389-407.
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