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Two families of rules for the adjudication of conflicting claims

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  • William Thomson

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Abstract

We define two families of rules to adjudicate conflicting claims. The first family contains the constrained equal awards, constrained equal losses, Talmud, and minimal overlap rules. The second family, which also contains the constrained equal awards and constrained equal losses rules, is obtained from the first one by exchanging, for each problem, how well agents with relatively larger claims are treated as compared to agents with relatively smaller claims. In each case, we identify the subfamily of consistent rules.

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File URL: http://hdl.handle.net/10.1007/s00355-008-0302-3
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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 31 (2008)
Issue (Month): 4 (December)
Pages: 667-692

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Handle: RePEc:spr:sochwe:v:31:y:2008:i:4:p:667-692

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References

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  1. 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.
  2. William Thomson, 2006. "The Two-Agent Claims-Truncated Proportional Rule Has No Consistent Extension: A Constructive Proof," RCER Working Papers 529, University of Rochester - Center for Economic Research (RCER).
  3. William Thomson, 2007. "On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach," Review of Economic Design, Springer, vol. 11(3), pages 225-251, November.
  4. Thomson, William & Yeh, Chun-Hsien, 2008. "Operators for the adjudication of conflicting claims," Journal of Economic Theory, Elsevier, vol. 143(1), pages 177-198, November.
  5. Chun, Youngsub & Thomson, William, 2005. "Convergence under replication of rules to adjudicate conflicting claims," Games and Economic Behavior, Elsevier, vol. 50(2), pages 129-142, February.
  6. Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer, vol. 21(2), pages 241-261, 03.
  7. Juan D. Moreno-Ternero & Antonio Villar, 2006. "On the Relative Equitability of a Family of Taxation Rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 8(2), pages 283-291, 05.
  8. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
  9. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer, vol. 13(1), pages 51-59, January.
  10. 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).
  11. José Alcalde & María Marco & José Silva, 2005. "Bankruptcy games and the Ibn Ezra’s proposal," Economic Theory, Springer, vol. 26(1), pages 103-114, 07.
  12. Antonio Villar Notario & Juan D. Moreno Ternero, 2001. "The Tal-Family Of Rules For Bankruptcy Problems," Working Papers. Serie AD 2001-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  13. 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.
  14. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer, vol. 28(4), pages 511-520.
  15. 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.
  16. José Alcalde & María Marco & José Silva, 2008. "The minimal overlap rule revisited," Social Choice and Welfare, Springer, vol. 31(1), pages 109-128, June.
  17. Gustavo Bergantiños & Luciano Méndez-Naya, 2001. "Additivity in bankruptcy problems and in allocation problems," Spanish Economic Review, Springer, vol. 3(3), pages 223-229.
  18. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
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Citations

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Cited by:
  1. Thomson, William, 2013. "A characterization of a family of rules for the adjudication of conflicting claims," Games and Economic Behavior, Elsevier, vol. 82(C), pages 157-168.
  2. William Thomson, 2007. "Lorenz rankings of rules for the adjudication of conflicting claims," RCER Working Papers 538, University of Rochester - Center for Economic Research (RCER).
  3. LUTTENS, Roland Iwan, 2010. "Lower bounds rule!," CORE Discussion Papers 2010069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Rene van den Brink & Yukihiko Funaki & Gerard van der Laan, 2008. "The Reverse Talmud Rule for Bankruptcy Problems," Tinbergen Institute Discussion Papers 08-026/1, Tinbergen Institute, revised 27 Mar 2008.
  5. van den Brink, René & Funaki, Yukihiko & van der Laan, Gerard, 2013. "Characterization of the Reverse Talmud bankruptcy rule by Exemption and Exclusion properties," European Journal of Operational Research, Elsevier, vol. 228(2), pages 413-417.

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