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Operators for the adjudication of conflicting claims

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Author Info

  • William Thomson

    ()
    (University of Rochester)

  • Chun-Hsien Yeh

    (Institute of Economics, Academia Sinica, Taipei 115, Taiwan.)

Abstract

We consider the problem of dividing some amount of an infinitely divisible and homogeneous resource among agents having claims on this resource that cannot be jointly honored. A "rule" associates with each such problem a feasible division. Our goal is to uncover the structure of the space of rules. For that purpose, we study "operators" on the space, that is, mappings that associate to each rule another one. Duality, claims truncation, attribution of minimal rights, and convex combinations are the four operators we consider. We first establish a number of results linking these operators, such as idempotence, commutativity, and distributivity. Then, we determine which properties of rules are preserved under each of these operators, and which are not.

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File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_531.pdf
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Bibliographic Info

Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 531.

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Length: 37 pages
Date of creation: Jun 2006
Date of revision:
Handle: RePEc:roc:rocher:531

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Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

Related research

Keywords: Conflicting claims; Division rules; Operators; Minimal rights; Maximal claims; Duality; Convexity.;

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References

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  1. Carmen Herrero Blanco, 1998. "- Minimal Rights In Claims Problems," Working Papers. Serie AD 1998-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  2. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
  3. 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.
  4. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
  5. Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer, vol. 21(2), pages 241-261, 03.
  6. Biung-Ghi Ju & Eiichi Miyagawa & Toyotaka Sakai, 2003. "Non-Manipulable Division Rules in Claim Problems and Generalizations," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200307, University of Kansas, Department of Economics, revised Aug 2005.
  7. 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.
  8. Antonio Villar Notario & Carmen Herrero Blanco, 2000. "The Three Musketeers: Four Classical Solutions To Bankruptcy Problems," Working Papers. Serie AD 2000-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  9. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
  10. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer, vol. 28(4), pages 511-520.
  11. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer, vol. 13(1), pages 51-59, January.
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Cited by:
  1. JU, Biung-Ghi & MORENO-TERNERO, Juan D., . "Progressive and merging-proof taxation," CORE Discussion Papers RP -2280, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2012. "Rationing in the presence of baselines," Discussion Papers of Business and Economics 8/2012, Department of Business and Economics, University of Southern Denmark.
  3. Kristof Bosmans & Luc Lauwers, 2011. "Lorenz comparisons of nine rules for the adjudication of conflicting claims," International Journal of Game Theory, Springer, vol. 40(4), pages 791-807, November.
  4. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2012. "A unifying framework for the problem of adjudicating conflicting claims," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 107-114.
  5. Diego Dominguez, 2013. "Lower bounds and recursive methods for the problem of adjudicating conflicting claims," Social Choice and Welfare, Springer, vol. 40(3), pages 663-678, March.
  6. LUTTENS, Roland Iwan, 2010. "Lower bounds rule!," CORE Discussion Papers 2010069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Marieke Quant & Peter Borm, 2011. "Random conjugates of bankruptcy rules," Social Choice and Welfare, Springer, vol. 36(2), pages 249-266, February.
  8. William Thomson, 2008. "Two families of rules for the adjudication of conflicting claims," Social Choice and Welfare, Springer, vol. 31(4), pages 667-692, December.
  9. JU, Biung-Ghi & MORENO-TERNERO, Juan D., 2006. "Progressivity, inequality reduction and merging-proofness in taxation," CORE Discussion Papers 2006075, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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