Skip to main content
SpringerLink
Log in

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

  • Original Paper
  • Published:
Review of Economic Design Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aumann R, Maschler M (1985) Game theoretic analysis of a bankruptcy problem from the Talmud. J Econ Theory 36:195–213

    Article  Google Scholar 

  • Balinski M, Young P (1982) Fair representation. Yale University Press, New Haven

    Google Scholar 

  • Chambers C, Thomson W (2002) Group order preservation and the proportional rule for bankruptcy problems. Math Soc Sci 44:235–252

    Article  Google Scholar 

  • Chun Y (1999) Equivalence of axioms for bankruptcy problems. Int J Game Theory 28:511–520

    Article  Google Scholar 

  • Dagan N (1996) New characterizations of old bankruptcy rules. Soc Choice Welf 13:51–59

    Article  Google Scholar 

  • Dagan N, Volij O (1997) Bilateral comparisons and consistent fair division rules in the context of bankruptcy problems. Int J Game Theory 26:11–25

    Article  Google Scholar 

  • Davis M, Maschler M (1965) The kernel of a cooperative game. Nav Res Logist Q 12:223–259

    Article  Google Scholar 

  • Dominguez D, Thomson W (2006) A new solution to the problem of adjudicating conflicting claims. Econ Theory 28:283–307

    Article  Google Scholar 

  • Hokari T, Thomson W (2000) On properties of division rules lifted by bilateral consistency, mimeo

  • Hokari T, Thomson W (2003) Bankruptcy problems and weighted Talmud rules. Econ Theory 21:241–261

    Article  Google Scholar 

  • Kaminski M (2000) Hydraulic rationing. Math Soc Sci 40:131–155

    Article  Google Scholar 

  • Kaminski M (2006) Parametric rationing methods. Games Econ Behav 54:115–133

    Article  Google Scholar 

  • Lensberg T (1988) Stability and the Nash solution. J Econ Theory 45:330–341

    Article  Google Scholar 

  • Maschler M, Owen G (1989) The consistent Shapley value for hyperplane games. Int J Game Theory 18:389–407

    Article  Google Scholar 

  • Moulin H (2000) Priority rules and other asymmetric rationing methods. Econometrica 68:643–684

    Article  Google Scholar 

  • O’Neill B (1982) A problem of rights arbitration from the Talmud. Math Soc Sci 2:345–371

    Article  Google Scholar 

  • Peleg B (1985) An axiomatization of the core of cooperative games without side-payments. J Math Econ 14:203–214

    Article  Google Scholar 

  • Sasaki H, Toda M (1992) Consistency and characterization of the core of two-sided matching problems. J Econ Theory 56:218–227

    Article  Google Scholar 

  • Schummer J, Thomson W (1997) Two derivations of the uniform rule. Econ Lett 55:333–337

    Article  Google Scholar 

  • Tadenuma K, Thomson W (1991) No-envy and consistency in economies with indivisible goods. Econometrica 59:1755–1767

    Article  Google Scholar 

  • Thomson W (1988) A study of choice correspondences in economies with a variable number of agents. J Econ Theory 46:247–259

    Article  Google Scholar 

  • Thomson W (1994) Consistent extensions. Math Soc Sci 28:35–49

    Article  Google Scholar 

  • Thomson W (2001) A characterization of a family of rules for the resolution of conflicting claims, mimeo, revised 2006

  • Thomson W (2002) Two families of rules for the adjudication of conflicting claims, mimeo

  • Thomson W (2003) Axiomatic and strategic analysis of bankruptcy and taxation problems: a survey. Math Soc Sci 45:249–297

    Article  Google Scholar 

  • Thomson W (2006) Consistent allocation rules, mimeo

  • Thomson W (2007) The claims-truncated proportional rule has no consistent extension: a geometric proof. Econ Lett (forthcoming)

  • Thomson W, Lensberg T (1989) The axiomatic theory of bargaining with a variable number of agents. Cambridge University Press, Cambridge

    Google Scholar 

  • Thomson W, Myerson RB (1980) Monotonicity and independence axioms. Int J Game Theory 9:37–49

    Article  Google Scholar 

  • Thomson W, Yeh C-H (2001) Minimal rights, maximal claims, duality and convexity for division rules, mimeo, revised 2003

  • Young P (1987) On dividing an amount according to individual claims or liabilities. Math Oper Res 12: 398–414

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, Harkness Hall, University of Rochester, Rochester, NY, 14627, USA

    William Thomson

Authors
  1. William Thomson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to William Thomson.

Additional information

I gratefully acknowledge support from NSF under grant SBR-9731431 and SES 0214691, and the comments of Carmen Bevia, Rodrigo Velez, Chun-Hsien Yeh, and a referee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Thomson, W. On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach. Rev. Econ. Design 11, 225–251 (2007). https://doi.org/10.1007/s10058-007-0027-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10058-007-0027-2

Keywords

JEL Classification

Search

Navigation