, Volume 16, Issue 2, pp 272–283 | Cite as

Up methods in the allocation of indivisibilities when preferences are single-peaked

Original Paper


We consider allocation problems with indivisible goods when agents’ preferences are single-peaked. We propose natural rules (called up methods) to solve such a class of problems and axiomatically characterize them. We also prove that these methods can be interpreted as extensions to the indivisible case of the so-called equal distance rule.


Allocation problem Indivisibilities Single-peaked preferences Priority standard Up method 

Mathematics Subject Classification (2000)

D61 D63 91B14 91B32 


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  1. Ching S (1994) An alternative characterization of the uniform rule. Soc Choice Welf 11:131–136 CrossRefGoogle Scholar
  2. Chun Y (1999) Equivalence of axioms for bankruptcy problems. Int J Game Theory 28:511–520 CrossRefGoogle Scholar
  3. Herrero C (1999) Individual rights and collective responsibility: the rights-egalitarian solution. Math Soc Sci 37:59–77 CrossRefGoogle Scholar
  4. Herrero C, Martínez R (2006) Allocation problems with indivisibilities when preferences are single-peaked. Mimeo Google Scholar
  5. Herrero C, Martínez R (2008) Balanced allocation methods for claims problems with indivisibilities. Soc Choice Welf 30:603–617 CrossRefGoogle Scholar
  6. Herrero C, Villar A (1999). The equal distance rule in allocation problems with single-peaked preferences. In: Current trends in economics: theory and practice. Springer, Berlin, pp 215–223 Google Scholar
  7. Herrero C, Villar A (2000) An alternative characterization of the equal-distance rule for allocations problems with single-peaked preferences. Econ Lett 66:311–317 CrossRefGoogle Scholar
  8. Herrero C, Villar A (2001) The three musketeers: four classical solutions to bankruptcy problems. Math Soc Sci, 42:307–328 CrossRefGoogle Scholar
  9. Herrero C, Villar A (2002) Sustainability in bankruptcy problems. Top 10:261–273 CrossRefGoogle Scholar
  10. Hokari T, Thomson W (2004) On properties of division rules lifted by bilateral consistency. Mimeo Google Scholar
  11. Moulin H, Stong R (2002) Fair queuing and other probabilistic allocation methods. Math Oper Res 27:1–30 CrossRefGoogle Scholar
  12. Sprumont Y (1991) The division problem with single-peaked preferences: A characterization of the uniform allocation rule. Econometrica 59:509–519 CrossRefGoogle Scholar
  13. Thomson W (1994) Consistent solutions to the problem of fair division when preferences are single-peaked. J Econ Theory 63:219–245 CrossRefGoogle Scholar
  14. Thomson W (1995) Population-monotonic solutions to the problem of fair division when preferences are single-peaked. Econ Theory 5:229–246 CrossRefGoogle Scholar
  15. Thomson W (1998) Consistency and its converse: an introduction. Rochester Cent Econ Res 448 Google Scholar
  16. Yeh C-H (2004) Sustainability, exemption, and the constrained equal awards rule: a note. Math Soc Sci 47:103–110 CrossRefGoogle Scholar
  17. Yeh C-H (2006) Protective properties and the constrained equal awards rule for claims problems: a note. Soc Choice Welf 27:221–230 CrossRefGoogle Scholar
  18. Young HP (1994) Equity: theory and practice. Princeton University Press, Princeton Google Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2008

Authors and Affiliations

  1. 1.Departamento de Fundamentos del Análisis Económico and Instituto Valenciano de Investigaciones EconómicasUniversity of AlicanteAlicanteSpain
  2. 2.Department of EconomicsBrown UniversityProvidenceUSA

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