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Allocation Problems With Indivisibilities When Preferences Are Single-Peaked

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  • Carmen Herrero Blanco

    (Instituto Valenciano de Investigaciones Económicas)

  • Ricardo Martínez

    (Universidad de La Rioja)

Abstract

We consider allocation problems with indivisible goods when agents’ preferences are single-peaked. Two natural procedures (up methods and temporary satisfaction methods) are proposed to solve these problems. They are constructed by using priority methods on the cartesian product of agents and integer numbers, interpreted either as peaks or opposite peaks. Thus, two families of solutions arise this way. Our two families of solutions satisfy properties very much related to some well-known properties studied in the case of perfectly divisible goods, and they have a strong relationship with the continuous uniform and equal-distance rules, respectively.

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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2006-14.

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Length: 21 pages
Date of creation: Jul 2006
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2006-14

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Keywords: Allocation problem; indivisibilities; single-peaked preferences; temporary satisfaction method; up method.;

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References

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  1. Sonmez, Tayfun, 1994. "Consistency, monotonicity, and the uniform rule," Economics Letters, Elsevier, vol. 46(3), pages 229-235, November.
  2. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
  3. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  4. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer, vol. 15(4), pages 257-291, December.
  5. Salvador Barbera, 1995. "Strategy-Proof Allotment Rules," Discussion Papers 1142, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Nir Dagan, 1996. "A Note on Thomson's Characterizations of the Uniform Rule," Economic theory and game theory 003, Nir Dagan.
  7. Carmen Herrero Blanco & Ricardo Martínez, 2004. "Egalitarian Rules In Claims Problems With Indivisible Goods," Working Papers. Serie AD 2004-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  8. Carmen Herrero, 2002. "General allocation problems with single-peaked preferences: path-independence and related topics," Spanish Economic Review, Springer, vol. 4(1), pages 19-40.
  9. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer, vol. 28(4), pages 511-520.
  10. HERRERO, Carmen & MARTINEZ, Ricardo, 2006. "Balanced allocation methods for claims problems with indivisibilities," CORE Discussion Papers 2006066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
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Cited by:
  1. Carmen Herrero & Ricardo Martínez, 2008. "Up methods in the allocation of indivisibilities when preferences are single-peaked," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(2), pages 272-283, December.

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