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Allocation Problems With Indivisibilities When Preferences Are Single-Peaked

Author

Listed:
  • 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.

Suggested Citation

  • Carmen Herrero Blanco & Ricardo Martínez, 2006. "Allocation Problems With Indivisibilities When Preferences Are Single-Peaked," Working Papers. Serie AD 2006-14, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    • Handle: RePEc:ivi:wpasad:2006-14
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    References listed on IDEAS

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    1. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
    2. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    3. 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.
    4. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
    5. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    6. 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).
    7. Carmen Herrero & Ricardo Martínez, 2008. "Balanced allocation methods for claims problems with indivisibilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(4), pages 603-617, May.
    8. Carmen Herrero, 2002. "General allocation problems with single-peaked preferences: path-independence and related topics," Spanish Economic Review, Springer;Spanish Economic Association, vol. 4(1), pages 19-40.
    9. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
    10. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
    11. Dagan, Nir, 1996. "A Note on Thomson's Characterizations of the Uniform Rule," Journal of Economic Theory, Elsevier, vol. 69(1), pages 255-261, April.
    12. Thomson, W., 1991. "Resource-Monotonic Solutions to the Problem of Fair Divosion when Preferences are Single-Peaked ," RCER Working Papers 301, University of Rochester - Center for Economic Research (RCER).
    13. Sonmez, Tayfun, 1994. "Consistency, monotonicity, and the uniform rule," Economics Letters, Elsevier, vol. 46(3), pages 229-235, November.
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    Citations

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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;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 272-283, December.
    2. Vito Fragnelli & Stefano Gagliardo & Fabio Gastaldi, 2014. "Integer solutions to bankruptcy problems with non-integer claims," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 892-933, October.
    3. R. Pablo Arribillaga & Jordi Massó & Alejandro Neme, 2019. "All Sequential Allotment Rules Are Obviously Strategy-proof," UFAE and IAE Working Papers 966.19, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    4. Vito Fragnelli & Stefano Gagliardo & Fabio Gastaldi, 2016. "Bankruptcy problems with non-integer claims: definition and characterizations of the ICEA Solution," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 88-130, April.

    More about this item

    Keywords

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

    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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