IDEAS home Printed from https://ideas.repec.org/p/pab/wpaper/06.30.html
   My bibliography  Save this paper

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

Author

Listed:
  • Carmen Herrero

    (Department of Economics, Universidad de Alicante)

  • Ricardo Martinez

    (Department of Economics, Universidad de Alicante & Department of Economics, Universidad Pablo de Olavide)

Abstract

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. We analyzed the properties those methods satisfy and we provide a characterization of them. We also prove that these methods can be interpreted as extensions to the indivisible case of the so-called equal-distance rule.

Suggested Citation

  • Carmen Herrero & Ricardo Martinez, 2006. "Up methods in the allocation of indivisibilities when preferences are single-peaked," Working Papers 06.30, Universidad Pablo de Olavide, Department of Economics.
    • Handle: RePEc:pab:wpaper:06.30
    as

    Download full text from publisher

    File URL: http://www.upo.es/serv/bib/wps/econ0630.pdf
    File Function: First version, 2006
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Carmen Herrero & Ricardo Martínez, 2011. "Allocation problems with indivisibilities when preferences are single-peaked," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 453-467, December.
    2. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
    3. 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.
    4. 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.
    5. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    6. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
    7. Carmen Herrero & Antonio Villar, 2002. "Sustainability in bankruptcy problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 261-273, December.
    8. Hervé Moulin & Richard Stong, 2002. "Fair Queuing and Other Probabilistic Allocation Methods," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 1-30, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. José-manuel Giménez-gómez & Cori Vilella, 2017. "Recursive methods for discrete claims problems," Economics Bulletin, AccessEcon, vol. 37(3), pages 1653-1665.
    2. Susana Díaz & Bernard Baets & Susana Montes, 2011. "On the Ferrers property of valued interval orders," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 421-447, December.
    3. 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.
    4. Vito Fragnelli & Fabio Gastaldi, 2017. "Remarks on the integer Talmud solution for integer bankruptcy problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 127-163, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Siwei Chen, 2015. "Systematic favorability in claims problems with indivisibilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 283-300, February.
    2. Carmen Herrero & Ricardo Martínez, 2011. "Allocation problems with indivisibilities when preferences are single-peaked," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 453-467, December.
    3. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    4. Flores-Szwagrzak, Karol, 2015. "Priority classes and weighted constrained equal awards rules for the claims problem," Journal of Economic Theory, Elsevier, vol. 160(C), pages 36-55.
    5. Juan D Moreno-Ternero & John E Roemer, 2006. "Impartiality, Priority, and Solidarity in the Theory of Justice," Econometrica, Econometric Society, vol. 74(5), pages 1419-1427, September.
    6. Youngsub Chun, 2006. "The Separability Principle in Economies with Single-Peaked Preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 239-253, April.
    7. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2010. "Baseline Rationing," Discussion Papers 10-16, University of Copenhagen. Department of Economics.
    8. 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.
    9. William Thomson, 2014. "Compromising between the proportional and constrained equal awards rules," RCER Working Papers 584, University of Rochester - Center for Economic Research (RCER).
    10. Moreno-Ternero, Juan D. & Roemer, John E., 2012. "A common ground for resource and welfare egalitarianism," Games and Economic Behavior, Elsevier, vol. 75(2), pages 832-841.
    11. Jens Hougaard & Juan Moreno-Ternero & Lars Østerdal, 2013. "Rationing with baselines: the composition extension operator," Annals of Operations Research, Springer, vol. 211(1), pages 179-191, December.
    12. René Brink & Juan D. Moreno-Ternero, 2017. "The reverse TAL-family of rules for bankruptcy problems," Annals of Operations Research, Springer, vol. 254(1), pages 449-465, July.
    13. William Thomson, 2015. "For claims problems, compromising between the proportional and constrained equal awards rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(3), pages 495-520, November.
    14. Juan Moreno-Ternero & John E. Roemer, 2004. "Impartiality and Priority. Part 2: A Characterization with Solidarity," Cowles Foundation Discussion Papers 1477B, Cowles Foundation for Research in Economics, Yale University, revised May 2005.
    15. Martínez, Ricardo & Moreno-Ternero, Juan D., 2022. "Compensation and sacrifice in the probabilistic rationing of indivisible units," European Journal of Operational Research, Elsevier, vol. 302(2), pages 740-751.
    16. Ricardo Martínez, 2007. "Strong Composition Down. Characterizations Of New And Classical Bankruptcy Rules," Working Papers. Serie AD 2007-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    17. Christopher P. Chambers & Juan D. Moreno-Ternero, 2017. "Taxation and poverty," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 153-175, January.
    18. Alcalde-Unzu, Jorge & Gallo, Oihane & Inarra, Elena & Moreno-Ternero, Juan D., 2024. "Solidarity to achieve stability," European Journal of Operational Research, Elsevier, vol. 315(1), pages 368-377.
    19. Hokari, Toru & Thomson, William, 2008. "On properties of division rules lifted by bilateral consistency," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1057-1071, December.
    20. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 307-328, November.

    More about this item

    Keywords

    Allocation problem; indivisibilities; single-peaked preferences; standard of comparison; up method.;
    All these keywords.

    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pab:wpaper:06.30. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Publicación Digital - UPO (email available below). General contact details of provider: https://edirc.repec.org/data/deupoes.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.