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Balanced allocation methods for claims problems with indivisibilities

Author

Listed:
  • HERRERO, Carmen
  • MARTINEZ, Ricardo

Abstract

We study claims problems in which a certain amount of indivisible units (of an homogeneous good) has to be distributed among a group of agents, when this amount is not enough to fully satisfy agents' demands. We are interested in finding solutions satisfying robustness and fairness properties. To do that, we define the M-down methods, which are the unique robust (composition down and consistency) and fair (balancedness or conditional full compensation ) rules. Besides, we also establish the relationships between these M-down methods and the constrained equal awards rule.

Suggested Citation

  • 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).
  • Handle: RePEc:cor:louvco:2006066
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    File URL: https://uclouvain.be/en/research-institutes/immaq/core/dp-2006.html
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    References listed on IDEAS

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    1. Moulin, Herve, 1985. "Egalitarianism and Utilitarianism in Quasi-linear Bargaining," Econometrica, Econometric Society, vol. 53(1), pages 49-67, January.
    2. Juan Moreno-Ternero & Antonio Villar, 2006. "New characterizations of a classical bankruptcy rule," Review of Economic Design, Springer;Society for Economic Design, vol. 10(2), pages 73-84, August.
    3. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 51-59, January.
    4. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    5. Hervé Moulin & Richard Stong, 2002. "Fair Queuing and Other Probabilistic Allocation Methods," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 1-30, February.
    6. 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.
    7. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
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    Citations

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    Cited by:

    1. 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.
    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. 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.
    4. repec:ebl:ecbull:eb-17-00032 is not listed on IDEAS
    5. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    6. Peter Csoka & P. Jean-Jacques Herings, 2016. "Decentralized Clearing in Financial Networks," IEHAS Discussion Papers 1603, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    7. 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.
    8. 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.
    9. 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.
    10. Csoka, Péter & Herings, P. Jean-Jacques, 2016. "Decentralized Clearing in Financial Networks (RM/16/005-revised-)," Research Memorandum 037, Maastricht University, Graduate School of Business and Economics (GSBE).
    11. Vito Fragnelli & Gianfranco Gambarelli, 2014. "Further open problems in cooperative games," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 4, pages 51-62.
    12. repec:spr:topjnl:v:25:y:2017:i:1:d:10.1007_s11750-016-0426-z is not listed on IDEAS

    More about this item

    Keywords

    claims problems; indivisibilities; monotonic standard; balancedness; down method;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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