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Systematic favorability in claims problems with indivisibilities

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  • Siwei Chen

Abstract

We study claims problems with indivisible goods. Due to indivisibilities, in certain situations, two agents with equal claims may have to receive unequal amounts. Our main goal is to find rules that deal with these situations in a consistent way. We propose three “systematic favorability” properties. We define a subfamily of up (down) rules studied in Moulin and Stong (Math Oper Res 27:1–30, 2002 ). We show that the subfamily are the only rules satisfying our first systematic favorability property, composition up, and bilateral consistency. Another family of rules we study are the sequential priority rules. Given a priority order over agents, we satisfy their claims one agent at a time until the resource runs out. These rules are the only ones that satisfy our second systematic favorability property, composition down, and bilateral consistency. Using duality, we also provide another characterization of the sequential priority rules, with our third systematic favorability property. Besides, we provide an alternative characterization of the rules studied in Herrero and Martinez (Soc Choice Welf 30:603–617, 2008 ). Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
  • Handle: RePEc:spr:sochwe:v:44:y:2015:i:2:p:283-300
    DOI: 10.1007/s00355-014-0828-5
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    References listed on IDEAS

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    1. Juan Moreno-Ternero & Antonio Villar, 2006. "The TAL-Family of Rules for Bankruptcy Problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 231-249, October.
    2. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
    3. Thomson, William & Yeh, Chun-Hsien, 2008. "Operators for the adjudication of conflicting claims," Journal of Economic Theory, Elsevier, vol. 143(1), pages 177-198, November.
    4. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    5. 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.
    6. 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.
    7. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    8. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    9. Hervé Moulin & Richard Stong, 2002. "Fair Queuing and Other Probabilistic Allocation Methods," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 1-30, February.
    10. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    11. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    12. Chun-Hsien Yeh, 2006. "Protective Properties and the Constrained Equal Awards Rule for Claims Problems: A Note," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 221-230, October.
    13. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
    14. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
    15. 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.
    16. 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.
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    Cited by:

    1. 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).
    2. 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.
    3. 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.
    4. Péter Csóka & P. Jean-Jacques Herings, 2018. "Decentralized Clearing in Financial Networks," Management Science, INFORMS, vol. 64(10), pages 4681-4699, October.
    5. José-manuel Giménez-gómez & Cori Vilella, 2017. "Recursive methods for discrete claims problems," Economics Bulletin, AccessEcon, vol. 37(3), pages 1653-1665.
    6. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2020. "On the difficulty of budget allocation in claims problems with indivisible items of different prices," ThE Papers 20/09, Department of Economic Theory and Economic History of the University of Granada..
    7. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices," Group Decision and Negotiation, Springer, vol. 30(5), pages 1133-1159, October.
    8. William Thomson, 2015. "For claims problems, another compromise between the proportional and constrained equal awards rules," RCER Working Papers 592, University of Rochester - Center for Economic Research (RCER).

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    More about this item

    Keywords

    Claims problems; Indivisibilities; Standard of comparison; Systematic favorability; C79; D63; D74;
    All these keywords.

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • 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

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