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Endowment additivity and the weighted proportional rules for adjudicating conflicting claims

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  • Patrick Harless

    (University of Rochester)

Abstract

We propose and study a new axiom, restricted endowment additivity, for the problem of adjudicating conflicting claims. This axiom requires that awards be additively decomposable with respect to the endowment whenever no agent’s claim is filled. For two-claimant problems, restricted endowment additivity essentially characterizes weighted extensions of the proportional rule. With additional agents, however, the axiom is satisfied by a great variety of rules. Further imposing versions of continuity and consistency, we characterize a new family of rules which generalize the proportional rule. Defined by a priority relation and a weighting function, each rule aims, as nearly as possible, to assign awards within each priority class in proportion to these weights. We also identify important subfamilies and obtain new characterizations of the constrained equal awards and proportional rules based on restricted endowment additivity.

Suggested Citation

  • Patrick Harless, 2017. "Endowment additivity and the weighted proportional rules for adjudicating conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 755-781, March.
    • Handle: RePEc:spr:joecth:v:63:y:2017:i:3:d:10.1007_s00199-016-0960-9
    DOI: 10.1007/s00199-016-0960-9
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    Cited by:

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    2. Stovall, John E., 2020. "Equal sacrifice taxation," Games and Economic Behavior, Elsevier, vol. 121(C), pages 55-75.
    3. Biung†Ghi Ju & Juan D. Moreno†Ternero, 2017. "Fair Allocation Of Disputed Properties," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58(4), pages 1279-1301, November.
    4. 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.
    5. Arin, J. & Benito-Ostolaza, J. & Inarra, E., 2017. "The reverse Talmud family of rules for bankruptcy Problems: A characterization," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 43-49.
    6. Jaume García-Segarra & Miguel Ginés-Vilar, 2023. "Additive adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 93-116, March.
    7. Karol Flores-Szwagrzak & Jaume García-Segarra & Miguel Ginés-Vilar, 2020. "Priority and proportionality in bankruptcy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 559-579, April.
    8. Gong, Doudou & Dietzenbacher, Bas, 2024. "Equal treatment of unsatisfied agents," Research Memorandum 010, Maastricht University, Graduate School of Business and Economics (GSBE).
    9. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "On how to allocate the fixed cost of transport systems," Annals of Operations Research, Springer, vol. 301(1), pages 81-105, June.

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    More about this item

    Keywords

    Claims problem; restricted endowment additivity; Weighted proportional rule; Priority-augmented weighted proportional rule;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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