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Collective Rationality and Monotone Path Division Rules

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  • Stovall, John

    (University of Warwick)

Abstract

We impose the axiom Independence of Irrelevant Alternatives on division rules for the conflicting claims problem. With the addition of Consistency and Resource Monotonicity, this characterizes a family of rules which can be described in three different but intuitive ways. First, a rule is identified with a fixed monotone path in the space of awards, and for a given claims vector, the path of awards for that claims vector is simply the monotone path truncated by the claims vector. Second, a rule is identified with a set of parametric functions indexed by the claimants, and for a given claims problem, each claimant receives the value of his parametric function at a common parameter value, but truncated by his claim. Third, a rule is identified with an additively separable, strictly concave social welfare function, and for a given claims problem, the amount awarded is the maximizer of the social welfare function subject to the constraint of choosing a feasible award. This third way of describing the family of rules is similar to Lensberg's (1987) solution for bargaining problems applied to conflicting claims problems.

Suggested Citation

  • Stovall, John, 2014. "Collective Rationality and Monotone Path Division Rules," The Warwick Economics Research Paper Series (TWERPS) 1035, University of Warwick, Department of Economics.
  • Handle: RePEc:wrk:warwec:1035
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. repec:eee:matsoc:v:90:y:2017:i:c:p:43-55 is not listed on IDEAS
    5. 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.
    6. Bossert, Walter & Peters, Hans, 2017. "Choice on the simplex domain," Research Memorandum 030, Maastricht University, Graduate School of Business and Economics (GSBE).
    7. Erlanson, Albin & Flores-Szwagrzak, Karol, 2015. "Strategy-proof assignment of multiple resources," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 137-162.
    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).

    More about this item

    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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