Endowment additivity and the weighted proportional rules for adjudicating conflicting claims

Abstract

Harless, P. (2017) Endowment additivity and the weighted proportional rules for adjudicating conflicting claims. Economic Theory, 63(3), pp. 755-781. (doi:10.1007/s00199-016-0960-9) This is the author's final accepted version.There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it.http://eprints.gla.ac.uk/129220/ AbstractWe 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.Keywords: claims problem, restricted endowment additivity, weighted proportional rule, priority-augmented weighted proportional rule.JEL Classification Numbers: D63, D70, D71. * Address: Department of Economics, University of Rochester, Rochester, NY 14627, USA; e-mail: patrick.harless@rochester.edu. I thank Karol Flores-Szwagrzak and Juan Moreno-Ternero, and three anonymous referees for comments. I am grateful to William Thomson for comments, encouragement, and guidance.

Fair Allocation of Disputed Properties

“…Each agent i 2 N has a preference relation R i defined on R`+, which satisfies the classical conditions of rationality (completeness and transitivity), continuity (lower and upper contour sets are closed), strong monotonicity, and convexity (upper contour sets are convex). 10 Let R denote the domain of such admissible preferences.…”

“…14 Finally, agents have 9 Denote by |N | the cardinality of set N . 10 As usual, we denote by P i the strict preference associated with R i , and by I i the corresponding indi↵erence relation.…”

“…18 The two principles were mentioned in passing by Thomson (2014) for the specific case of (unidimensional) bankruptcy problems. More recently, Harless (2016) has used them in the axiomatic characterization of a broad family of rules for such a context. We consider them here for our more general (multidimensional) framework.…”

The Reverse TAL-Family of Rules for Bankruptcy Problems

“…11 Thomson (2015b) and Harless (2016) are also instances of recent proposals for families of rules. In both cases, the motivation is to compromise between the proportional rule and the constrained equal-awards rule (or the constrained equal-losses rules).…”

For claims problems, another compromise between the proportional and constrained equal awards rules

“…As we documented in the introduction, in the context of the adjudication of conflicting claims, notions of proportionality and of equality, of awards or of losses, can be expressed in multiple ways. Additional families of rules that can be thought of as further generalizing the proportional, constrained equal awards, and constrained equal losses rules have come out of recent axiomatic work (Ju, Miyagawa, and Sakai, 2007;Harless, 2015;Stovall, 2014; Flores-Szwagrzak, 2015; Chambers and Moreno-Ternero, 2015). Consistency has played an important role in most of these developments.…”