Endowment additivity and the weighted proportional rules for adjudicating conflicting claims

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

Learning matters: reappraising object allocation rules when agents strategically investigate

Individuals form preferences through search, interviews, discussion, and investigation. In a stylized object allocation model, we characterize the equilibrium learning strategies induced by different allocation rules and trace their welfare consequences. Our analysis reveals that top trading cycles rules dominate serial priority rules under inequality‐averse measures of social welfare

A School Choice Compromise: Between Immediate and Deferred Acceptance

School assignment procedures aim to improve student welfare, but must balance efficiency and equity goals and provide incentives for students to report their preferences truthfully. Debate centers largely on two rules: immediate acceptance (IA), the so-called Boston mechanism, and deferred acceptance (DA). IA's strength is efficiency, while DA is touted for its superior strategic properties. Thinking of these as extremes, we advocate a compromise rule, immediate-acceptance-with-skips (IA+), which slightly modifies IA to achieve better strategic properties while retaining efficiency. IA+ proceeds in rounds of applications and, like IA, �finalizes assignments in each round. However, unlike IA or DA, IA+ allows students to "skip" applications to schools with no remaining capacity. We show that IA+ is efficient and less manipulable than IA+. Unfortunately, IA+ violates solidarity properties that both IA and DA satisfy. Considering robustness, we �find that each of the three rules satisfies a different set of three natural invariance properties

Efficient Rules for Probabilistic Assignment

We propose an algorithm to construct sd-efficient probabilistic allocations of objects. Our algorithm proceeds in discrete rounds and distributes probability shares of objects sequentially yielding two natural degrees of freedom: selection rules governing the choice of objects in each round and distribution rules governing the dispensation of probability shares. The transparent procedure tightly connects properties of the rule to these choices making it ideally suited for practical applications. First proving that the algorithm identifies all sd-efficient allocations, we apply the technique to obtain a surprising and “decentralized” representation of the serial rule. Further applications construct new sd-efficient rules.24 month embargo; available online 31 July 2019.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Wary of the worst: Maximizing award guarantees when new claimants may arrive

When rationing a resource or adjudicating conflicting claims, the arrival of new agents necessitates revision. Adopting a worst-case perspective, we introduce guarantee structures to measure the protection a rule provides to either individuals or groups in these circumstances. With the goal of maximizing guarantees for those in the original group, we characterize the constrained equal awards rule. Requiring that a rule provide protection for both the original and arriving agents, so that both gains and losses are shared, we characterize the Talmud rule

On endowments and indivisibility: partial ownership in the Shapley–Scarf model

We introduce a parameterized measure of partial ownership, the a-endowment lower bound, appropriate to probabilistic allocation. Strikingly, among all convex combinations of efficient and group strategy-proof rules, only Gale's Top Trading Cycles is sd efficient and meets a positive alpha-endowment lower bound (Theorem 2); for efficiency, partial ownership must in fact be complete. We also characterize the rules meeting each alpha-endowment lower bound (Theorem 1). For each bound, the family is a semi-lattice ordered by strength of ownership rights. It includes rules where agents' partial ownership lower bounds are met exactly, rules conferring stronger ownership rights, and the full endowments of TTC. This illustrates the trade-off between sd efficiency and flexible choice of ownership rights .12 month embargo; published online: 12 July 2019This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Essays on social choice and object allocation.

Thesis (Ph. D.)--University of Rochester. Department of Economics, 2016.This collection of essays studies the properties of collective decision procedures when monetary compensation is unavailable. The first three chapters consider abstract social choice settings, emphasizing solidary and strategic properties of rules. The final chapter narrows the focus to object allocation and investigates efficiency and strategic properties. Broadly, solidarity requires that, when some aspect of the environment changes, all individuals are affected similarly, either sharing the benefits or losses. Recognising other individuals as a relevant component of one's environment, we apply this principle to changes in the population or preferences of other individuals. Narrowing our solidarity requirement, our properties ask that individuals be affected in the same direction, avoiding only those cases in which some gain while others lose. Chapter 1 begins our study of social choice. When choosing between two alternatives, we find that only rules satisfying our solidarity requirements and efficiency require consensus: Each rule selects pre-determined alternative unless all individuals prefer the other. We further derive logical relationships among solidarity and strategic properties extend the model to accommodate individuals who are indifferent between the alternatives. Moving beyond the binary setting, we quickly reach an impossibility: No efficient rules satisfy our solidarity property. Chapter 2 moves to preference aggregation. Supposing that individuals report rankings over alternatives, we adopt a conservative approach to infer limited preferences over orders. Adapting the solidarity principle to the resulting incomplete preferences, we formulate new axioms requiring solidarity when the preferences of some agents chance. Although the most general requirement proves incompatible with efficiency, restriction to the smallest change in preferences, transposition of a single pair of alternatives, leads to a characterization of the "status quo" rules. We further extend these rules to allow indifferences in the status quo order and offer a simple algorithm to apply these rules. Chapter 3 considers another specialized model of social choice, the problem of choosing the level of a public good when individuals have single-peaked preferences over the feasible levels. Imposing a measure on the space of preferences, we introduce a parameterized family of solidarity axioms which restrict the conclusion to preference changes below a threshold size. With these axioms, we test the robustness of previous results characterizing the "target" rules by efficiency and unrestricted solidarity axioms. In fact, together with efficiency, each restricted axiom also characterizes the target rules. Moving away from social choice, Chapter 4 studies to object allocation. In this setting, we propose to evaluate rules by their performance ex-ante, before individuals learn their own preferences. To do so, we introduce an appropriate strengthening of efficiency which applies at the ex-ante stage and identify rules satisfying this property. When combined with standard incentive properties, our efficiency notion characterizes the family of priority rules. However, the negative implications of this narrow are tempered in symmetric environments where we find that other incentive-compatible rules achieve the same utilitarian welfare as the priority rules and lead to more equitable distributions of expected utility