In Memoriam: Patrick Harless
Scholar, teacher, friend - 1980-2020
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.
Reaching consensus: solidarity and strategic properties in binary social choice
We study solidarity and strategic properties in binary social choice. We consider both the standard setting with strict preferences and the “full” preference domain which allows for indifference. Two solidarity properties drive our investigation: “Welfare dominance under preference replacement”, which says that when the preferences of one agent change, the other agents all weakly gain or all weakly lose; and “population monotonicity”, which requires the same conclusion when one agent leaves. We identify the families of rules satisfying these properties on each preference domain. Additionally requiring efficiency characterizes the “consensus” rules in each case. We also relate welfare dominance to other properties. Two results highlight the role of indifference: Welfare dominance implies “anonymity” when preferences are strict, but not otherwise; “group strategy-proofness” implies welfare dominance when indifference is allowed, but not otherwise. Finally, we introduce a “duality” operator which structures the space of rules and extends our results to a model in which rules may select neither alternative. Only in this case are our solidarity properties consistent with “neutrality”.
Immediate acceptance with or without skips? Comparing school assignment procedures
The standard execution of the popular Immediate Acceptance, or Boston Mechanism, requires that students apply to schools that have reached capacity whereas its variant allows students to skip these applications. While the modification appears reasonable, even obviously desirable, a complete axiomatic comparison is unfavorable. The variant does reduce manipulability, but only narrowly, advantaged only when some schools have no available seats. On the other hand, the standard approach enjoys monotonicity and robustness properties lost with the variant under which adding school seats may perversely harm students. Efficiency criteria favor neither approach with each performing better in some settings.
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.
Scribing: A Technology-Based Instructional Strategy
In this article, the author presents one instructional strategy--scribing--tailored to the Tablet PC. He illustrates the role of the scribe during discussion through two classroom examples: (1) generalizing the polygon sum theorem; and (2) proving the third angle theorem. Then he analyzes scribing as an instructional strategy as well as students' reflections on their experiences with scribing. (Contains 3 figures.)
Solidarity in preference aggregation: Improving on a status quo
Working in the Arrowianframework, we search for preference aggregation rules with desirable solidarity properties. In a fixed-population setting, we formulate two versions of the solidarity axiom welfare dominance under preference replacement. Although the stronger proves incompatible with efficiency, the combination of efficiencyand our second version leads to an important class of rules which improve upon a “status quo” order. These rules are also strategy-proof, which reveals a further connection between solidarity and incentive properties. Allowing the population to vary, we again characterize the status quo rules by efficiencyand a different solidarity axiom, population monotonicity. This extends a similar characterization of a subclass of these rules by Bossert and Sprumont(2014).