Lars Ehlers | Search arXiv

arXiv2026

Priority Blockers: Welfare and Incentives in Matching under General Constraints

Institutions often face constraints richer than a single capacity. Protecting the priority of a student who cannot be accommodated may then block a lower-priority student who fits. We introduce COP-and-Choose, a cumulative offer process followed by a choice step, and show that its greedy version, which skips such blockers, leaves no student worse off than any fair matching or Knapsack Deferred Acceptance (KDA). Greedy is the unique consistent rule preserving this guarantee. With substitutability and size monotonicity at every school, greedy is strategy-proof and Pareto-undominated among strategy-proof mechanisms. If either fails at a school, one additional capacity-one school yields a market where, under every proposal order, greedy is manipulable and no strategy-proof mechanism weakly Pareto dominates it. In a three-resource refugee-resettlement calibration with simulated preferences, 19--33 percent of families gain relative to KDA and none lose, while 21--83 percent strongly envy another family.

econ.TH↗

arXiv2026

Strategy-Proof and Minimally Wasteful Random Assignment

We study random assignment of indivisible objects among a set of agents with strict preferences and outside options. When agents may rank some objects as unacceptable, we consider different notions of measuring waste of object(s) from an ex-ante perspective. The most natural one is $q$-agent-object-waste whereby both one agent and one of his acceptable objects are unassigned with at least probability $q$. On the one hand, we show that any mechanism satisfying equal treatement of almost equals (whereby any two agents with identical rankings over objects receive the same probability shares for objects they both regard acceptable), strategy-proofness and ex-post weak non-wastefulness (whereby in any assignment in the support we cannot have that both one agent and one of his acceptable objects are unassigned) must be $q$-agent-object-wasteful with $q\geq \frac{1}{6}$. On the other hand, we show that random serial dictatorship (RSD) attains the minimal bound of $\frac{1}{6}$ in this class for four agents or three objects. In addition, we consider $q$-object-wastefulness where an object remains unassigned with probability $q$, while agents, who consider it acceptable, remain unassigned with aggregate probability $q$. We again show that RSD attains the minimal bound of $\frac{1}{4}$ in this class of mechanisms with respect to $q$-object-wastefulness for three objects. Finally, we show that random deferred acceptance (RDA) may be strictly less agent-object-wasteful than RSD (but at the cost of violating equal treatment of almost equals).

econ.TH↗