Improving on a Lottery: Efficient Estimation of Optimal Assignment Rules

Economics > Econometrics [Submitted on 22 Dec 2025 (v1), last revised 16 Jun 2026 (this version, v3)] Title:Improving on a Lottery: Efficient Estimation of Optimal Assignment Rules View PDF HTML (experimental)Abstract:Scarce opportunities are often allocated by lotteries. We study how to improve such allocations by estimating optimal assignment rules that maximize welfare net of a Kullback--Leibler penalty for departing from the benchmark randomization. The framework covers discrete, continuous, and mixed treatments. Regret is asymptotically quadratic in the estimation error, so inefficient estimation raises the mean of limiting regret, not merely its dispersion. We show that inverse probability weighting with known assignment probabilities is inefficient, whereas estimated-propensity and doubly robust welfare criteria attain the efficient regret distribution. Simulations and a commitment-savings application quantify the resulting precision gains. Submission history From: Yue Fang [view email][v1] Mon, 22 Dec 2025 10:10:35 UTC (138 KB) [v2] Sat, 7 Feb 2026 02:47:14 UTC (138 KB) [v3] Tue, 16 Jun 2026 10:55:17 UTC (910 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.