Smooth Partial Lotteries for Stable Randomized Selection
Alexander Goldberg, Giulia Fanti, Nihar B. Shah

TL;DR
This paper introduces a new stable partial lottery mechanism called the Clipped Linear Lottery, which improves stability and fairness in randomized selection processes while maintaining near-optimal regret bounds.
Contribution
The paper formalizes the principle of smoothness for partial lotteries, introduces the Clipped Linear Lottery mechanism, and demonstrates its superior stability and utility tradeoff both theoretically and empirically.
Findings
Clipped Linear Lottery's worst-case regret matches theoretical lower bounds.
Existing lottery designs are highly unstable under small score perturbations.
Empirical results show Clipped Linear Lottery outperforms alternatives in real peer review data.
Abstract
Competitive selection processes, from scientific funding to admissions and hiring, use evaluations to score candidates, and eventually choose a subset of them based on those scores. Recently, many organizations have adopted partial lotteries, which randomize selection based on evaluation scores. However, existing lottery designs are inherently unstable, as a small change to a single candidate's score can cause large shifts in their selection probabilities. This instability undermines a key goal of lotteries: reducing the influence of fine-grained score distinctions near the decision boundary. We propose smoothness as a design principle for partial lotteries, formalizing it as a Lipschitz condition on the mapping from review scores over candidates to selection probabilities. We introduce the Clipped Linear Lottery, a simple mechanism in which selection probabilities scale linearly with…
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