Clipped Linear Lottery brings stability to randomized selection

A team led by Alexander Goldberg (CMU), Giulia Fanti (Berkeley), and Nihar Shah (CMU) published a paper introducing the Clipped Linear Lottery (CLL), a mechanism for randomized selection in competitive processes like grant funding, admissions, and hiring. The key innovation is formalizing 'smoothness' as a Lipschitz condition on the mapping from candidate scores to selection probabilities. Existing partial lotteries are highly unstable: a tiny change to a single candidate's score can cause wild swings in everyone's odds, undermining the very purpose of introducing randomness near decision boundaries. The CLL solves this by making selection probabilities scale linearly with score between two thresholds — above the top threshold you're always accepted, below the bottom you're always rejected. The authors prove the CLL's worst-case regret matches a theoretical lower bound for any smooth selection rule, up to a factor of (1 − k/n) where k/n is the acceptance rate.

In real-world tests on peer review data from ICLR 2025, NeurIPS 2024, and the Swiss National Science Foundation, existing lottery designs showed dramatic instability even under perturbations to a single score. The Clipped Linear Lottery, by contrast, maintained stable probabilities and achieved a better smoothness-utility tradeoff than alternatives based on Individual Fairness or Differential Privacy. This work provides a principled, provably near-optimal solution for organizations that want the benefits of randomization (reducing gaming of fine-grained scores) without the chaos of unstable outcomes. The paper is available on arXiv (2605.20069).