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arXiv · 2602.08871

Distortion of Metric Voting with Bounded Randomness

Ziyi Cai·D. D. Gao·Prasanna Ramakrishnan·Kangning Wang
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Abstract

We study the design of voting rules in the metric distortion framework. It is known that any deterministic rule suffers distortion of at least $3$, and that randomized rules can achieve distortion strictly less than $3$, often at the cost of reduced transparency and interpretability. In this work, we explore the trade-off between these paradigms by asking whether it is possible to break the distortion barrier of $3$ using only "bounded" randomness. We answer in the affirmative by presenting a voting rule that (1) achieves distortion of at most $3 - \varepsilon$ for some absolute constant $\varepsilon > 0$, and (2) selects a winner uniformly at random from a deterministically identified list of constant size. Our analysis builds on new structural results for the distortion and approximation of Maximal Lotteries and Stable Lotteries.

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Ziyi Cai, D. D. Gao, Prasanna Ramakrishnan, Kangning Wang. 2026-02-09. Distortion of Metric Voting with Bounded Randomness. https://arxiv.org/abs/2602.08871

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