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arXiv · 2608.24193

Optimal Rank Lotteries for Truthful Unit-Interval Covering

Alexandros A. Voudouris
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Abstract

In truthful interval covering, each agent has a private interval of unit length, and the goal is to decide where to place a public unit interval so as to minimize the total uncovered length while incentivizing the agents to be truthful. Previous work proposed a universally strategyproof lottery over order-statistic mechanisms with approximation ratio at most $5/3$, and established a lower bound of $3/2-o(1)$ for this class of mechanisms. We close this gap by characterizing the approximation ratio of every report-independent lottery over order-statistics. In particular, we show that, for every $n\ge2$, the optimal approximation ratio for this class is $\frac32-\frac{1}{2\lfloor n/2\rfloor}$. Beyond rank lotteries, we show that every universally strategyproof randomized mechanism has approximation ratio at least $9/8$.

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Alexandros A. Voudouris. 2026-08-25. Optimal Rank Lotteries for Truthful Unit-Interval Covering. https://arxiv.org/abs/2608.24193

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