Author

Prasanna Ramakrishnan

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Preprint Sep 2026

Stable Voting Rules on the Edge of Optimal Metric Distortion

We prove the existence of a randomized voting rule with metric distortion at most $2.13713$, within $0.025$ of the lower bound of $2.11264$. Our rule comes from a generalization of stable $k$-lotteries developed in the context of committee selection. In contrast to prior work, our rule samples from a single distributio...

Zi-Yi Cai, Moses Charikar, Jabari Hastings et al. · 0 citations

Preprint Sep 2026

Optimal Shallow Circuits for Majority

Four decades on, H{\aa}stad's classical $2^{\Omega(n^{1/(d-1)})}$ lower bound for depth-$d$ circuits computing Parity remains the best known $\mathrm{AC}^0$ circuit lower bound for any explicit function. Majority has long been a compelling candidate for stronger lower bounds: the most natural circuits computing it are...

Victor Lecomte, Prasanna Ramakrishnan · 0 citations