Pessimal Elections for Approximately Dominating Sets

Moses Charikar; Prasanna Ramakrishnan; Kangning Wang

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arXiv · 2608.06872

Pessimal Elections for Approximately Dominating Sets

Moses Charikar·Prasanna Ramakrishnan·Kangning Wang

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Abstract

Condorcet's paradox is a foundational result in social choice theory, showing that no matter which candidate wins an election, a majority of voters may prefer some losing candidate. Worse still, even if the election can choose a committee of $k$ winners, some loser may beat every winner in a majority vote. Recent work showed that this obstruction can be sidestepped by relaxing the majority threshold. For all $\varepsilon > 0$, any election can select a committee of $O(1/\varepsilon^2)$ winners such that no loser is preferred to every winner by $\frac12 + \varepsilon$ fraction of voters. We present a simple construction, found by GPT-5.6 Sol Ultra, which proves that this result is tight up to a constant factor.

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Moses Charikar, Prasanna Ramakrishnan, Kangning Wang. 2026-08-07. Pessimal Elections for Approximately Dominating Sets. https://arxiv.org/abs/2608.06872

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