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arXiv · 2402.11104

Computing Voting Rules with Elicited Incomplete Votes

Daniel Halpern·Safwan Hossain·Jamie Tucker-Foltz
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Abstract

Motivated by the difficulty of specifying complete ordinal preferences over a large set of $m$ candidates, we study voting rules that are computable by querying voters about $t < m$ candidates. Generalizing prior works that focused on specific instances of this problem, our paper fully characterizes the set of positional scoring rules that can be computed for any $1 \leq t < m$, which, notably, does not include plurality. We then extend this to show a similar impossibility result for single transferable vote (elimination voting). These negative results are information-theoretic and agnostic to the number of queries. Finally, for scoring rules that are computable with limited-sized queries, we give parameterized upper and lower bounds on the number of such queries a deterministic or randomized algorithm must make to determine the score-maximizing candidate. While there is no gap between our bounds for deterministic algorithms, identifying the exact query complexity for randomized algorithms is a challenging open problem, of which we solve one special case.

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Daniel Halpern, Safwan Hossain, Jamie Tucker-Foltz. 2024-02-16. Computing Voting Rules with Elicited Incomplete Votes. https://arxiv.org/abs/2402.11104

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