Tree Plurality Veto: Voting in Few Rounds with Efficient Communication and Low Metric Distortion

We consider the metric distortion framework for voting, where $n$ voters and $m$ candidates are embedded in an unknown metric space. A voting rule selects a candidate using only voters' ordinal preferences, and its distortion is the worst-case ratio between the social cost of the selected candidate and the minimum social cost. We study how round complexity trades off against total communication in deterministic voting protocols with low distortion. Deterministic rules can achieve the optimal distortion of $3$ in one round by eliciting complete rankings using $Θ(nm\log m)$ bits, while a direct sequential implementation of PluralityVeto achieves the same distortion using only $O(n\log m)$ b...

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