The communication complexity of a voting rule is the worst-case number of bits that n voters must transmit to a central authority under the most efficient elicitation protocol in an election with m candidates. We study the communication complexity of Instant-Runoff Voting (IRV). Conitzer and Sandholm [2005] established an upper bound of O(n (log m)${}^2$), but did not provide a matching lower bound beyond $Ω$(n log m). We resolve this open problem by raising the lower bound to $Ω$(n (log m)${}^2$) using the fooling set technique, thereby showing that the communication complexity of IRV is $Θ$(n (log m)${}^2$). We further show that this complexity drops to $Θ$(n log m) under the single-peakedness restriction, and that both the IRV-Average variant and Single Transferable Vote (STV), the multiwinner extension of IRV, have the same asymptotic communication complexity as IRV.

翻译：投票规则的通信复杂度是指在候选人数量为m的选举中，n位选民在最有效的征询协议下，必须向中央机构传输的最坏情况下的比特数。我们研究了即时复决投票（IRV）的通信复杂度。Conitzer与Sandholm [2005] 给出了O(n (log m)${}^2$)的上界，但未提供超过$Ω$(n log m)的匹配下界。我们通过使用愚弄集技术将此下界提升至$Ω$(n (log m)${}^2$)，从而解决了这一开放问题，证明IRV的通信复杂度为$Θ$(n (log m)${}^2$)。我们进一步证明，在单一峰值限制下，该复杂度降至$Θ$(n log m)，且IRV平均变体以及IRV的多赢家扩展——单一可转移投票（STV），具有与IRV相同的渐近通信复杂度。