AI 中文总结
本文针对多数民意调查场景提出k参数化的批准投票协议，经度量失真框架评估，最优k下协议度量失真约4.236，且Bucklin规则失真至多为5，协议上界紧且鲁棒性良好。
AI 中文摘要
批准投票是一种简单且广受认可的投票规则：选民提交批准选票（即候选人子集），获得最多批准票的候选人获胜。批准投票的一个主要局限是，若选民对候选人有潜在的严格排序，他们应批准哪些候选人尚不明确。本文针对一种简单的信息场景——多数民意调查，展开批准投票的研究，即假设已知每位候选人获得选民列为首选的比例。基于这些多数民意调查，我们提出一种由分数k∈(0,1)参数化的简单协议：每位选民应批准其偏好列表中包含至少k比例选民首选的最短前缀。我们通过度量失真框架评估该协议，结果表明，当k取最优值时，该规则达到的度量失真为2+√5≈4.236。用于该结论的证明技术还显示，Bucklin投票规则的度量失真至多为5。最后，我们评估协议对噪声的鲁棒性，结果表明所获协议的上界是紧的。
英文摘要
Approval voting is a simple and well-regarded voting rule: voters submit approval ballots (subsets of the candidates) and the candidate receiving the most approvals wins. One major limitation of approval voting is that it is not clear which candidates voters should approve if they have an underlying strict order over the candidates. In this paper, we initiate the study of approval voting under a simple kind of information: plurality polls. That is, we assume that for each candidate we know the share of voters who rank this candidate as their top choice. Using these plurality polls, we suggest a simple protocol parameterized by a fraction $k \in (0,1)$: every voter should approve the smallest prefix of their preference list containing the first choices of at least a fraction $k$ of the voters. We evaluate this protocol via the framework of metric distortion and show that for the optimal choice of $k$, this rule achieves a metric distortion of $2 + \sqrt{5} \simeq 4.236$. The proof techniques we use for this statement also show that the Bucklin voting rule has a metric distortion of at most $5$. Finally, we evaluate the robustness of our protocol to noise and show that the upper bounds obtained for our protocol are tight.
