AI 中文总结
研究社交网络投票前社交互动下的多数正确性，基于狂热者 - 逆向选民模型，刻画了完全混合选民群体及不同网络的情况，建立有限选民群体的孔多塞型保证，发现聚合失败，揭示拓扑结构对投票相关性及多数准确性的影响。
AI 中文摘要
我们研究了在社交网络上进行持续社交互动后再投票时的多数正确性。受孔多塞陪审团定理启发，考虑在存在竞争的坚定领导者（狂热者）情况下，不知情选民通过重复互动来修正投票意图的二元选择。在这个狂热者 - 逆向选民模型中，选民可能模仿或反对他们遇到的观点。对于完全混合的选民群体，我们刻画了投票的长期分布以及选民之间产生的相关结构，并表明在对领导者影响力进行适当重新缩放后，厄多斯 - 雷尼网络表现出相同的多数正确性行为。基于这些结果，我们建立了有限选民群体的孔多塞型保证：当审议后的个体正确性超过随机选择时，严格多数比随机选择的选民更有可能选择正确的选项。同时，我们也发现了一种聚合失败：相对于选民仅对狂热者做出反应的无审议基准，社交互动会降低多数准确性。随着选民规模趋于无穷大，除非社交更新纯粹是从众的，否则这种有限选民群体的优势就会消失，这揭示了完全从众的临界点：任何持续的逆向更新都会使个体和多数正确性降至二分之一的随机选择水平。在无标度、环形和小世界网络上的模拟进一步表明，拓扑结构很重要，因为它塑造了由社会影响产生的投票相关性：中心节点主导的结构产生更强的正相关性和更低的多数准确性，而空间结构化网络产生较弱的相关性，保留更多有效的独立判断数量，并提高多数准确性。
英文摘要
We study majority correctness when voting is preceded by sustained social interaction on a social network. Motivated by the Condorcet Jury Theorem, we consider a binary choice with an objectively correct alternative, where uninformed voters revise their vote intentions through repeated interaction in the presence of competing committed leaders (zealots). In this zealot--contrarian voter model, voters may either imitate or oppose the views they encounter. For fully mixed electorates, we characterize the long-run distribution of votes and the correlation structure induced among voters, and we show that Erdős--Rényi networks exhibit the same majority-correctness behavior after an appropriate rescaling of leader influence. Building on these results, we establish a finite-electorate Condorcet-type guarantee: when post-deliberation individual correctness exceeds random choice, a strict majority is more likely to select the correct alternative than a randomly chosen voter. At the same time, we identify an aggregation failure: social interaction can reduce majority accuracy relative to a no-deliberation benchmark in which voters respond only to zealots. As the electorate size tends to infinity, this finite-electorate advantage disappears unless social updating is purely conformist, revealing a tipping point at full conformity: any persistent contrarian updating drives both individual and majority correctness to the random choice level of one half. Simulations on scale-free, ring, and small-world networks further show that topology matters because it shapes the vote correlations generated by social influence: hub-dominated structures generate stronger positive correlations and lower majority accuracy, whereas spatially structured networks generate weaker correlations, preserve a larger effective number of independent judgments, and improve majority accuracy.
Comments48 pages, 8 figures
