孔多塞陪审团定理在多AI顾问情境下的潜在维度
A latent dimension of Condorcet's jury theorem for multiple AI advisers
- Institute of Science Tokyo（东京科学研究所）
- Carnegie Mellon University（卡内基梅隆大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文揭示孔多塞陪审团定理在多AI顾问情境下的潜在维度：增加顾问使分歧更显眼，且当准确率低于0.8时，可见分歧比正确多数更可能发生，影响顾问数量选择与结果呈现。
中文摘要 AI 辅助
当多个AI顾问被问及同一问题时，如在自洽性和LLM作为评审团的应用中，孔多塞陪审团定理预测，增加独立且能干的顾问会使多数决策更加可靠。然而，从用户的视角来看，该定理存在一个潜在维度：增加顾问也会使分歧更加显眼。一个二项模型揭示，随着顾问数量的增加，这种“可见分歧”几乎不可避免，且可靠性与分歧都趋近于确定性，但收敛速率不同。这两个速率在顾问准确率为4/5（0.8）处交叉。低于此值时，可见分歧趋近确定性的速度快于可靠性，且当顾问足够多时，可见分歧比正确多数更可能发生。即使是独立且能干的理想顾问小组，整体上可能是正确的，但表面上却显得分裂；这种分歧本身并不表明聚合失败。顾问的分裂方式也为预测多重性、协调负担和依赖校准提供了共同基础。这些结果表明，在使用多个AI顾问时存在两个不同的决策：咨询多少顾问，以及如何呈现和解读他们的裁决。
英文摘要
When the same question is asked of multiple AI advisers, as in self-consistency and LLM-as-a-judge panels, Condorcet's jury theorem predicts that adding independent, competent advisers makes the majority more reliable. The theorem, however, has a latent dimension when viewed from the user's vantage: adding advisers also makes disagreement more visible. A binomial model reveals that this ``visible dissent'' becomes nearly inevitable as the number of advisers grows, and that reliability and disagreement approach certainty at rates that cross at an adviser accuracy of 4/5 (0.8); below it, visible dissent eventually becomes more likely than a correct majority. Even ideal panels of independent and competent advisers can be correct in aggregate but appear divided; such disagreement does not by itself indicate aggregation failure. The way advisers split also provides a common basis for predictive multiplicity, reconciliation load, and reliance miscalibration. These results separate aggregation from disclosure and turn the latter into testable questions about how disagreement should be presented and interpreted.
