Majority voting is one of the few black-box interventions that can improve a fixed stochastic predictor: repeated access can be cheaper than changing a high-capability model. Classical fixed-competence theory makes this intervention look monotone -- more votes help above the majority threshold and hurt below it. We show that this picture is fundamentally incomplete. Under the de Finetti representation for exchangeable repeated correctness, voting is governed by a latent distribution of per-example correctness probabilities. Even simple latent mixtures can generate sharply different voting curves, including nonmonotone behavior and, in an explicit construction, infinitely many trend changes. The full latent law determines the curve, but the curve does not determine the law. The exact object recovered by voting is a signed voting signature: at each binomial variance scale, it records excess latent mass above rather than below the majority threshold. Our main theorem proves that the complete odd-budget curve and this signature are equivalent: the curve increments are signed Hausdorff moments, and the full curve recovers the signature uniquely. This viewpoint explains shape phenomena, branch-symmetric nonidentifiability, realizability, variation, and endpoint rates. It also separates estimation regimes: direct per-example success-probability information targets the full signature, whereas fixed-depth grouped labels reveal only a finite prefix.

翻译：多数投票是少数能改进固定随机预测器的黑盒干预手段之一：重复调用可能比修改高能力模型更经济。经典固定能力理论使这种干预看起来是单调的——在多数阈值以上，更多选票有帮助，在阈值以下则有害。我们表明这一图景本质上是不完整的。在可交换重复正确性的德·菲内蒂表示下，投票由每个示例正确概率的潜在分布支配。即使是简单的潜在混合也能生成显著不同的投票曲线，包括非单调行为，并在显式构造中产生无限多次趋势变化。完整的潜在律决定了曲线，但曲线并不决定潜在律。投票精确恢复的对象是带符号的投票签名：在每个二项方差尺度上，它记录了高于而非低于多数阈值的潜在质量盈余。我们的主要定理证明，完整的奇数预算曲线与该签名是等价的：曲线增量是带符号的豪斯多夫矩，而完整曲线唯一恢复该签名。这一观点解释了形状现象、分支对称非可辨识性、可实现性、变化及端点速率。它还将估计状态分离：直接的每个示例成功概率信息针对完整签名，而固定深度的分组标签仅揭示有限前缀。