投票关联下的液体民主：关于平均化与排中律的谬误
Liquid democracy under vote correlation: On the fallacies of averaging and the excluded middle
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中文总结 AI 辅助
本研究针对投票关联下的液体民主场景，提出三种新型委托机制，解决平均化与排中律的谬误问题，保障投票的多数正确性与终端能力提升。
中文摘要 AI 辅助
液体民主允许选民直接投票或将选票委托给他人。现有算法分析为每位选民分配一个单一标量参数，将其解释为投票支持真实结果的独立概率。当委托发生在公共信息以不同方式改变不同选民可靠性之前时，这种表示方式并不适用。在本研究中，我们针对这一现象构建了一个极简的公共信号模型：委托发生在二元公共信号实现之前，投票则在之后进行。以该信号为条件， sink 投票是独立的，且每位选民具有与信号相关的特定能力；从边际来看，正确事件通过公共信号产生关联。我们证明，基于平均能力的委托并非安全的标量化方法：它可能违反“不造成伤害”原则，且一项有益的委托规则可能将选票发送给平均能力更低的选民。我们针对该场景提出并分析了三种新型委托机制：第一种是保守交集机制，仅将选票委托给在所有信号状态下能力均超过委托者预设阈值的邻居，该机制继承了标量能力场景下委托的所有保证；第二种是混杂集机制，允许委托给在某一状态下更受青睐、而在另一状态下能力至多低至预设容忍度的邻居，针对该机制，我们证明了预期边际界限，并确定了获得多数正确性保证所需的权重分散和机制集中条件；最后，在有界度图上，多轮认证路径机制传播非负二维路径认证，该机制无环、可实现逐状态终端能力提升，并能为路径长度和终端投票权重提供统一界限。
英文摘要
Liquid democracy permits voters to vote directly or delegate their votes to others. Existing algorithmic analyses assign each voter a single scalar parameter, interpreted as an independent probability of voting for the ground truth. This representation is inadequate when delegation is fixed before public information changes different voters' reliability in different ways. In this work, we study a minimal common-signal model of this phenomenon. Delegation occurs before a public binary signal is realised, while voting occurs afterwards. Conditional on the signal, sink votes are independent, and each voter has a signal-specific competence; marginally, correctness events are correlated through the common signal. We show that delegation based on average competence is not a safe scalarisation: it can violate do-no-harm, and a beneficial delegation rule may send votes to voters with lower average competence. We present and analyse three novel delegation mechanisms for this setting. The first is a conservative intersection mechanism that delegates only to neighbours whose competence exceeds the delegator's by a prescribed margin in every signal state; the conservative intersection mechanism inherits all the guarantees of delegation in the scalar competence setting. The next mechanism is a confounded-set mechanism that enable the delegation to neighbours who are favoured in one state and worse by at most a prescribed tolerance in the other. For this mechanism, we prove expected-margin bounds, and identify the weight-dispersion and mechanism-concentration conditions needed to obtain majority-correctness guarantees. Finally, on bounded-in-degree graphs, a multi-round certified-path mechanism propagates nonnegative two-dimensional path certificates; it is acyclic, yields statewise terminal competence improvement, and gives uniform bounds on path length and terminal voting weight.
