具有变化相关衰减速度的概率投票模型
Probabilistic Voting Models with Varying Speeds of Correlation Decay
AI总结：
本文提出了一种具有变化相关衰减速度的概率投票模型，用于研究群体规模增长对社会凝聚力的影响以及投票行为的多样性。
摘要：
我们利用de Finetti测度的序列来建模多群体设置下的投票行为，采用de Finetti测度来描述投票行为。de Finetti测度描述了选民与可能的外部影响之间的相互作用。我们假设对于每个群体规模，可能存在不同的de Finetti测度，并且随着群体规模的增长，de Finetti测度序列弱收敛到原点的Dirac测度，表示随着群体规模增大，社会凝聚力趋于减弱。所得到的模型涵盖了广泛的行为范围，从在快速收敛下趋于独立投票，到具有自身行为模式的临界收敛速度，再到产生与现实世界投票数据一致的亚临界收敛速度的模型，与之前用于研究投票的概率模型不同。这些模型可以用于研究两层投票系统中的最优投票权重问题。
英文摘要：
We model voting behaviour in the multi-group setting of a two-tier voting system using sequences of de Finetti measures. Our model is defined by using the de Finetti representation of a probability measure (i.e. as a mixture of conditionally independent probability measures) describing voting behaviour. The de Finetti measure describes the interaction between voters and possible outside influences on them. We assume that for each population size there is a (potentially) different de Finetti measure, and as the population grows, the sequence of de Finetti measures converges weakly to the Dirac measure at the origin, representing a tendency toward weakening social cohesion as the population grows large. The resulting model covers a wide variety of behaviour, ranging from independent voting in the limit under fast convergence, a critical convergence speed with its own pattern of behaviour, to a subcritical convergence speed which yields a model in line with empirical evidence of real-world voting data, contrary to previous probabilistic models used in the study of voting. These models can be used, e.g., to study the problem of optimal voting weights in two-tier voting systems.
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