论文标题
概率投票模型具有不同的相关衰减速度
Probabilistic Voting Models with Varying Speeds of Correlation Decay
论文作者
论文摘要
我们使用de Finetti措施序列在两层投票系统的多组设置中对投票行为进行建模。我们的模型是通过使用概率度量的DE Finetti表示（即有条件独立概率度量的混合物）来定义的，该模型描述了投票行为。 De Finetti措施描述了选民与可能的外部影响之间的相互作用。我们假设对于每个人口规模，有一个（潜在的）De Finetti措施，随着人口的增长，De Finetti措施的序列薄弱地与起源处的DIRAC度量相聚，这代表着随着人口的增长而削弱社会凝聚力的趋势。最终的模型涵盖了各种各样的行为，从快速收敛下的独立投票，一种具有自身行为模式的关键收敛速度，到亚临界收敛速度，与现实世界投票数据的经验证据相一致，与现实世界中使用的先前概率模型相反，该模型在投票的研究中使用。可以使用这些模型，例如研究两层投票系统中最佳投票权重的问题。
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.
