论文标题
社会两极分化的数学措施
Mathematical measures of societal polarisation
论文作者
论文摘要
在意见动力学中，就像一般用法一样，极化是主观的。要了解两极分化，我们需要开发更精确的方法来衡量社会中的协议。本文介绍了从社会的图和网络表示以及信息理论差异或距离指标中得出的四个数学衡量标准。其中两种方法是最小值流量和光谱半径，依赖于图理论，并根据网络的结构特征定义了极化。其他两种方法表示意见为概率密度函数，并将Kullback Leibler Divergence和Hellinger距离作为极化度量。我们提供了来自两个通用模型的一系列意见动力学模拟，以测试方法的有效性。结果表明，这四个措施提供了对极化不同方面的见解，并允许对社交网络进行实时监控以实现极化指标。这三个措施，光谱半径，kullback leibler发散和地狱林的距离，在不同量的极化之间平稳地描绘了模拟中有多少个群集，同时还可以使用更加粒度测量模拟如何与共识进行测量。 Min-Max流无法完成这种细微差别。
In opinion dynamics, as in general usage, polarisation is subjective. To understand polarisation, we need to develop more precise methods to measure the agreement in society. This paper presents four mathematical measures of polarisation derived from graph and network representations of societies and information theoretic divergences or distance metrics. Two of the methods, min-max flow and spectral radius, rely on graph theory and define polarisation in terms of the structural characteristics of networks. The other two methods represent opinions as probability density functions and use the Kullback Leibler divergence and the Hellinger distance as polarisation measures. We present a series of opinion dynamics simulations from two common models to test the effectiveness of the methods. Results show that the four measures provide insight into the different aspects of polarisation and allow real-time monitoring of social networks for indicators of polarisation. The three measures, the spectral radius, Kullback Leibler divergence and Hellinger distance, smoothly delineated between different amounts of polarisation, i.e. how many cluster there were in the simulation, while also measuring with more granularity how close simulations were to consensus. Min-max flow failed to accomplish such nuance.
