Time scales in the dynamics of political opinions and the voter model

P. Meyer, Ralf Metzler
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Abstract

Opinions in human societies are measured by political polls on time scales of months to years. Such opinion polls do not resolve the effects of individual interactions but constitute a stochastic process. Voter models with zealots (individuals who do not change their opinions) can describe the mean-field dynamics in systems where no consensus is reached. We show that for large populations, the voter model with zealots is equivalent to the noisy voter model and it has a single characteristic time scale associated with the number of zealots in the population. We discuss which parameters are observable in real data by analysing time series of approval ratings of several political leaders that match the statistical behaviour of the voter model using the technique of the time-averaged mean squared displacement. The characteristic time scale of political opinions in societies is around 12 months, so it cannot be resolved by analysing election data, for which the resolution is several years. The effective population size in all fitted data sets is much smaller than the real population size, which indicates positive correlations of successive voter model steps. We also discuss the heterogeneity of voters as a cause of subdiffusion on long time scales, i.e., slow changes in the society.
政治观点动态的时间尺度和选民模型
人类社会的舆论是通过政治民意测验来衡量的,时间尺度从几个月到几年不等。这种民意测验并不解决个体互动的影响,而是构成一个随机过程。带有狂热者(不改变观点的个体)的选民模型可以描述无法达成共识的系统中的均值场动态。我们的研究表明,对于大群体而言,带有狂热者的选民模型等同于噪声选民模型,而且它具有与群体中狂热者数量相关的单一特征时间尺度。我们通过分析几位政治领袖支持率的时间序列,讨论了哪些参数可以在真实数据中观测到,这些数据与选民模型的统计行为相吻合,我们使用了时间平均均方差技术。社会政治观点的特征时间尺度约为 12 个月,因此无法通过分析选举数据来解决,因为选举数据的分辨率为数年。所有拟合数据集的有效人口规模都远小于实际人口规模,这表明连续选民模型步骤之间存在正相关。我们还讨论了选民的异质性是导致长时间尺度亚扩散的原因,即社会的缓慢变化。
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