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

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.