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.