Election Turnout Statistics in Many Countries: Similarities, Differences, and a Diffusive Field Model for Decision-Making

Abstract

We study in details the turnout rate statistics for 77 elections in 11 different countries. We show that the empirical results established in a previous paper for French elections appear to hold much more generally. We find in particular that the spatial correlation of turnout rates decay logarithmically with distance in all cases. This result is quantitatively reproduced by a decision model that assumes that each voter makes his mind as a result of three influence terms: one totally idiosyncratic component, one city-specific term with short-ranged fluctuations in space, and one long-ranged correlated field which propagates diffusively in space. A detailed analysis reveals several interesting features: for example, different countries have different degrees of local heterogeneities and seem to be characterized by a different propensity for individuals to conform to the cultural norm. We furthermore find clear signs of herding (i.e., strongly correlated decisions at the individual level) in some countries, but not in others.

Competing opinions and stubborness: Connecting models to data

“…In this section, we show that the CCIS model can reproduce two empirical observations: (1) distributions of votes received by candidates, when appropriately rescaled, follow a nearly universal function [12,13] and (2) correlations between voters decrease only logarithmically as a function of distance [22,34]. We find agreement between the CCIS model and both empirical observations using spatially extended networks with heavytailed degree distribution (a reasonable model for social Table I for the definitions of parameters).…”

“…Next, we show that the CCIS model creates correlations that decrease logarithmically with distance, as seen in empirical studies [22,34]. This behavior is not unique to our model because many models can create logarithmically decreasing correlations as they approach the VM Universality Class [55] in some special parameter range.…”

“…2) showing that the logarithmically decreasing correlations are robust. Inset: similar correlations are seen for data from the year 2000 United States Presidential election [34].…”

“…5 are calculated. To be consistent with previous work [22,34] and Fig. 5a, we define the normalized correlation in our figures as:…”

“…Recent empirical studies have shown that the spatial correlation of vote-shares in United States elections and the spatial correlation of turn-out rates in European elections decreases as the log of the distance between two voting districts [22,34]. This contrasts to correlations of spins in many statistical mechanic spin models, which decrease as a power law or exponentially with distance [35], but is a prediction of some spin (or opinion) models, such as the VM, at an arbitrary, fixed time [9,10,36].…”