Spatial correlations in vote statistics: a diffusive field model for decision-making

TL;DR

This paper analyzes French election data to reveal stable spatial correlations in turnout rates, proposing a diffusive cultural field model to explain how regional decision biases evolve and influence voting behavior.

Contribution

It introduces a novel diffusive field model for decision-making, linking spatial correlations in voting data to a two-dimensional diffusion process of cultural influences.

Findings

Turnout rate distributions are stable over time.

Spatial correlations decay logarithmically with distance.

A diffusive cultural field explains regional voting patterns.

Abstract

We study the statistics of turnout rates and results of the French elections since 1992. We find that the distribution of turnout rates across towns is surprisingly stable over time. The spatial correlation of the turnout rates, or of the fraction of winning votes, is found to decay logarithmically with the distance between towns. Based on these empirical observations and on the analogy with a two-dimensional random diffusion equation, we propose that individual decisions can be rationalised in terms of an underlying "cultural" field, that locally biases the decision of the population of a given region, on top of an idiosyncratic, town-dependent field, with short range correlations. Using symmetry considerations and a set of plausible assumptions, we suggest that this cultural field obeys a random diffusion equation.