Eur. Phys. J. B 75, 395-404 (2010)
https://doi.org/10.1140/epjb/e2010-00151-1

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

¹ Service de Physique de l'État Condensé, Orme des Merisiers, CEA Saclay, 91191 Gif-sur-Yvette, France
² Science & Finance, Capital Fund Management, 6-8 Bd Haussmann, 75009 Paris, France

Corresponding authors: ^a christian.borghesi@cea.fr - ^b jean-philippe.bouchaud@cea.fr

Received: 14 March 2010
Revised: 27 April 2010
Published online: 19 May 2010

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.