Multiple options noisy voter model: application to European elections

Abstract

[eng] In the following master thesis we are going to present a noisy voter model based on social influence and recurrent mobility. The state of the agents of the model is described through a ternary option a = {−1, 0, 1}, and interactions between elements holding opposite opinion are not permitted (-1 and 1). The aim is to observe if our model is capable to reproduce the time evoution of real general elections, and the Spanish political context is chosen for a confrontation: IU, PSOE, and PP will correspond respectively to the options (-1,0,1) of our model. During the time evolution the agents will move repeatedly between the municipality in which they live and the municipality in which they work (commuting network), and at each time all agents present in the same municipality will be considered reciprocally neighbours. The commuting network is constructed according with the spanish census data, and electoral results of year 2000 are used as initial state of the whole system. A preliminar statistical analysis of real elections show us that the three options considered can be divided into majoritarian (PSOE and PP) and minoritarian (IU).The original version of the model will not be able to capture the statistical features of real elections data, giving rise to stationary states in which the three options result to be statistically equivalent (on the contrary of what observed in real election data). However, a simple modification of the same model (well sustained theoretically) will permit us to reproduce most of the aspects of time evolution showed by real data, as the stationarity of the vote sharing standard deviations , the conservation of the shape of the vote sharing distrutions, and the time evolution of the average vote sharing of the minoritarian option, which in this modification keep staying minoritarian.