Analyzing the impacts of socio-economic factors on French departmental elections with CoDa methods

The vote shares by party on a given subdivision of a territory form a vector called composition (mathematically, a vector belonging to a simplex). It is interesting to model these shares and study the impact of the characteristics of the territorial units on the outcome of the elections. In the political economy literature, few regression models are adapted to the case of more than two political parties. In the statistical literature, there are regression models adapted to share vectors including Compositional Data (CoDa) models, but also Dirichlet models, and others. Our goal is to discuss and illustrate the use CoDa regression models for political economy models for more than two parties. The models are fitted on French electoral data of the 2015 departmental elections.