Assessing uncertainty of voter transitions estimated from aggregated data. Application to the 2017 French presidential election

Inferring electoral individual behaviour from aggregated data is a very active research area, with ramifications in sociology and political science. A new approach based on linear programming is proposed to estimate voter transitions among parties (or candidates) between two elections. Compared to other linear and quadratic programming models previously published, our approach presents two important innovations. Firstly, it explicitly deals with new entries and exits in the election census without assuming unrealistic hypotheses, enabling a reasonable estimation of vote behaviour of young electors voting for the first time. Secondly, by exploiting the information contained in the model residuals, we develop a procedure to assess the uncertainty in the estimates. This significantly distinguishes our model from other published mathematical programming methods. The method is illustrated estimating the vote transfer matrix between the first and second rounds of the 2017 French presidential election and measuring its level of uncertainty. Likewise, compared to the most current alternatives based on ecological regression, our approach is considerably simpler and faster, and has provided reasonable results in all the actual elections to which it has been applied. Interested scholars can easily use our procedure with the aid of the R-function provided in the Supplemental Material.