Interpretation of Electoral Results: A Bayesian Analysis

In the days which follow a political election, both the media and the politicians center their discussions on the reallocation of the votes which has taken place from the last election: who has won votes from whom, who has lost votes to whom. Typically, the arguments are only more or less informed guesses based on a simple comparison the global final results in both elections, with no attempt at a formal statistical analysis. In this paper, we formalize the problem, we review the basic elements of the Bayesian paradigm which make it possible to solve it, and we summarize a Bayesian estimation method for the transition probabilities which describe the reallocation of the votes, based on a hierarchical analysis of the results obtained in both elections in a selected set of constituencies. The procedure is illustrated with results obtained at some recent Spanish elections.