Adjustment of initial estimates of voter transition probabilities to guarantee consistency and completeness

Abstract

The estimation of voter shifts (stayers and switchers) between elections is an active area of research that, for decades, has attracted the interest of many scholars. The voter transitions are typically summarised in a row-standardised proportion (probability) matrix. This matrix is usually unknown, despite it being of interest to many agents, including party teams, the media and political scientists. When surveys are used to approximate this matrix, it is not uncommon for the estimated matrix to be inconsistent and even incomplete. The iterative proportional fitting algorithm solves inconsistency but cannot fix incompleteness. Hierarchical Bayesian models that combine aggregate and survey estimates can solve both problems, but are extremely complex and data-demanding. This paper details all the scenarios concerning the available information that can be reasonably considered and, within the linear programming framework, develops specific models to reach consistency and completeness. The models are, moreover, quite flexible as they allow analysts to have missing values and to introduce through weights their relative confidences in the different a priori transition proportions. The usefulness of the proposed models is illustrated with real data. Interested readers can easily use these new models with their data as they have been programmed in the function lp_apriori of the R-package lphom.