Estimation of voter transitions and the ecological fallacy

This paper attempts an investigation into the features of ecological fallacy in the context of estimation of voter transitions between two elections. After reviewing some theoretical findings from a statistical point of view, we discuss two tools for checking whether bias is present: (1) fitting models with covariates; (2) comparing the standard errors of transition probabilities computed under ideal conditions against those based on bootstrap methods. Concerning the effect of covariates, we describe two different data generating mechanisms, depending on whether voting decisions are affected by variables measured at the (1) aggregate or (2) the individual level. By theoretical arguments and empirical evidence, we show that, while modelling the effect of covariates removes bias in the first case, it may fail in the second because only aggregate level covariates are usually available. Our investigation relies on the analysis of real and artificial data sets: the latter are obtained by a computer software which mimics voting behaviour and is such that, artificial electoral data with designed size and direction of ecological bias can be produced. An application to a recent election in the city of Turin is also used to illustrate our methodology and findings.