Estimating Vote Transition Counts in Ecological Inference

The article is about methods for estimating a table of vote transition counts between two elections, ensuring consistency with the observed marginals, given an estimated table of transition probabilities obtained by some method of ecological inference. We argue that count data are essential for conducting in-depth investigations into voting behavior. Several new methods are compared with Iterative Proportional Fitting (IPF), known for its speed and reliability. To evaluate their performance, we use both simulated data and real electoral results from the 2011 New Zealand general election. An algorithm for simulating artificial electoral data according to the modified Brown and Payne model is presented and models that account for strategic voting are applied to the New Zealand data to reduce ecological bias. Among the methods initially considered, only two valid competitors of IPF emerged, constrained maximum likelihood and minimum Chi-square, with the latter performing significantly better than IPF. We illustrate the potential insights which may be gained from tables of transition counts by an application to transitions from a parliamentary and a regional elections in Umbria, Italy.