Evaluating Voter–Candidate Proximity in a Non-Euclidean Space

When applying the proximity model in electoral studies, scholars face the challenge of estimating voter–candidate proximity when voters' responses to issues/policies in a multidimensional policy space are correlated. In this article, we contend that voters' correlated evaluations can be captured by the structure of a non-orthogonal policy space. After orthogonalizing such a space using the Gram-Schmidt process, we can improve our estimation of the spatial distance between voters and candidates. Moreover, our study suggests that in multidimensional space neither the city-block nor the Euclidean distance is ideal for estimating proximity. We propose to use a generalized parametric Minkowski model and our analysis demonstrates that the most appropriate distance metric for a particular study is an empirical issue that hinges on the particular structure of a dataset.