Evaluating Voter–Candidate Proximity in a Non-Euclidean Space

Abstract

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.

A Matter of Representation: Spatial Voting and Inconsistent Policy Preferences

“…This functional form implies that voters are risk averse in policy distance (see Berinsky and Lewis 2007;Ye, Li, and Leiker 2011), which has the important implication that variance in policy beliefs negatively affects expected utility. Assuming other commonly employed norms (e.g., Euclidean or city block norm) makes a conclusion later on analytically intractable, but does not change the intuition of the analysis.…”