The Structure of Utility in Spatial Models of Voting

Abstract

Empirical models of spatial voting allow legislators’ locations in an abstract policy or ideological space to be inferred from their roll call votes. These are typically random utility models of Euclidean spatial voting, where voters assign utility to each of two alternatives associated with each roll call. The specific functional forms of the utility functions are generally assumed rather than estimated. In this paper, we attempt to infer important features of these utility functions. We first consider a model in which legislators’ utility functions are assumed to be a mixture of the two most commonly assumed utility functions (the Gaussian function assumed by NOMINATE and the quadratic function assumed by IDEAL and many other estimators). Applying this estimator to large number of roll call data sets, we find that in nearly every case legislators’ utility functions are estimated to be very nearly Gaussian. We then relax the usual assumption that each legislator is equally sensitive to policy change and find that extreme legislators are generally more sensitive to policy change than their more centrally located counterparts. This result is substantively important to the formation and interpretation of law, because it suggests that extremists are ideologically rigid whereas moderates are more likely to consider influences that arise outside liberal–conservative conflict. Finally, we considered a third model extension examining the possibility that legislators have asymmetric utility functions. Our results tentatively suggest that, conditional on party, as legislators become more conservative their sensitivity to policy alternatives on the right increases.