The Structure of Utility in Spatial Models of Voting

40 Pages Posted: 22 Aug 2009 Last revised: 16 Nov 2009

See all articles by Royce Carroll

Royce Carroll

University of Essex - Department of Government; Rice University - Department of Political Science

Jeffrey B. Lewis

University of California, Los Angeles (UCLA)

James Lo

University of California, Los Angeles (UCLA) - Department of Political Science

Keith T. Poole

University of Georgia - School of Public and International Affairs

Howard Rosenthal

New York University (NYU) - Wilf Family Department of Politics

Date Written: Novermber 13, 2009

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.

Suggested Citation

Carroll, Royce and Lewis, Jeffrey B. and Lo, James and Poole, Keith T. and Rosenthal, Howard, The Structure of Utility in Spatial Models of Voting (Novermber 13, 2009). CELS 2009 4th Annual Conference on Empirical Legal Studies Paper. Available at SSRN: https://ssrn.com/abstract=1459808 or http://dx.doi.org/10.2139/ssrn.1459808

Royce Carroll

University of Essex - Department of Government ( email )

Wivenhoe Park
Colchester CO4 3SQ, CO4 3SQ
United Kingdom

Rice University - Department of Political Science ( email )

MS-24
P.O. Box 1892
Houston, TX 77251-1892
United States
713-348-2103 (Phone)
772-264-8530 (Fax)

HOME PAGE: http://rcarroll.web.rice.edu

Jeffrey B. Lewis

University of California, Los Angeles (UCLA) ( email )

405 Hilgard Avenue
Box 951361
Los Angeles, CA 90095
United States

James Lo

University of California, Los Angeles (UCLA) - Department of Political Science ( email )

Loas Angeles, CA
United States

Keith T. Poole (Contact Author)

University of Georgia - School of Public and International Affairs ( email )

Baldwin Hall
Athens, GA 30602-6254
United States

Howard Rosenthal

New York University (NYU) - Wilf Family Department of Politics ( email )

715 Broadway
New York, NY 10003
United States

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