The Geometry of Multidimensional Quadratic Utility in Models of Parliamentary Roll Call V oting

Keith T. Poole

No 2000-17, GSIA Working Papers from Carnegie Mellon University, Tepper School of Business

Abstract: In a standard spatial model of Parliamentary roll call voting with quadratic utility, the ligislator votes for the policy outcome corresponding to Yea if her utility for Yea is greater than her utility for Nay. The voting decision of the legislator is modeled as a function of the difference between these two utilities. This utility difference has a simple geometric interpretation that can be exploited to estimate legislator ideal points and roll call parameters in a standard framework where the stochastic portion of the utility function is normally distributed. The geometry is almost identical to that used in Poole (2000) to develop a non-parametric unfolding of binary choice data and the algorithms developed by Poole (2000) can be easily modified to implement the standard maximum likelihood model.

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