The Geometry of Multidimensional Quadratic Utility in Models of Parliamentary Roll Call Voting
- 4 January 2001
- journal article
- website
- Published by Cambridge University Press (CUP) in Political Analysis
- Vol. 9 (3), 211-226
- https://doi.org/10.1093/polana/9.3.211
Abstract
The purpose of this paper is to show how the geometry of the quadratic utility function in the standard spatial model of choice can be exploited to estimate a model of parliamentary roll call voting. In a standard spatial model of parliamentary roll call voting, the legislator 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. With quadratic utility, this 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 by Poole (2000) to develop a nonparametric unfolding of binary choice data and the algorithms developed by Poole (2000) can be easily modified to implement the standard maximum-likelihood model.Keywords
This publication has 13 references indexed in Scilit:
- D-Nominate after 10 Years: A Comparative Update to Congress: A Political-Economic History of Roll-Call VotingLegislative Studies Quarterly, 2001
- Estimation and Inference Are Missing Data Problems: Unifying Social Science Statistics via Bayesian SimulationPolitical Analysis, 2000
- Nonparametric Unfolding of Binary Choice DataPolitical Analysis, 2000
- Linear Probability Models of the Demand for Attributes with an Empirical Application to Estimating the Preferences of LegislatorsThe RAND Journal of Economics, 1997
- Patterns of Congressional VotingAmerican Journal of Political Science, 1991
- A Spatial Model for Legislative Roll Call AnalysisAmerican Journal of Political Science, 1985
- Maximum likelihood estimation of item response parameters when some responses are omittedPsychometrika, 1983
- On the precision of a euclidean structurePsychometrika, 1979
- An Expository Development of a Mathematical Model of the Electoral ProcessAmerican Political Science Review, 1970
- A generalized solution of the orthogonal procrustes problemPsychometrika, 1966