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The Geometry of Multidimensional Quadratic Utility in Models of Parliamentary Roll Call Voting

  • Keith T. Poole (a1)

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.

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Alvin M. Best , Forrest W. Young , and Robert G. Hall 1979. “On the Precision of a Euclidean Structure.” Psychometrika 44: 395408.

Otto A. Davis , Melvin J. Hinich , and Peter C. Ordeshook 1970. “An Expository Development of a Mathematical Model of the Electoral Process.” American Political Science Review 64: 426448.

Phoebus J. Dhrymes 1978. Introductory Econometrics. New York: Springer-Verlag.

James J. Heckman , and James M. Snyder 1997. “Linear Probability Models of the Demand for Attributes with an Empirical Application to Estimating the Preferences of Legislators.” Rand Journal of Economics 28: 142189.

Simon Jackman . 2000. “Estimation and Inference are Missing Data Problems: Unifying Social Science Statistics via Bayesian Simulation.” Political Analysis 8(4): 307332.

Krishna K. Ladha 1991. “A Spatial Model of Legislative Voting with Perceptual Error.” Public Choice 68: 151174.

John B. Londregan 2000. “Estimating Legislators’ Preferred Points.” Political Analysis 8(1): 3556.

F. M. Lord 1983. “Unbiased Estimates of Ability Parameters, of Their Variance, and of Their Parallel Forms Reliability.” Psychometrika 48: 477482.

Keith T. Poole 2000. “Non-parametric Unfolding of Binary Choice Data.” Political Analysis 8(3): 211237.

Keith T. Poole , and Howard Rosenthal . 1985. “A Spatial Model for Legislative Roll Call Analysis.” American Journal of Political Science 29: 357384.

Keith T. Poole , and Howard Rosenthal . 1991. “Patterns of Congressional Voting.” American Journal of Political Science 35: 228278.

Keith T. Poole , and Howard Rosenthal . 2001. “D-NOMINATE After 10 Years: A Comparative Update to Congress: A Political-Economic History of Roll Call Voting.” Legislative Studies Quarterly 26: 526.

Peter H. Schonemann 1966. “A Generalized Solution of the Orthogonal Procrustes Problem.” Psychometrika 31: 110.

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Political Analysis
  • ISSN: 1047-1987
  • EISSN: 1476-4989
  • URL: /core/journals/political-analysis
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