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

Published online by Cambridge University Press:  04 January 2017

Keith T. Poole
Keith T. Poole*
Affiliation:
Department of Political Science, University of Houston, Houston, TX 77204-3011
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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.

Type
Research Article
Information
Political Analysis , Volume 9 , Issue 3 , January 2001 , pp. 211 - 226
Copyright
Copyright © 2001 by the Society for Political Methodology 

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References

Best, Alvin M., Young, Forrest W., and Hall, Robert G. 1979. “On the Precision of a Euclidean Structure.” Psychometrika 44: 395–408.Google Scholar
Clinton, Joshua, Jackman, Simon, and Rivers, Douglas. 2000. “The Statistical Analysis of Legislative Behavior: A Unified Approach.” Paper presented at the Southern California Area Methodology Program, University of California, Santa Barbara, May 12–13.Google Scholar
Coombs, Clyde. 1964. A Theory of Data. New York: Wiley.Google Scholar
Davis, Otto A., and Hinich, Melvin J. 1966. “A Mathematical Model of Policy Formation in a Democratic Society.” In Mathematical Applications in Political Science II, ed. Bernd, J. Dallas, TX: Southern Methodist University Press.Google Scholar
Davis, Otto A., and Hinich, Melvin J. 1967. “Some Results Related to a Mathematical Model of Policy Formation in a Democratic Society.” In Mathematical Applications in Political Science III, ed. Bernd, J. Charlottesville: University of Virginia Press.Google Scholar
Davis, Otto A., Hinich, Melvin J., and Ordeshook, Peter C. 1970. “An Expository Development of a Mathematical Model of the Electoral Process.” American Political Science Review 64: 426–448.Google Scholar
Dhrymes, Phoebus J. 1978. Introductory Econometrics. New York: Springer-Verlag.CrossRefGoogle Scholar
Heckman, James J., and Snyder, James M. 1997. “Linear Probability Models of the Demand for Attributes with an Empirical Application to Estimating the Preferences of Legislators.” Rand Journal of Economics 28: 142–189.CrossRefGoogle Scholar
Jackman, Simon. 2000. “Estimation and Inference are Missing Data Problems: Unifying Social Science Statistics via Bayesian Simulation.” Political Analysis 8(4): 307–332.Google Scholar
Ladha, Krishna K. 1991. “A Spatial Model of Legislative Voting with Perceptual Error.” Public Choice 68: 151–174.Google Scholar
Londregan, John B. 2000. “Estimating Legislators’ Preferred Points.” Political Analysis 8(1): 35–56.CrossRefGoogle Scholar
Londregan, John B., and Poole, Keith T. 2001. “Estimating Standard Errors for Spatial Models of Parliamentary Voting,” Manuscript. Houston, TX: University of Houston.Google Scholar
Lord, F. M. 1983. “Unbiased Estimates of Ability Parameters, of Their Variance, and of Their Parallel Forms Reliability.” Psychometrika 48: 477–482.Google Scholar
MacRae, Duncan Jr. 1958. Dimensions of Congressional Voting. Berkeley: University of California Press.Google Scholar
Poole, Keith T. 2000. “Non-parametric Unfolding of Binary Choice Data.” Political Analysis 8(3): 211–237.Google Scholar
Poole, Keith T., and Rosenthal, Howard. 1985. “A Spatial Model for Legislative Roll Call Analysis.” American Journal of Political Science 29: 357–384.Google Scholar
Poole, Keith T., and Rosenthal, Howard. 1991. “Patterns of Congressional Voting.” American Journal of Political Science 35: 228–278.Google Scholar
Poole, Keith T., and Rosenthal, Howard. 1997. Congress: A Political-Economic History of Roll Call Voting. New York: Oxford University Press.Google Scholar
Poole, Keith T., and Rosenthal, Howard. 2001. “D-NOMINATE After 10 Years: A Comparative Update to Congress: A Political-Economic History of Roll Call Voting.” Legislative Studies Quarterly 26: 5–26.Google Scholar
Rasch, G. 1961. “On General Laws and the Meaning of Measurement in Psychology.” Proceedings of the IV Berkeley Symposium on Mathematical Statistics and Probability 4: 321–333.Google Scholar
Schonemann, Peter H. 1966. “A Generalized Solution of the Orthogonal Procrustes Problem.” Psychometrika 31: 1–10.Google Scholar