Description
This book presents a simple geometric model of voting as a tool to analyze parliamentary roll call data. Each legislator is represented by one point and each roll call is represented by two points that correspond to the policy consequences of voting Yea or Nay. On every roll call each legislator votes for the closer outcome point, at least probabilistically. These points form a spatial map that summarizes the roll calls. In this sense a spatial map is much like a road map because it visually depicts the political world of a legislature. The closeness of two legislators on the map shows how similar their voting records are, and the distribution of legislators shows what the dimensions are. These maps can be used to study a wide variety of topics including how political parties evolve over time, the existence of sophisticated voting and how an executive influences legislative outcomes.
Chapter
Psychometrics and Tests of Spatial Theory
Why So Few Dimensions? Psychometrics and Multidimensional Scaling
The Breakthrough: The Two-Space Theory
The 1964 Civil Rights Act
A Road Map to the Rest of This Book
2 The Geometry of Parliamentary Roll Call Voting
The Geometry in One Dimension
The Rasch Model From Educational Testing
The Pick-Any-N Data Model from Marketing
Summary: One-Dimensional Perfect Voting
The Geometry in More than One Dimension
Summary: Perfect Voting in More than One Dimension
The Relationship to the Geometry of Probit and Logit
Appendix: Proof that if Voting Is Perfect in One Dimension, then the First Eigenvector Extracted from the Double-Centered…
3 The Optimal Classification Method
The One-Dimensional Maximum Classification Scaling Problem - The Janice Algorithm
The Effect of Very Low Error in One Dimension
The Effect of Higher Levels of Error in One Dimension
The Multidimensional Maximum Classification Scaling Problem
Estimating a Roll Call Cutting Plane Given the Legislator Ideal Points
Estimating the Legislator Ideal Points Given the Roll Call Cutting Planes
Appendix: Two Matrix Decomposition Theorems
Theorem I (Singular Value Decomposition)
Theorem II (Eckart and Young)
4 Probabilistic Spatial Models of Parliamentary Voting
The Deterministic Portion of the Utility Function
The Stochastic Portion of the Utility Function
Estimation of Probabilistic Spatial Voting Models
The NOMINATE (Normal-Normal) Model
The Quadratic-Normal (QN) Model
The Bayesian Simulation Approach
5 Practical Issues in Computing Spatial Models of Parliamentary Voting
Standardized Measures of Fit
How to Get Reasonable Starting Values for the Legislator Ideal Points
How Many Dimensions Should I Estimate?
The Problem of Constraints
Computing Made Easy – Some Simple Tricks to Make Estimation Tractable
6 Conducting Natural Experiments with Roll Calls
Multiple-Individuals Experiments
Testing the Effect of a Party Switch
Testing for Shifts in Position Before an Election
Testing for Last-Period and Redistricting Effects
Large-Scale Experiments Using DW-NOMINATE
Experiments with Shift Distances
Experiments with Adding and Subtracting Sets of Roll Calls
Estimating a Common Spatial Map for Two Different Legislatures
The Scientific Status of Geometric Models of Choice and Judgment
Specifying the Sources of Constraint
Unsolved Engineering Problems
Spatial Models of Parliamentary Voting
( Analytical Methods for Social Research )
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