The Problem With Analyzing Parliamentary Roll Call Votes With Probit or Logit

Remarks Delivered at CASBS
16 October 2003

Keith T. Poole

1. Introduction -- The Problem of Perfect Voting
   
   
   1. Perfect Voting in Two Dimensions
      
      
   2. Basic Matrix Representation
      
      
2. The Geometry of the Problem
   
   
   1. The Geometry of Probit and Logit
      
      
   2. The Cutting Plane and Normal Vector
      
      
   3. Exploding Probabilities
      
      
   4. Probabilistic Models and Low Levels of Error
      
      
3. The Cutting Plane Procedure
   
   
   1. Exploiting the Basic Geometry to Solve the Problem
      
      
   2. Given the Normal Vector, Find the Best Cutting Plane -- The Janice Algorithm
      
      
   3. Changing the Orientation of the Cutting Plane to find a Better Normal Vector
      
      
   4. Examples
      
      
4. References