A simple visualization of similarities in voting records.

Legislators are positioned in the plane whereby two voters tend to appear closer to each other the more often their votes agree. Roll calls tend to appear close to those other roll calls which split voters along similar lines.

This procedure is known as “Multidimensional Scaling” (MDS), and solves the following problem: given a set of items and some measure of “dissimilarity” between any pairs of items, how to position these items in the plane so that the pair-wise euclidean distances are a “good” approximation of the dissimilarities? Specifically, the algorithm used here is known as “classical” or “Torgerson” scaling and minimizes the difference between squared dissimilarities and squared distances.

The following measures for dissimilarity are currently available.

For legislators:

- “Euclidean”
- Roughly the square root of the number of opposing votes. (In this case, MDS reduces to a decomposition in “principal components”.)

For roll calls:

- “Rajski”
- Based on Mutual Information
- “Projective”
- Distance in projective space

Dependencies: | NumPy, MDP. (In jython: Jama.) |
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