8
in error (for full set of chamber measure see Appendix 1). A single dimension does a
more than adequate job of accounting for roll call voting in most of the legislatures. The
average percentage of correctly predicted roll calls for our chambers is about 89% for
both sessions with several chambers well above 90% correct predictions. The Nebraska
Unicameral with its nonpartisanship shows the lowest success in correct predictions,
conforming with prior findings . Adding a second dimension added very little
improvement to most one-dimensional predictions, generally yielding only a less than
two percent improvement for most of the chambers.
2
[Table 1 about here]
While easy to interpret, the correct predictions criterion can be misleading since
the prediction success can be quite high with just naive guessing of the largest marginals.
Hence, the preferred method is to look at how well the one or two dimensional solutions
improve upon what would be achieved with naïve guessing. These measures are
provided in the third and fourth columns of Table 1 (see Appendix 1 for entire set of
chambers). The improvements over raw guessing are substantial in most cases. The
APRE1 (one dimensional aggregate proportion reduction in error) measures are largest
for the Wisconsin House and Senate, Michigan House and Senate, and the Georgia
Senate over the two legislative sessions. Finally, the fourth column of Table 1 shows the
improvement in fit gained by including a second dimension. This number varies
considerably both across legislative chambers, as well as over time within a particular
chamber.
2
The percent correctly classified with the addition of a second dimension is omitted from Table 1 to save
space. The Illinois House and Nebraska chambers saw the greatest improvement in fit (percent correctly
classified) using 2-dimensions. One of these chambers will be explored extensively below.
Convention