Unearthing Power Lines

Votes are cast by the full membership in each house of Congress,
but much of the important maneuvering occurs in committees. Graph
theory and linear algebra are two mathematics subjects that have
revealed a level of organization in Congress groups of committees
above the known levels of subcommittees and committees. The result
is based on strong connections between certain committees that can
be detected by examining their memberships, but which were
virtually unknown until uncovered by mathematical analysis.
Mathematics has also been applied to individual congressional
voting records. Each legislator.s record is represented in a matrix
whose larger dimension is the number of votes cast (which in a
House term is approximately 1000). Using eigenvalues and
eigenvectors, researchers have shown that the entire collection of
votes for a particular Congress can be approximated very well by a
two-dimensional space. Thus, for example, in almost all cases the
success or failure of a bill can be predicted from information
derived from two coordinates. Consequently it turns out that some
of the values important in Washington are, in fact, eigenvalues.
For More Information: Porter, Mason A; Mucha, Peter J.; Newman, M.
E. J.; and Warmbrand, Casey M., A Network Analysis of Committees in
the United States House of Representatives, Proceedings of the
National Academy of Sciences, Vol. 102 [2005], No. 20, pp.
7057-7062.