…Considering the decisions with another technique known as singular value decomposition, Dr. Sirovich has also found considerably less diversity than might be expected.

It would take nine dimensions for a mathematician to describe the voting patterns of the nine uncorrelated justices. But Dr. Sirovich has found that just two dimensions are needed to describe almost all the decisions of the Rehnquist court.

Although his refusal to draw any political implications from his analysis may disappoint some people, the neutrality of the approach is what makes it appealing to political and legal scholars.

"People typically come up with a single dimension, readily interpretable as a left-right point of view," said Jeffrey Segal, a political scientist at the State University of New York at Stony Brook. "He comes up with two dimensions but doesn't label them."

Dr. Yochai Benkler of the New York University Law School said the analysis was important, because instead of starting from some theory about the politics of the court, Dr. Sirovich had used a purely mathematical analysis, yet one whose results fit with common sense observation.

"What you see here is not someone trying to prove a point, but someone who has said, `Beyond the stories, this is the math of how people behave and how they ally,' " Professor Benkler said. "And the interesting thing here is the fit between the mathematical observation and the widely held intuition about the politics of adjudication."