Ideal Justice: Mathematicians judge the Supreme Court

The U.S. Supreme Court–already in the news this week for its decisions on affirmative action–is highlighted in a scientific journal. The court is driven by politics far less than Congress is, a new analysis suggests.

Lawrence Sirovich, a mathematician at Mount Sinai School of Medicine in New York City, calculated that the current Supreme Court of nine judges behaves as if it were made up of about 4.68 “ideal” judges–adjudicators who make their decisions completely independently of each other. To put that figure in perspective, Sirovich says, a court with a strict liberal-conservative divide would behave as if it had only one judge because all decisions would be determined purely by which faction made up the majority.

“The analysis shows that there is a great deal of independence among the justices,” he says. Sirovich reports his findings in the June 24 Proceedings of the National Academy of Sciences.

In contrast, earlier studies of the U.S. Congress by political scientists Keith Poole of the University of Houston and Howard Rosenthal of Princeton University confirmed the conventional wisdom that members of Congress usually vote along fairly strict party lines.

Sirovich’s approach strips the legal content from the decisions, whereas previous studies of the Supreme Court have often been driven by preconceptions, says law professor Yochai Benkler of New York University. “This is a novel mode of analysis that is innocent of hypotheses and simply looks at what is,” he says.

To assess judicial independence, Sirovich examined the Supreme Court’s rulings over the past 8 years in light of a measure of information content developed in the 1940s by mathematician Claude Shannon. Roughly, the more independent the judges, the less predictable their rulings, so the greater the information contained in each ruling.

Coalitions drive down the number of ideal judges. “Suppose we have two judges who always vote the same way,” Sirovich says. “Then, from the point of view of information, we have eight justices, not nine.”

During the past 8 years, Justices Antonin Scalia and Clarence Thomas voted the same way more than 93 percent of the time, and Justices Ruth Bader Ginsburg and David Souter voted the same way more than 90 percent of the time. The fact that the number of ideal judges is as high as 4.68 is encouraging, Sirovich says.

Sirovich’s work is an interesting analysis, Poole says. However, he cautions, many other studies suggest that the justices are heavily swayed by political viewpoints. “Only about 9 percent of their choices aren’t explained by a simple liberal-to-conservative ordering,” he says. “The court is very ideological.”

Benkler says that, from Sirovich’s analysis, it’s clear that “judges do a whole lot more than follow the party line. But particular judges with particular worldviews do align.”

In the new work, Sirovich applied the pattern-analysis techniques that he had used previously to study turbulent fluid flow, face recognition, and the structure of the brain.

“That’s what tickled me most about this paper,” says mathematician Steven Strogatz of Cornell University. “The beauty of mathematics is in realizing that some things are the same problem, even though they don’t appear to be.”


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