While we're on the subject of Supreme Court decisions, Glenn "Instapundit" Reynolds and Sasha Volokh both note a New York Times article about a mathematical analysis of Supreme Court decisions. The analysis, by Dr. Lawrence Sirovich, a mathematician at the Mount Sinai School of Medicine in Manhattan, has determined that the justices are not entirely independent in their decision-making. In particular, the nine of them are the effective equivalent of 4.68 completely independent justices.

"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," writes Times reporter Nicholas Wade. In fact, one doesn't need to delve into politics to question the interpretation of Sirovitch's result as characterizing the independence of the justices' thinking. It appears to me, in fact, that the analysis says as much about the nature of the lower courts as about the Supreme Court itself.

Cases may reach the Supreme Court for several different reasons. A case may be deemed so important and controversial that a Supreme Court decision is necessary to resolve it. The Supreme Court may be dissatisfied with lower court rulings on the matter, or two different lower courts may have ruled differently on it. Or the Supreme Court itself may be divided enough to want to hear and resolve the case through its own deliberations.

In the first three instances, it would not necessarily be unexpected for the court to rule 9-0--say, if a "rogue circuit" issued a bizarre appeals court ruling that the Supreme Court saw fit to overrule. Thus the ratio of cases from each category (which likely fluctuates considerably over time) can have a significant effect on the "apparent independence" of justices' opinions.

To see this point more clearly, imagine a world without lower courts, in which all cases made it to the Supreme Court. The vast majority of those cases would be easy, and decided 9-0 by the justices. A mathematical analysis would therefore indicate a high court of strongly correlated thinkers--the effective equivalent of not much more than a single justice.

Now imagine that the same Supreme Court were suddenly supplied with a "perfect" lower court system--in the sense of being almost perfectly capable of anticipating the propensities of the higher court. The result would be that only the most difficult, marginal cases would make it to the Supreme Court--the rest would be decided by lower courts and allowed to stand by a satisfied high court. In those cases, the justices' choices would naturally be somewhat arbitrary, hinging on legal niceties that the lower courts couldn't anticipate--the kinds of judgment calls that justices might easily differ on, compared with more straightforward legal decisions. Professor Sirovitch's analysis would therefore suggest strong independence among justices. Nothing would have changed about the justices themselves, of course--only the skill of the lower courts in "filtering" cases for the high court.

I would speculate that certain types of event--say, a period of high turnover in the court system, or a flurry of controversial legal issues, perhaps emanating from a political crisis--would increase the number of cases of the first three types, thus reducing the apparent independence of justices. A more careful analysis of the origins of cases that make it to the Supreme Court, might help determine whether the apparently low "entropy" of Supreme Court opinions is a reflection of polarization within the court or merely an artifact of turmoil in the lower courts.