...the chief justice's only real power comes during the Supreme Court's conferences, where cases are decided. In these meetings, the chief justice speaks first, followed by each justice in order of seniority....
By contrast, in a court of Jewish law, the Mishna sets out the order of deliberations as follows (Sanhedrin IV:1):
In civil cases, and regarding defilement and purity, they begin by asking the opinion of the eldest, while in criminal cases they begin with those who are sitting on the side. (i.e., the most junior)
Is there an optimal approach? Is justice better served if deliberations start with the most senior judge or with the most junior?
On the one hand, if the most senior judge speaks first, the junior judges may be reluctant to disagree with him, either out of respect for his knowledge and position or out of a political desire to please him. Legitimate dissenting positions may thus be suppressed.
If the most senior judge speaks last, on the other hand, his (presumably) more extensive expertise and insight will be unavailable through most of the debate, with the junior judges forming their positions based on a partial analysis. If they heard the arguments of their superiors first, perhaps they could point to flaws in them or otherwise improve upon them.
Economists Marco Ottaviani and Peter Sorensen apply economic modelling techniques to this question in a 2000 paper, "Information aggregation in debate: Who should speak first?" (PDF). I haven't plowed through the whole paper, and I'm skeptical as to the usefulness of mathematical modelling of such scenarios. Still, the results look intriguing. They conclude, in part, that the "anti-seniority rule" is not necessarily optimal.
Whichever process is optimal, what can be the logic behind the Talmudic ruling that deliberations begin with the senior judge in civil and ritual cases, but with the junior judge in criminal and capital cases?
I would suggest the following: In civil and ritual cases, the court's primary objective is to reach a verdict by the most precise application of the relevant laws. Thus, the senior judges begin the discussion, setting out the issues with the greatest possible sophistication, with their junior colleagues learning from their analysis and adding their own contributions in full awareness of the precedents at hand. The eventual verdict may or may not be the optimal one, but it will be well-grounded in law and precedent, and the process of deliberation will expose junior judges to the analytical techniques of their senior colleagues.
In criminal and capital cases, however, a man's dignity, or even his life, is at stake. In such cases, the quest for truth takes a back seat; the priority is to protect the defendant's civil rights by affording him every possible opportunity for acquittal. The court cannot take the risk that if the senior judges vote to convict, their juniors will defer to their seniority or expertise and acquiesce, condemning a man without a thorough deliberation. Rather, they must be allowed to speak first, before voices of greater authority have rendered their opinions. Each junior judge may be the defendant's only chance to clear his name.
Thus, the main flaw in Ottaviani and Sorensen's analysis is not the use of economic modelling techniques, but the very assumption that the objective of a decision procedure is necessarily to reach the optimal decision in terms of its truth value. Other legitimate objectives of a decision procedure can include allowing different judges to express their views, according respect to senior judges, affording a learning process to junior judges, and reaching a decision which is accepted as legitimate by the court, the litigants and the public.
In criminal proceedings, biasing the deliberation in the defendant's favor can itself be an objective of the process. We explicitly prefer according him the benefit of the doubt rather than always striving for the objectively "optimal" decision. In the broader context of society, it is more important that the process be optimal than that its decisions be.