Are More Heads Better Than One, or a Few?

Adrian Vermeule is John H. Watson Professor of Law, Harvard Law School. His book Law and the Limits of Reason is now available. He has also written, Mechanisms of Democracy: Institutional Design Writ Small (2007) and Terror in the Balance: Security, Liberty and the Courts, co-authored with Eric A. Posner (2007). In the post below Vermeule looks the wisdom of crowds.

In countless settings, an important question of institutional design involves the size of the group that will be charged with making a decision. Some of these settings are political. How many legislators should sit in Congress? Should we have a single President, or an executive council? Should administrative agencies be advised by panels of experts, and if so, how many experts should the panel contain? Some of these settings arise in personal life, and in markets. Should one accept the diagnosis of a single doctor, or is it better to consult a team of doctors? If one is to make a major life decision, is it better to take the advice of a single trusted friend, or to consult widely?

Of course these settings are heterogeneous, and the issues are complex. An important question is whether we care not only about the accuracy of the decision but also about the cost of decision making (including the time it takes to make the decision, or its opportunity cost). For simplicity, however, let us focus solely on cases in which the cost of decision making is not important and in which accuracy is well-defined. The classic case involves a criminal verdict of innocent or guilty. Should the verdict be issued by a single person (perhaps a judge), or by a multi-member panel (typically a jury?) If we use a jury, should it have six members, or twelve, or some other number? Or perhaps we might have differently sized juries for different issues.

In these settings, a familiar thought is that many heads are better than one, or a few. The thought goes back at least as far as Homer, who said that “two heads together grasp advantages which one would miss” (Iliad 10.234). Unfortunately, it turns out that things are not so simple. The thought that more heads are better than one is much too simple and sometimes wrong. A large contribution of modern social science is to show the weakness of the idea, and to help state the conditions under which it is right or wrong.

The most important reason why more heads might not be better than fewer is that, in a larger group, some will free-ride on the cognitive efforts of others. (Different social scientists use different terms to denote this problem. Mark Seidenfeld calls it “cognitive loafing,” while Christian List and Philip Pettit call it “epistemic free-riding.”) In a large jury, for example, some jurors will predictably daydream while others pay close attention to the evidence and arguments. In the limiting case, all jurors might daydream – expecting others to pay attention, or because each reasons that if others are defecting from their duties, only a chump would perform his duty unilaterally, or because each reasons that whatever others do, it is selfishly best to daydream. In an illuminating treatment of this problem, Kaushik Mukhopadhaya of Emory University shows that under highly plausible conditions, a twelve-person jury panel will indeed make worse decisions than a six-person jury, and a one-person jury can plausibly be best of all. (“Jury Size and the Free Rider Problem,” J. Law, Econ. & Org. 19(1), 2003, at p. 24, 38). Of course this is not necessarily the case; it depends upon whether the extra information and multiple perspectives that many heads can produce outweigh the incentives for cognitive free-riding that arise in groups. But at a minimum, it is not obvious that many heads are better than one, even if all we care about is the accuracy of decisions.

As applied to the judiciary, rather than to lay jurors, the problem of cognitive free-riding has interesting implications. It suggests that district judges or three-member appellate panels, where free-riding is easy to monitor and check, might ascertain the law more accurately than a large en banc appellate panel or even a multi-member high court. It also suggests grounds for skepticism about a common claim offered by legal theorists influenced by Edmund Burke and F.A. Hayek. According to this claim, precedents embody the distilled wisdom of many generations of judges. We can immediately see, however, that some or even all judges participating in the line of precedent might be free-riding on other judges, cognitively speaking; they might be hoping that other judges will figure it all out, and might then be following the lead of others, who may be following the lead of yet others. It is quite possible – not merely logically possible, but really possible – that the precedents generated through the collective wisdom of the whole bench and bar might actually contain less information than they would if one judge, or a small number, had been charged with formulating the legal rules.