The following post was co-written with Adrian Vermeule.

An earlier entry on this blog discusses the puzzle of King v. Burwell: given that six out of the nine judges to vote on the merits have ruled in favor of the agency, isn’t it difficult to say that the agency’s view is clearly unreasonable? The issue generalizes. Under what conditions should judges take into account the information contained in the votes of other judges? We are currently working on a paper on the subject, and lay out some very preliminary and tentative thoughts here.

The issue generalizes well beyond judges, of course. It arises whenever a multimember decisionmaking body, or a hierarchy of such bodies, has to decide whether a legal standard is clearly satisfied. Disagreement among the voters is itself informative about whether the standard is met.  Thus a famous puzzle about juries, stemming from James Fitzjames Stephen, is whether majority rule can coherently be combined with the reasonable-doubt rule. The argument that it cannot goes like this: Imagine that the jury votes 7-5 to convict the defendant. Doesn’t the close vote itself suggest the existence of a reasonable doubt? Related literature in positive political theory involves the “swing voter’s curse” and strategic voting on juries under unanimity rule. But we will confine ourselves to the judicial setting for now.

The relationship between Supreme Court and the lower federal courts is fertile terrain for these issues. If N courts of appeal say that a statute clearly means X, and another N courts of appeal say that a statute clearly means Y, doesn’t that tend to show, all else equal, that the statute is ambiguous? Or in cases about qualified immunity, if some appellate courts say that a certain rule counts as “clearly established law,” and some say it doesn’t, does that mean it doesn’t? What if the second group says not merely that the rule isn’t clearly established, but that the opposite rule is clearly established?

But let us focus on the cleanest setting — voting within a multimember group of Justices at the Supreme Court. And we will use Chevron examples, in light of King v. Burwell.

Here are some cases of interest:

(1) At the conference after oral argument, five Justices say that the ordinary meaning of the statute is clearly X, four say that it is clearly Y. Shouldn’t all nine update their views and learn from the aggregate information contained in the votes of colleagues? Shouldn’t all entertain the possibility that the vote reveals the statute to be ambiguous?

(2) A harder case: At the conference after oral argument, five Justices say that the statute clearly means X, four say that it is ambiguous as between X and Y. Should the five obtain some information from the votes of the four, albeit not as much as in case (1)? After all, the four do not agree that the statute clearly means X. And how about vice-versa — should the four update their own views, in light of the views of the five?

(3) Four justices say that the statute clearly means X, four that it clearly means Y. The swing justice thinks the statute is ambiguous, so the agency wins. Two puzzles:

(A) What exactly is the judgment of “the Court,” for purposes of the Brand X rules? Is it that the statute is ambiguous, so that the agency may flip back and forth between interpretation X and interpretation Y as future administrations come and go?

(B) If so, is that a sensible result? After all, eight Justices viewed the statute as unambiguous (although they disagreed on its putatively unambiguous content).

So far we have assumed that all Justices are using a common interpretive theory (in the examples, we have assumed that the Justices are all trying to determine the ordinary meaning of the text). But puzzles also arise at the meta-level of competing approaches to interpretation. In case (1), suppose that the five Justices are purposivists who think that purposive sources clearly suggest X, and the four are textualist who think that the ordinary meaning clearly indicates Y (or vice-versa). Does that undermine the argument for ambiguity? Or should all nine Justices recognize that reasonable minds can disagree about the proper approach to interpretation, and then say that the agency has second-order discretion to choose among reasonable interpretive approaches? On that logic, the agency wins as well, not because the statute is ambiguous within any particular interpretive approach, but because there is second-order ambiguity in the choice of interpretive approaches.

The puzzles are endless. Clearly some sort of analytic framework is needed, and basic decision theory supplies one. We sketch out such a framework in our next post.