Unanimity under ambiguity

This paper considers a binary decision to be made by a committee - canonically, a jury - through a voting procedure. Each juror must vote on whether a defendant is guilty or not guilty. The voting rule aggregates the votes to determine whether the defendant is convicted or acquitted. We focus on the unanimity rule (convict if and only if all vote guilty), and we consider jurors who share ambiguous prior beliefs as in Ellis (2016). Our contribution is twofold. First, we identify all symmetric equilibria of these voting games. Second, we show that ambiguity may drastically undermine McLennan's (1998) results on decision quality: unlike in the absence of ambiguity, the ex ante optimal symmetric strategy profile need not be an equilibrium; indeed, there are games for which it is possible to reduce both types of error starting from any (non-trivial) equilibrium.