Who should cast the casting vote? Using sequential voting to amalgamate information

In this study, we are concerned with how agents can best amalgamate their private information about a binary state of Nature. The agents are heterogeneous in their ‘ability’, the quality of their private information. The agents cannot directly communicate their private information but instead can only vote between the two states (say ‘Innocent’ or ‘Guilty’ on a criminal jury). We first describe possible methods of sequential majority voting, and then we analyze a particular one: the first $n‐1$ jurors vote simultaneously and, in the case of a tie, the remaining juror has the casting vote. We prove that when $n=3$ (a common situation for a tribunal of three judges), the probability of a correct verdict is maximized when the agent of median ability has the casting vote.