Optimizing voting order on sequential juries: a median voter theorem and beyond

We consider an odd-sized "jury", which votes sequentially between two states of Nature (say A and B, or Innocent Guilty) with the majority opinion determining verdict. Jurors have private information in form a signal [-1,+1], higher signals indicating more likely. Each juror has ability [0,1], is proportional to probability given positive signal, analog Condorcet's p for binary signals. assume that jurors vote honestly alternative they view likely, their prior voting, because are experts who want enhance reputation (after actual state revealed). For fixed set jury abilities, reliability verdict depends on voting order. size three, optimal ordering always as follows: middle first, then highest ability, lowest. sufficiently heterogeneous juries, sequential reliable than simultaneous fact (allowing non-honest voting). When average fixed, increasing heterogeneity. medium-sized we find through simulation median should still first remaining ones decreasing abilities.