Are two better than one? A note

This note examines the possibility of extending the Condorcet Jury Theorem (CJT) by relaxing the assumption of homogeneous individual decision-making skills. Our main result provides two sufficient conditions for advantageous extension of a group. These conditions are referred to as (Weak) “Two Are Better than One” (WTBO) and TBO. The latter requires that the average decision-making competence of the two added members exceeds those of any existing group member. The weaker condition WTBO requires that the sum of the optimal weights of the two added members is larger than the optimal weight of any existing group member. Immediate special cases of our result include CJT settings wherein decision-making skills are assumed to be identical as well as situations wherein such skills are of two types: low and high.