Preference aggregation versus truth-tracking: asymptotic properties of a related story

This paper is concerned with the asymptotic behavior of some global quantities relating to weighted decision rules when the number of small voters tends to infinity. First, voting is assumed to be motivated by interests, so that the collective decision is "preference aggregation". Here the quantity whose asymptotic behavior is analyzed is the "complaisance" of the decision-making body which was introduced by Coleman in 1971 as the "power of a collectivity to act". Second, decision-making is assumed to the "truth-tracking", so that there is a right answer but voters only have a partial information and imperfect competence for detecting the truth. The quantity considered here is the collective competence of the decision-making body: the probability of its arriving at the correct decision. This is the problem considered by Condorcet's Jury Theorem. The paper provides a generalization of this celebrated theorem by reinterpreting complaisance in terms of errors in a statistical sense.