Majority Systems and the Condorcet Jury Theorem

The «Condorcet Jury Theorem» theorem states that if n=2m+1 jurists act independently, each with probability p>1/2 of making the correct decision, then the probability h 2m+1 (p) that the jury (deciding by majority rule) makes the correct decision increases monotonically to 1 as m increases to infinity. Condorcet argued therefore that there are situations in which it is advisable to entrust a decision to a group of individuals of lesser competence than to a single individual of greater competence. Some generalisations of this theorem will be presented in which (a) voter competencies vary, and (b) there is a dependence between voter decisions. Furthermore, the concept of an indirect majority system will be discussed and compared with a simple majority system