The essential ranking of decision rules in small panels of experts

For small panels of experts (e.g., boards of managers, courts, specialized committees), n ≦ 5, this paper provides an algorithm for ranking the seven efficient and commonly used weighted majority rules by their respective performance. These rules are terned efficient since they constitute the set of potentially optimal decision rules in uncertain, symmetric, pairwise choice situations. The main contribution of this study is the discovery of an essential ordering of six of these rules which entails that the set of possible ranking of the seven rules is almost single peaked. The essential ordering significantly reduces the number of possible rankings of the rules, and thus, simplifies the development of the ranking algorithm. The essential ordering has important applications when the available information on the experts' decisional skills is incomplete.