Performance evaluation of some special classes of weighted majority rules

The main concern of this paper is the performance evaluation of four classes of decision rules: the expert rule, the balanced expert rules, the simple majority rule, and the restricted simple majority rules. Employing the uncertain dichotomous choice model we first establish the necessary and sufficient conditions for the optimality of these four types of decision rules. For small groups consisting of less than six members the optimality conditions cover all the potentially optimal decision rules. Consequently, we are able to pursue a complete analysis of the small group cases. The analysis of the special (small group) cases as well as that of the general (n-member group) cases is based on the assumption that individual decisional skills are uniformly distributed. In evaluating the quality of a decision rule we resort to four alternative criteria: the expected optimality likelihood of the rule, the expected probability of yielding a correct collective decision given complete information on decisional skills, the expected probability of yielding a correct collective judgement given complete inability of skills verification, and, finally, the sensitivity of the rule to skills verifiability.