Inferiority of restricted majority decision rules

The case in which a group of decision makers appoints a committee to choose between two symmetrical alternatives by a simple majority vote, namely restricted majority decision rule, is one member of the set of weighted majority decision rules. It is shown that for any group of decision makers one of the restricted majority decision rules is always the worst of all weighted majority decision rules. This inferiority exists both in terms of the efficiency and in terms of effectiveness of the decision rule. The importance of this finding should be kept in mind when deciding the size of the committee because a seemingly irrelevant change in the number of decision makers may result in the inferior rule, instead of the optimal rule, being used. Moreover, because of the widespread use of restricted majority decision rules and the relatively small number of such rules, the probability of the inferior rule being used is relatively high.