- There is a large body of research studying the conditions under which majority decisions are best. In particular, in many circumstances, the probability of a group to decide correctly is higher than that of a random subgroup. Moreover, the latter probability increases as the subgroup size grows. Here we generalize those results by showing that, in the same setup, the simple majority rule is the most effective of all weighted majority rules when weights are distributed randomly between group members. For special families of weighted majority rules, rule effectiveness increases as we get "closer" to the simple majority rule. Copyright © 2008 Blackwell Publishing, Inc..