Consider a situation in which n members of a group are asked to determine whether a proposition is true or false. In the simplest case, where all make their decisions independently of each other, a straightforward majority rule is best in the sense of maximizing the probability of a correct group decision. Where, however, there is a substantial degree of statistical dependence among the group members' decisions, other rules may be better. A model of individual decision making is considered assuming a possibly strong correlation among members of certain subgroups. It is shown that some indirect majority rules (e.g. the electoral college system) and intermediate rules may in such case be better than direct majority rule.