Fair indirect majority rules
Abstract
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.