Between the expert and majority rules

Sapir (1998) calculated the probabilities of the expert rule and of the simple majority rule being optimal under the assumption of exponentially distributed logarithmic expertise levels. Here we find the analogous probabilities for the family of restricted majority rules, including the above two extreme rules as special cases, and the family of balanced expert rules. We compare the two families, the rules within each family, and all rules of the two families with the extreme rules.