Judgmental competence of individuals and groups in a dichotomous choice situation: Is a majority of heads better than one?

We present a simple combinatorial model of group decision‐making in a dichotomous choice situation. The independent variables in the model are group size and mean judgmental competence of group members. The dependent variables are the probabilities that the majority judgment of the group will be correct and that the best member of the group will be more likely to be correct than the group majority. Two applications of this model are given: one a determination of isocompetence curves of groups of differing sizes and mean competence levels, the other an explication of the potential mechanisms accounting for Parkinson's only partly tongue‐in‐cheek observation that the point of ineffectiveness in a group seems to be reached when its total membership exceeds 20 or 21.