In the current paper we analyze the effect of expansions and substitutions on the (optimal) performance of a group that makes decisions in pairwise choice situations. Within our framework expansions cannot be detrimental to group performance. Proposition 1 provides a necessary and sufficient condition for the invariance of group performance to expansions of order m. This condition implies that group performance is never invariant to such expansions if the original group consists of an even number of homogeneous members. In such a case any expansion always favorably affects group performance. Substituting an individual with at least one more skillful individual obviously results in increased group performance. Our search for conditions ensuring the invariance or the inferiority of group performance to substitutions is therefore naturally confined to individually quality-reducing substitutions, i.e. some group member is replaced by individuals whose decisional competencies are inferior to his. Proposition 2 provides a sufficient condition for the inferiority of individually quality-reducing substitutions of order m, m ≥ 2. Proposition 3 establishes that in a homogeneous group with an odd number of members, individually quality-reducing substitutions of order 2 always adversely affect group performance.
- Dichotomous choice
- Group decision-making