THE EFFECT OF EXPANSIONS AND SUBSTITUTIONS ON GROUP DECISION-MAKING

In the current paper we analyze the effect of expansions and substitut ions on the (optimal) performance of a group that makes decisions in p airwise choice situations. Within our framework expansions cannot be d etrimental to group performance. Proposition 1 provides a necessary an d sufficient condition for the invariance of group performance to expa nsions of order m. This condition implies that group performance is ne ver invariant to such expansions if the original group consists of an even number of homogeneous members. In such a case any expansion alway s 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 o r the inferiority of group performance to substitutions is therefore n aturally confined to individually quality-reducing substitutions, i.e. some group member is replaced by individuals whose decisional compete ncies are inferior to his. Proposition 2 provides a sufficient conditi on for the inferiority of individually quality-reducing substitutions of order m, m greater than or equal to 2. Proposition 3 establishes th at in a homogeneous group with an odd number of members, individually quality-reducing substitutions of order 2 always adversely affect grou p performance.