A dynamical group decision model

The optimal aggregation of (expert) opinion has been a focus of much research, and there is a clear resemblance to the problem of the optimal combination of multiple items or tests (e.g. Meehl, 1999). For binary choice situations with a correct alternative, it has been shown that a weighted sum of individual choices is the optimal aggregation rule, where the weights proportional to the odds of an individual choosing the correct alternative (Nitzan & Paroush, 1984). Results such as these view the aggregation problem from the viewpoint of a supra decision maker, who combines all individual choices into a single group choice. This paper presents a decentralised model of the group situation, in which each individual combines the information in the group to form his or her own choice. As such, the model describes a social validation process in which individuals validate their choices by comparing them to those of others. Each individual chooses from a set of discrete alternatives the alternative that has a maximum subjective likelihood of being correct. The likelihoods are estimated on the basis of the previous decisions of all group members and the subjective estimations of the competencies of all group members. At the first stage, all group members make independent choices. At subsequent stages, each individual combines the competency estimates and the previous choices into likelihood estimates, which form the basis of the subsequent choice. In this way, dependencies between the choices arise. The process is repeated until the decisions in the group reach equilibrium. Implications of the model for the probability of group consensus are described.