IV.B. Toward a Theory of Group Estimation

The term "Delphi" has been extended in recent years to cover a wide variety of types of group interaction. Many of these are exemplified in the present volume. It is difficult to find clear common features for this rather fuzzy set. Some characteristics that appear to be more or less general are: (1) the exercise involves a group; (2) the goal of the exercise is information; i.e., the exercise is an inquiry, (3) the information being sought is uncertain in the minds of the group; (4) some preformulated systematic procedure is followed in obtaining the group output. This vague characterization at least rules out group therapy sessions (not inquiries), team design of state-of-the-art equipment (subject matter not uncertain), brainstorming (procedure not systematic), and opinion polls (responses are not treated as judgments, but as self-reports). However, the characterization is not sufficiently sharp to permit general conclusions, e.g., concerning the effectiveness of types of aggregation procedures. Rather than trying to deal with this wide range of activities, the present essay is restricted to a narrow subset. The subject to be examined is group estimationthe use of a group of knowledgeable individuals to arrive at an estimate of an uncertain quantity. The quantity will be assumed to be a physical entity—a date, a cost, a probability of an event, a performance level of an untested piece of equipment, and the like. Another kind of estimation, namely, the identification and assessment of value structures (goals, objectives, etc.) has been studied to some extent, and a relevant exercise is described in Chapter VI. Owing to the difficulty of specifying objective criteria for the performance of a group on this task, it is not considered in the present paper. To specify the group estimation process a little more sharply, we consider a group I = { Ii } of individuals, an event space E = { Ej } where E can be either discrete or continuous, and a response space R = { R i j } which consists of an estimate for each event by each member of the group. In addition, there is an external process P={ P ( Ej ) }, which determines the alternatives in E which will occur. Depending on the problem, P can either be a ð (delta)-function on E— i.e., a specification of which event will occur-or a probability distribution Pj on the event space. In general Pj is unknown. For some formulations of the group estimation process, it is necessary to refer to the a priori probability of an event. This is not the same as the external process, but rather, is (in the present context) the probability that is ascribed to an event without knowing the individual or group estimates. This a priori probability will be designated by U = { U ( Ej ) }.