Consensus in a multi-expert system
Authors: Keung-Chi Ng, Bruce Abramson
Venue: Proceedings of the 1990 ACM annual conference on Cooperation (1990)

Most existing expert systems contain a single rule base. Any extension of this model to group decision-making must account for the possibility of conflicting rules encoded by different group members. The inability to reconcile conflicts, however, is one of the most clearly established shortcomings of rule-based knowledge representations [4] [11]. Thus, multi-expert rule-bases are likely to be inelegant and confusing at best, incorrect and useless at worst. The creation of advisory systems whose recommendations are based on the input of multiple experts, then, calls for an alternative knowledge representation. Despite their preeminence in the artificial intelligence (AI) community, production systems are not the only models of expertise. Several graphical models, including influence diagrams [10] [14] and Bayesian networks [11], have recently been introduced as paradigmatic bases for expert systems, with rather encouraging results; preliminary tests on PATHFINDER [9] demonstrate their latent power. These models graphically represent a domain's objects as nodes and the interactions among them as arcs and arc values. In PATHFINDER, for example, the graph's nodes represent diseases and symptoms, the arcs indicate dependence between diseases and symptoms, and the arc weights specify the degree of probabilistic dependence. PATHFINDER has only one disease node, which consists of a mutually exclusive and exhaustive set of hypotheses; any patient diagnosed by the system is assumed to have exactly one of the candidate diseases. The task of the diagnostician is to collect evidence that discriminates among them. Thus, at any point in time, PATHFINDER's partial diagnosis may be represented as a probability distribution over the N hypotheses. A diagnosis is complete when the probability of one of the diseases equals or approaches 1.0. The output provided by a belief network is easily extensible to multiple experts; any number of experts may encode their own knowledge bases and generate their own diagnoses, which will be combined into a single group diagnosis. Such combination has long been discussed by researchers concerned with mathematical aggregation for group decision making. It is important to note, however, that mathematical aggregation, as an arbitration scheme, will only strengthen a system's performance if the contributors share a general perspective as well as a common goal. A variety of aggregation functions have been proposed [6] [7] [13]. Of these proposals, the simplest is the linear opinion pool [6] [13], in which the consensus probability assigned to hypothesis Hj, (denoted &pgr;j), is a weighted sum of the probabilities assigned to Hj by each of the i = 1,&hellip;,M group members, or &pgr;j=&bgr;M &Sgr; i=1 wijpij, where pij denotes the probability assigned to Hj by member i, wij is the weight assigned to member i (for Hj), and &bgr; is a normalizing constant. The sum of each hypothesis' wij's is 1, and all wij's are non-negative. The weight wij is introduced to reflect the relative expertise or credibility assigned to individual i; at any given point, some experts could have more exposure than have others.