Group Decisions in the Face of Differences of Opinion

Abstract

Suppose a number of honest, intelligent individuals differ in their rankings of a set of possible actions. They may do so because they have difierent objectives, or they may do so solely because they disagree about what are the probable outcomes of the acts. The latter is the relevant case if they are acting disinterestedly as consultants. In this case how should the actions be ranked by the executive? Here the essential problem is that of "consensus theory"--to find a reasonable way of resolving the experts' differences of opinion about the facts (the circumstances determining the outcomes). To tackle this problem we enlarge it. We pose the problem mathematically in an abstract form which encompasses a very wide range of hypothetical cases, allowing small and big differences over objectives (utilities) as well as over probability assessments (of the facts). We then look for general rules for generating a group ranking for the acts which would simultaneously satisfy axioms referring to varying extreme cases. On certain assumptions the group ranking of acts implies an underlying consensus about the facts. The object of the paper is to show which axioms of group choice lead to which formulas for consensus. The paper arrives at both positive and negative results. Under two alternative sets of appealing axioms, the group's implicit consensus is given as a linear opinion pool; the consensual probabilities are weighted averages of the individuals' ones. On the other hand, under a third set of reasonable axioms, the group ranking cannot be arrived at by any rules for separately combining the probabilities and combining the utilities. However, this "impossibility" result depends on wanting the rule to work for cases of extreme differences over rankings of acts.