GROUP DECISIONS IN FACE OF DIFFERENCES OF OPINION

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.