Self-consistency of decision rules for group decision making

The author treats, in this paper, a group of decision makers, where each of them already has preference on a given set of alternatives but the group as a whole does not have a decision rule to make their group decision, yet. Then, the author examines which decision rules are appropriate. As a criterion of “appropriateness” the author proposes the concepts of self-consistency and universal self-consistency of decision rules. Examining the existence of universally self-consistent decision rules in two cases: (1) decision situations with three decision makers and two alternatives, and (2) those with three decision makers and three alternatives, the author has found that all decision rules are universally self-consistent in the case (1), whereas all universally self-consistent decision rules have one and just one vetoer in the essential cases in (2). The result in the case (2) implies incompatibility of universal self-consistency with symmetry. An example of applications of the concept of self-consistency to a bankruptcy problem is also provided in this paper, where compatibility of self-consistency with symmetry in a particular decision situation is shown.