Level r Consensus and Stable Social Choice

We propose the concept of level r consensus as a useful property of a preference profile which considerably enhances the stability of social choice. This concept involves a weakening of unanimity, the most extreme form of consensus. It is shown that if a preference profile exhibits level r consensus around a given preference relation, the associated majority relation is transitive. In addition, the majority relation coincides with the preference relation around which there is such consensus. Furthermore, if the level of consensus is sufficiently strong, the Condorcet winner is chosen by all the scoring rules. Level r consensus therefore ensures the Condorcet consistency of all scoring rules, thus eliminating the tension between decision rules inspired by ranking-based utilitarianism and the majority rule.