Consensus and Single - Peakedness

Consider a set of K alternatives. We say that an alternative is socially acceptable if the number of individuals that rank it among their most preferred half of the alternatives is at least as large as the number of individuals that rank it among the least preferred half. A Condorcet winner is not necessarily socially acceptable. We propose a concept of consensus as a condition on preference profiles that guarantees that majority rule yields a transitive preference relation and furthermore, that the resulting Condorcet winner is a socially acceptable alternative. This new condition is weaker than single-peakedness of preferences.