 Black (1948) proved that if the domain of the aggregation rule is restricted to the set of all profiles of individual preference orderings satisfying single-peakedness, majority cycles cannot occur, and the most preferred alternative of the median individual relative to the relevant left-right alignment is a Condorcet winner (assuming \(n\) is odd). Pairwise majority voting then satisfies the rest of Arrow’s conditions—a point also discussed in detail by Arrow (1951/1963).