Top monotonicity: A common root for single peakedness, single crossing and the median voter result

When the members of a voting body exhibit single peaked preferences, majority winners exist. Moreover, the median(s) of the preferred alternatives of voters is (are) indeed the majority (Condorcet) winner(s). This important result of Duncan Black has been crucial in the development of public economics and political economy. However, it only provides a sufficient condition, and there are many examples in the literature of environments where voting equilibria exist even if single peakedness does not hold. Some of them correspond to instances where other relevant conditions, not necessarily connected with single