In (2008), McMorris and Powers [A characterization of majority rule, J. Classif. 25 (2008) 153-158] proved that a hierarchical version of majority rule is the only consensus function satisfying restricted decisive neutrality, symmetry, monotonicity, and is biprofile nontrivial. We show that this result can be extended to any finite median semilattice X such that X is not a lattice, the height of X is greater than one, X contains at least two atoms, and X satisfies a condition we call special.