Bruno Leclerc proved that a finite lattice is upper semimodular if and only if, for any profile π and for any π-median m, the inequality c1/2(π) ≤ m holds where c1/2(π) denotes the value of the majority rule at π. We generalize this fact to posets. © 2000.
Powers, R. C. (1999). Medians and Majorities in Semimodular Posets. Electronic Notes in Discrete Mathematics, 2, 183. https://doi.org/10.1016/S1571-0653(04)00042-3