This paper addresses the question of whether it is possible to build a superval-uational semantics for the language of first order predicate logic with an added binary majority quantifier in such a way that a counterpart of the monotonicity condition is satisfied. I will show that this is not possible in the general case (for all partial models) and will propose a definition of a class of semipartial models for which it can be done. These remarks can be generalized at least to all binary quantifiers that are not left-monotone.