This paper is concerned about the aggregation function which plays a centralrole in the majority judgement that was recently proposed by Balinski and Laraki as anew voting mechanism. We raise two issues about their aggregation function, named orderfunction, and show that they are resolved by relaxing the strong monotonicity conditionimposed on the aggregation function, and that the anonymous, weakly monotonic andstrategy-proof aggregation function is completely determined by the set of final grades when the judges split deeply.