 Apart from providing an argument for majority rule based on four plausible procedural desiderata, the theorem helps us characterize other aggregation rules in terms of which desiderata they violate. Dictatorships and weighted majority rules with unequal individual weights violate anonymity. Asymmetrical supermajority rules (under which a supermajority of the votes, such as two thirds or three quarters, is required for a decision in favour of one of the alternatives, while the other alternative is the default choice) violate neutrality. This may sometimes be justifiable, for instance when there is a presumption in favour of one alternative, such as a presumption of innocence in a jury decision. Symmetrical supermajority rules (under which neither alternative is chosen unless it is supported by a sufficiently large supermajority) violate positive responsiveness. A more far-fetched example of an aggregation rule violating positive responsiveness is the inverse majority rule (here the alternative rejected by a majority wins).