Expanding the domain of majority rule is widely seen as desirable for the European Union. But the functioning of majority rule depends on preconditions that are seldom taken into account. The basic precondition is that overruled minorities accept majority decisions instead of exiting the voting unit. The specific problem of applying majority rule in the European Union is that overruled minorities at the European level are majorities at the nation-state level. By distinguishing between three dimensions of conflicts - content, time and space - the article analyses under what conditions it is possible to expect minorities to accept majority decisions, thus enabling the resolution of conflict by majority rule at the European level.