“Majority rule…never is merely majority rule. As a practical politician…said a long time ago: ‘The means by which a majority comes to be a majority is the more important thing: antecedent debates, modifications of view to meet the opinions of minorities, the relative satisfaction given the latter by the fact that it has had a chance and that next time it may be successful in becoming a majority…The essential need, in other words, is the improvement of the methods of conditions of debate, discussion and persuasion.”
There is a robust core of phenomena that count as deliberative democracy in all (versions of deliberative democracy). All agree, I think, that the notion includes collective decision making with the participation of all who will be affected by the decision or their representatives; this is the democratic part. Also, all agree that bit includes decision making by means of arguments offered by and to participants who are committed to the values of rationality and impartiality: this is the deliberative part.