The phrase "The Tyranny of the Majority" has a respectable pedigree, prior to the use of it last week by John Major. Some of the problems outlined in the Wikipedia article (linked) include the election of a demagogue, and the abandonment of rationality. Both seem particularly relevant this autumn.
In 1922, F Scott Fitzgerald wrote to his editor, Maxwell Perkins, "I think when I read Upton Sinclair's The Brass Check I made my final decision about America - that freedom has produced the greatest tyranny under the sun. I'm still a socialist, but sometimes I dread that things will grow worse and worse the more the people nominally rule. "
Significantly, the book to which he referred concerns the corruptive and corrosive power of the press.
Conceivably, the majority could use its democratically elected power to abolish democracy. This, in fact, is how Hitler came to power. Food for thought.