What does rule of mob mean?

Answer 1

Humorously: 'Mob rules' is a play on 'majority rules'

But the rule of mob refers to mob mentality. In a mob it is generally easier to become inflamed or angry because if everyone around believes something you are more likely to believe it as well.

The phrase 'None of us are as dumb as all of us' goes with this as well. It means that when you are with a bunch of people you generally start to lose accountability and will act without thinking as hard or with as much wisdom as you would individually, believing that the consequences will not affect you as much.