a minority can look like a majority, if it sits in the right places
Take a network. Colour a minority of people blue — say 25%. Now ask a random person: what fraction of your friends are blue? The answer is usually way higher than 25%, because blue people tend to befriend lots of people, and high-degree nodes get seen more. This is the majority illusion: a real minority that feels like the majority.
true blue fraction: –
what the average person sees in their friends: –
illusion factor: – (how many times bigger the minority looks)
degree bias = how strongly blue nodes prefer to connect to high-degree nodes. at 0, colour is random. at 1, blue nodes cluster on the hubs. the illusion gets stronger as bias grows — that's the whole trick: it's not that blue is loud, it's that blue is well-connected.