Puzzles

Are you less popular than your own friends?

Ask everyone in your friend group how many friends they have. On average, in almost any real social network, each person's friends have more friends than they do — and this holds true for nearly everybody in the network at once, not just the unpopular ones. That sounds like it can't possibly be true for everyone simultaneously. Can you see why the math actually allows it?

Reveal the answer

Popular people rack up a huge number of connections, so they show up as 'a friend' in far more people's friend-lists than an unpopular person does. Averaging friend-counts by walking through friendships (rather than by person) oversamples exactly those highly-connected people, dragging the average up for almost everyone who counts their friends' friends. Sociologist Scott L. Feld proved this in a 1991 paper literally titled 'Why Your Friends Have More Friends Than You Do.'

Scott L. Feld, Why Your Friends Have More Friends Than You Do — American Journal of Sociology, 1991

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