Berkson's Paradox

Attractive people seem less nice. Nice people seem less attractive. Does beauty corrupt character? Probably not. More likely: you only date people above some threshold of combined attractiveness and niceness. The gorgeous jerk and the plain sweetheart both clear the bar; the gorgeous sweetheart is rare at any threshold. Your dating pool makes attractiveness and niceness look negatively correlated when they’re not.

This is Berkson’s paradox: conditioning on a sum of two variables creates a spurious negative correlation between them. Named for Joseph Berkson, who noticed that hospital patients showed correlations between diseases that didn’t exist in the general population — because admission required some notable condition, having one made having another less necessary.

The paradox lurks wherever selection filters by combined criteria. Successful companies seem to trade off between culture and competence. Famous intellectuals seem to choose between rigor and accessibility. Good restaurants seem to sacrifice either food or ambiance. These trade-offs might be real — or might be artifacts of which companies, intellectuals, and restaurants you’re aware of.

The mechanism: if reaching a sample requires exceeding a threshold on X + Y, then within that sample, high X makes high Y less necessary and thus less common. The correlation within the sample is negative even if X and Y are independent or positively correlated in the population.

The antidote is remembering what population you’re observing. The visible subset has been filtered; the correlations you see are shaped by the filter. Asking “would this correlation exist without selection?” can reveal which patterns are real and which are artifacts.

This matters for learning from examples. Studying only successes, only failures, only famous cases — any restricted sample can create phantom patterns. The full population might look completely different. What you can see is shaped by what made things visible.