Same average. Different exposure.
Taleb connects antifragility with benefiting from variation through a convex response. Robustness is a different property: resistance to change.
Inside this model
Two equally likely inputs are −s and +s. Payoffs are 100 − kx²/100 (fragile), 100 (robust), and 100 + kx²/100 (convex). The graph plots their equally weighted means across shock sizes. All three receive the same input distribution.
Out in the world
A practical use
Compare a system whose failures accelerate under load with a portfolio of small experiments whose losses are capped and successes can expand.
A useful lens. Not a universal law.
- These quadratic response functions are invented teaching examples, not calibrated systems. The benefit depends on the response remaining convex over the relevant range; extreme shocks may change it.
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.
Taleb — Convexity and science ↗