Ergodicity
Whether time averages equal ensemble averages - a crucial distinction for risk and decision-making.
Also known as: Time vs ensemble averages, Non-ergodicity, Ergodic theory
Category: Concepts
Tags: statistics, probabilities, risks, decision-making, complexities
Explanation
Ergodicity is a mathematical property describing whether the average outcome for one person over time equals the average outcome across many people at one time. In ergodic systems, these are equivalent. In non-ergodic systems, they diverge - often catastrophically. Classic example: Russian roulette. The 'ensemble average' (average across 100 people playing once) shows 83% survive. But the 'time average' (one person playing 100 times) approaches certain death. Expected value is positive, but no individual should play. Most real-world decisions are non-ergodic: you can't 'ensemble average' your way out of individual ruin. Consequences for decision-making: avoid risks of ruin (no recovery possible), maximize geometric rather than arithmetic returns, prioritize survival over optimization, and recognize that 'expected value' can be misleading. Non-ergodic thinking explains: why insurance is rational despite negative expected value, why diversification matters beyond reducing variance, and why 'average' outcomes don't predict individual trajectories. For knowledge workers, ergodicity thinking helps: evaluate risks that could end the game, recognize when statistical averages don't apply to individuals, and prioritize robustness over optimization.
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