Polya Urn
Updated 2026-08-03
INTRODUCTION
English translation pending.
CORE DEFINITION
A stochastic process introduced by George Polya. An urn starts with balls of two colors; each step draws a ball at random, returns it, and adds another ball of the drawn color. The proportion of each color converges to a limit, but that limit is random and depends on the earliest draws rather than on the initial composition. The limiting distribution is uniform, so any final share is equally likely a priori. The process is the canonical model of path dependence and increasing returns, and it has no tendency to revert to an average.
SCAFFOLDING EFFECT
Reduce cognitive load
- Early window: treat the first few rounds as disproportionately decisive and invest there. - Lock-in check: ask whether the current leader is ahead because of merit or because of early luck. - Momentum design: build reinforcing feedback deliberately when you want an advantage to compound.
Anchor fast decisions
Each draw increases the weight of the color drawn, so the probability of drawing that color again rises with every occurrence. This is positive feedback: advantage compounds rather than being diluted. Because the reinforcement acts on whatever happened first, the trajectory becomes self-confirming, and the process converges to a random fixed point instead of an average. That is why an early lead, however small or accidental, can persist permanently.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E9%9E%85verified
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