Ergodicity

Statistics, probability, risk

Ergodicity is a concept that helps us differentiate between what happens to the group (ensemble probability) and what happens to an individual (time probability). On average, the stock market can yield 8% annual returns - this is what happens to the group. But an individual could get bankrupt, so they get -100%.

In ergodic systems, all the possible states are visited. So if an unlimited number of people participated in the lottery,  each with $1, we could expect there to be some who visit the minimum (losing $1), some who visit the maximum (jackpot) and everything in between. Here it is fine to think of ensemble probability; if the group is big enough, we can expect the group to visit all possible states. If something is possible, it will happen, given enough exposure.

Unfortunately, the lottery and stock market are non-ergodic for the individual. Once an individual goes broke, they can’t play anymore. They won’t visit every possible state.

Don't mix ergodic and non-ergodic systems with each other, and don’t think that every individual will get the average return for the group. It is possible for everything to look great on average, but disastrous for the individual.

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