Ergodicity

Ergodicity concerns the equivalence of suitable time and ensemble averages for a specified process and observable under appropriate conditions. In some multiplicative processes, expected wealth across possible paths differs sharply from typical long-run growth. This distinction matters when selecting a decision objective and interpreting an average.

Ergodicity concerns when averages over time can represent averages across possible states or realizations for a specified process and observable. It is not simply a label for a risky decision. In multiplicative processes, averaging wealth across many hypothetical paths can give a very different picture from the growth experienced along a typical repeated path.

The decision lesson is to specify the dynamics and the objective before using an average. Expected wealth, expected utility, probability of meeting an obligation, and long-run growth answer different questions. Nonergodicity does not make all expected-value reasoning wrong. It shows why an average chosen without regard to the actual process may fail to describe the outcome that matters.

When to use it

When repeated outcomes compound, when earlier outcomes constrain later participation, or when an average across hypothetical paths is being used to describe an individual's trajectory.

How it can help

Specify dynamics, the quantity being averaged, constraints, and the outcome that matters. Compare path-sensitive measures such as growth, survival, or meeting an obligation with expected outcomes instead of assuming one summary answers every decision question.