Definition
A non-ergodic system is a system in which the time average and the ensemble average of an outcome differ — the average outcome experienced by a single agent over time is not equal to the average outcome across many agents at a single moment.
Why it matters
Most everyday reasoning about probability and risk assumes implicitly that what is true on average across many people is also what an individual should expect over time. In non-ergodic systems this assumption fails, and reasoning from the population average to the individual path produces conclusions that mislead the individual making the decision. The distinction is what makes path-dependent analysis structurally necessary rather than a stylistic preference.
How it works
A system is non-ergodic when the dynamics of the variable being studied — wealth, income, return, survival — produce individual paths that can diverge irreversibly from the cross-sectional average. The most common source of non-ergodicity in financial systems is multiplicative dynamics combined with an absorbing barrier: when wealth grows or shrinks in proportion to its current size and can be driven to zero, individual trajectories spread out over time in ways that the arithmetic mean across many trajectories does not capture. The same dynamic appears in any single-realization decision — a one-time choice over a horizon long enough for compounding to operate but short enough that the agent cannot rerun the choice to recover an average. The structural test is whether the time average and ensemble average converge as the observation window lengthens; in a non-ergodic system they do not.
In practice
For an individual making a decision whose outcomes will compound over a long horizon — a retirement income choice, a long-term investment, a single-realization commitment — the question is whether the historical or simulated average outcome is what the individual should expect for their own path. The answer is generally no, because the individual will experience one path, not an average over many. Concretely, this means that Monte Carlo retirement projections, historical safe-withdrawal-rate studies, and expected-value comparisons across products all need to be interpreted as cross-sectional summaries rather than predictions of any single individual's actual experience. A professional engaging seriously with the question will distinguish the ensemble-average answer (what happens across many simulated paths) from the time-average answer (what an individual is likely to experience along one path), and will be explicit about which one a given finding represents.
In the Longevity Standard Framework
A non-ergodic system is the structural category in ergodicity economics that names the condition under which time-averaging and ensemble-averaging diverge, and is the category into which solo drawdown falls from the individual's perspective. This is what makes the cost-of-income framework's individual-path orientation analytically necessary rather than a stylistic choice — the framework operates on the individual's specific arrangement parameters and planning horizon and produces realized value as the metric of how much of the theoretical pooling benefit reaches the individual on their actual path. Pooled and transferred-risk arrangements partially address the non-ergodicity of solo drawdown by smoothing individual longevity outcomes through mortality credits, which is one mechanism by which their realized value can exceed solo drawdown for the same individual at the same planning horizon.
Related terms
- Ergodicity
- Time average
- Ensemble average
- Absorbing barrier
- Multiplicative dynamics
- Wealth trajectory
- Path dependency
- Solo drawdown