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The "Two Worlds, Two Urns" Experiment: A Teacher's Reflection on Ergodicity and Economic Methodology
Tomasz Kopczewski1, Tomasz Potocki2
1University of Warsaw, Poland.
Nonlinear Dynamics, Psychology, and Life Sciences
|December 18, 2025
Summary
This classroom experiment teaches ergodicity by contrasting ergodic (Urn B) and non-ergodic (Urn A) processes. It reveals how path dependence and time averages diverge in real-world behavioral economics, impacting risk and inequality.
Area of Science:
- Behavioral Economics
- Economic Pedagogy
Background:
- Ergodicity is crucial for understanding economic dynamics.
- Traditional models often overlook path dependence and time-averaged dynamics.
Purpose of the Study:
- To introduce a classroom experiment demonstrating ergodicity.
- To highlight limitations of static microeconomic models.
- To serve as a research protocol for history-dependent dynamics.
Main Methods:
- Contrasting an ergodic independent and identically distributed (i.i.d.) process (Urn B) with a non-ergodic Pólya process (Urn A).
- Empirical demonstration of time and ensemble average alignment and divergence.
- Providing a replicable protocol with instructions and analysis templates.
Main Results:
- Non-ergodic processes exhibit stochastic symmetry breaking and cumulative advantage.
- Early shocks in ergodic systems significantly alter transition probabilities.
- Identical initial conditions lead to increasing dispersion in non-ergodic systems.
Conclusions:
- The experiment illustrates microeconomic methodological limitations of static models.
- Ergodic reasoning is essential for research on risk, learning, and inequality.
- Lived trajectories, not just snapshots, determine outcomes in behavioral economics.
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