Ergodicity economics and psychology
1 Oct, 2025 at 19:44 | Posted in Economics | Leave a comment
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We will do decision theory by using mathematical models … The wealth process and the decision criterion may or may not remind you of the real world. We will not worry too much about the accuracy of these reminiscences. Instead we will ‘shut up and calculate’ — we will let the mathematical model create its world … Importantly, we need not resort to psychology to generate a host of behaviours, such as preference reversal as time passes or impatience of poorer individuals … Unlike utility functions, treated in mainstream decision theory as encoding psychological risk preferences, wealth dynamics are something about which we can reason mechanistically …
While I share many of the critiques that Peters and Adamou level against mainstream expected utility theory, I diverge from their conclusion regarding human decision-making. Contrary to their position, I contend that psychological factors are not merely incidental but are fundamental. Any framework that seeks to describe or predict human action must place them at its core.
When evaluating decisions, the way we measure ‘growth’ changes the story dramatically. Consider two very different processes. In the first (Gamble 1), an investor begins with $10,000 and passes through three rounds of wealth reduction, ending with just half a cent. In the second (Gamble 2), the investor faces a single gamble: a 99.9% chance of walking away with $10,000,000 and a 0.1% chance of ending with nothing.
In Gamble 1, the deterministic shrinking process is straightforward: each round reduces the investor’s wealth by a constant proportion. Mathematically, the wealth after three rounds is $0.005.The investor loses about 99% of wealth per round. The average per-round growth rate is about −99%. The result is a guaranteed catastrophe.
In Gamble 2, the investor risks everything on a single binary outcome — a 99.9% chance of $10,000,000, and a 0.1% chance of nothing. The expected value is huge — on average, the gamble turns $10,000 into $9,990,000. However, if the gamble were repeated many times with the entire bankroll at stake, ruin would be inevitable. Since there is always some probability of hitting zero, the long-run geometric growth rate is negative infinity. Once the investor reaches zero wealth, no recovery is possible.
Which gamble is regarded as superior depends on the objective. If the goal is maximising expected wealth from a one-off decision, Gamble 2 dominates, offering huge expected gains. But if the goal is preserving wealth over repeated plays, Gamble 2 is disastrous. Gamble 1 is equally unappealing — it guarantees destruction without the possibility of recovery.
The metric we use — arithmetic or geometric averages and growth rates — can give entirely different conclusions. From an expected value perspective, one would favour Gamble 1, since it offers a higher average growth rate. Yet I suspect very few investors — myself included — would actually share that preference.
When it comes to human decision-making, psychological factors are paramount. This is especially true when confronting uncertainty. The models and examples presented often operate, either explicitly or implicitly, within the realm of quantifiable risk. On this point, it is wise to recall the crucial distinction made by Keynes a century ago: measurable risk is fundamentally different from unmeasurable uncertainty. In the latter domain, where probabilistic calculations break down, psychology inevitably plays a decisive role.
Consequently, while ‘optimal growth rates’ may serve as a useful decision criterion in specific, well-defined contexts, they cannot be considered the sole or universally best guide for human action. A comprehensive theory of decision-making must account for the full spectrum of human cognition and attitude, particularly when navigating the unquantifiable unknowns of the real world.
