Ole Peters on the Ergodicity Problem

I have had this 2019 paper by Ole Peters bookmarked for a while, and today, I re-read the abstract and dived into actually reading it. (Ergodicity is an important but little known topic, that became “my favourite word” back in 2017 but still seen few use the term since.)

The 2019 paper is published in Nature under its “nature physics” subject area, but the title concerns economics.

The Ergodicity Problem in Economics
by Ole Peters in Nature, Dec 2019

And this quote below is the whole abstract, which stands as a better summary than I could attempt. Spot on.

“The ergodic hypothesis is a key analytical device of equilibrium statistical mechanics. It underlies the assumption that the time average and the expectation value of an observable are the same. Where it is valid, dynamical descriptions can often be replaced with much simpler probabilistic ones, time is essentially eliminated from the models. The conditions for validity are restrictive, even more so for non-equilibrium systems. Economics typically deals with systems far from equilibrium specifically with models of growth. It may therefore come as a surprise to learn that the prevailing formulations of economic theory, expected utility theory and its descendants, make an indiscriminate assumption of ergodicity. This is largely because foundational concepts to do with risk and randomness originated in seventeenth-century economics, predating by some 200 years the concept of ergodicity, which arose in nineteenth-century physics. In this Perspective, I argue that by carefully addressing the question of ergodicity, many puzzles besetting the current economic formalism are resolved in a natural and empirically testable way.”

Plenty of commentators have been voicing the warning that so much risk-based prediction in the world is flawed, anywhere resources interact with populations, not just in economics per se. Viral information and epidemiology of biological pandemics anyone? The arithmetic simplifications – time averages ignoring true (socially) interactive dynamics, etc – have been called “autistic” before. The likes of Taleb and Kauffman point out more bluntly that ignoring true non-ergodic behaviour is plain wrong and dangerous, and have the statistical epistemological skills to back it up. Peters’ paper includes the maths too.

Although I would never have used the language, I recorded way back in the late ’80’s – when doing management statistics – that knowing statistical formulae enough read them and to do the calculations is one thing. It’s not the same as the epistemology of understanding what they really mean or whether they are significant or even relevant. That sense of “something’s wrong” I noted as a driver for this whole two-decades-and-counting project of mine.

Peters’ claims from experimental research of their proposed “gambling” strategy – accounting for non-ergodicity – are modest but clear. Nevertheless:

“The present situation is […] dispiriting because economics is firmly stuck in the wrong conceptual space. Because the core mistake is 350 years old, the corresponding mindset is now firmly institutionalized.”

He does also point that at least recognition of the problem and opportunities to do better are “uplifting”. My ongoing fear – that institutional blockage – is that the misunderstanding is much wider and deeper than economics. (A great list of references in the paper.) Any evolving field of knowledge involving humans and populations is at risk. Contrary to myths of objectivity, that’s pretty much the whole of physical science, not just social sciences like economics.