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Ole Peters Profile picture
@ole_b_peters
Aug 21, 2019 • 7 tweets • 2 min read • Read on X
1/7 When we started thinking about how to model personal wealth in an economy of interacting people, we soon wrote down an equation we called Re-allocating Geometric Brownian Motion (RGBM). We felt logically forced to use this as a starting point.
dx.doi.org/10.2139/ssrn.2…
2/7 But the economics papers we saw on the topic all used much more complicated, intractable, and from what we could tell quite arbitrary models, i.e. equations trying to represent the same thing we were trying to model.
3/7 Undeterred, we went ahead with our analysis, with somewhat shocking results. It showed an unstable wealth distribution. Where you sit in the distribution is hugely non-ergodic, time scales are much longer than people thought, or non-existent.
ergodicityeconomics.com/2017/08/14/wea…
4/7 Very serious consequences for questions in welfare economics, financial markets, interest rates and on and on.

No economics journal wanted to publish it.
5/7 Then we noticed Bouchaud and Mezard had studied the same equation in 2000: they'd also felt there wasn't much choice in how to model this, and they'd come to similar conclusions. We picked up some great techniques from them.
lptms.u-psud.fr/membres/mezard…
6/7 Later, we saw, Liu and Serota also arrived at this equation, in 2017.
isiarticles.com/bundles/Articl…

And just the other day, we learned that Marsili, Maslov, and Zhang were studying it for the same reasons, in 1998.
arxiv.org/abs/cond-mat/9…
7/7 What does this mean?

4 teams of physicists independently, over 20 years, all arrived at the same equation to model a key economics problem, with alarming results.

I know of no study of this equation published in an economics journal -- do you?

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More from @ole_b_peters

Ole Peters Profile picture
May 28
1/
 How can I put this?
"Expected utility maximizers don't maximize utility."

Why? Because utility is not usually an ergodic quantity in the mathematical models used by economists, and maximizing its expected value doesn't mean much in the real world. Image
2/
 I've written a blog post about this with @hulme_oliver, where we spell out the mathematics and give you an interactive app.
Try it out for yourself. Maximizing expected utility destroys actual utility.
ergodicityeconomics.com/2025/05/28/exp…
3/
 What does that mean?
I would say it means that this core concept of orthodox economics -- utility -- is meaningless and misleading.
But don't take my word for it - this is known: empirically, expected-utility theory and its descendants like prospect theory etc don't work.
Read 6 tweets
Ole Peters Profile picture
May 17
1/thread🧵
Almost 20 years ago, I started thinking about the ergodicity problem in the context of economics. That turned out to be surprisingly fruitful, and now there's a book about it. Image
This work soon attracted the attention of some extraordinary thinkers. I had met them because we were all members of the community around the Santa Fe Institute @sfiscience. Among them were Murray Gell-Mann, Ken Arrow, Reuben Hersh, and Cormac McCarthy. Image
I benefited immensely from their encouragement and their generosity with their time.
Read 16 tweets
Ole Peters Profile picture
Mar 3
1/9
 I read @davidbessis book last year. It's brilliant!
It brought back many memories of conversations with Reuben Hersh, who is briefly mentioned.

Mathematics as a human creative act, not as axioms, deductions, and finally theorems. Seeing the answer, and using logic to check. Image
2/
 Pappus wrote (paraphrased by Polya).
'Analysis:' start from what is required (the result) and trace it back to something you know to be true.
'Synthesis:' reverse the process and walk back to the result.

The human process is analysis: see the result, then understand how you know it.

But we write too much synthesis.Image
3/
 @davidbessis emphasizes the most valuable aspect of mathematics: learning to educate our intuition.

This leads him to a critique of Kahneman's System 1 (intuition) and System 2 (logical mechanical 'thought').

System 1 is not fixed. The whole point is to change it: David's System 3.Image
Read 9 tweets
Ole Peters Profile picture
May 15, 2024
1/n
A thread about ergodicity economics and world peace, why not.

A quantity is ergodic if its average over an ensemble of systems is the same as its average over time.

Ergodicity economics questions whether ergodicity holds.

But what's that got to do with world peace?
In the social context, the ensemble is usually a population, and the ergodicity question becomes this: does the average over the population represent what happens to the typical individual over time?

So this is about the relationship between collectives and individuals.
You may think: whatever is good for the collective must be good for the individual because the collective is made up of individuals.

In economics, that corresponds to working with "the representative agent," and it's precisely the ergodicity error.
Read 9 tweets
Ole Peters Profile picture
Nov 22, 2023
Let's make a list of people who have discovered problems in economics.

Feel free to add your own favorites.
@ThomasHerndon1: as a graduate student exposed the Reinhart and Rogoff paper, which had had trillion-dollar austerity consequences around the world, as jaw-droppingly flawed.
@StephanieKelton: exposed that the public narrative about the mechanics of the monetary system, which is also taught in economics departments, has little to do with the mechanics of the monetary system.
Read 5 tweets
Ole Peters Profile picture
Aug 4, 2023
..emotions also running high on the blog.

Tom is rather upset about the coin toss. Mathematics is an emotional subject.

https://t.co/DNNxVbZbkiergodicityeconomics.com/2023/07/28/the…
Image
Update: Tom is still rather angry. He has now worked out how to compute expected value.

Perhaps tomorrow he will notice that we agree with his computation of the expected value but are also curious about the time average. Image
Next update: Tom seems less angry now because he has run his simulation successfully. We don't know what he has simulated, but everybody wins, and that, surely, is a good thing. Image
Read 8 tweets

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