1/
Sometimes it helps to say why we do things. So why worry about ergodicity in economics?

The ergodicity problem means, e.g., that economic models overlook the fundamental benefit of cooperation, a cornerstone of complexity theory - why structure emerges in living systems. 2/
Formally, the failure happens because expected utility theory (EUT) optimizes expected value, and expected value is irrelevant and inaccessible to decision makers (it's even called `expected' utility theory...)

EUT in turn is the basis for game theory.

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. 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…

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. 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.

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. 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.

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.

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.

..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…
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.

1/7
Since people seem curious, here's a bit more detail because it's a nice ergodicity story.

The question was: how can paupers and billionaires emerge in a population of identical agents?

I think the ergodicity-economics answer is underappreciated in economics.

https://twitter.com/ole_b_peters/status/1659823460753850368

2/7
Imagine a population of N agents all of whose growth rates have the same statistical properties.
In the simplest case, at each time step generate N Gaussian random variates and use them as the exponential growth rates.
Everyone's expected wealth is identical for all time.

1/4
Hysteresis is a fancy word for "it matters how you got there."

A 5% interest rate is one thing if you've arrived there from 10%; it's something else if it's been 0% for years.

Low and falling rates are systemically ingrained now.

ergodicityeconomics.com/2017/08/14/wea… 2/4
This raises a question I've been wondering about for some years: what happens when we (try to) increase interest rates again?

It's not (just) the level that matters but the path. After 40 years of falling rates, the economic system is used to the trend. Now what?

Help! I don't know the details of this work. Of course banks are unstable because of their key function in the financial system. Of course that instability manifests through bank runs.
Did these researchers just say as economists what everyone else knew or is it something deeper?

https://twitter.com/philipcball/status/1579506011358244865

I know that the financial sector is sort of non-existent in a general competitive equilibrium view of the world. Ken Arrow listed it as one of the failings of economics: that finance shouldn't really be there but clearly is. Did they discover the financial sector for economics?

1/7
People ask me why ergodicity is interesting in the context of modeling human social behavior, like markets, economies, or democracies. Some thoughts... 2
In this context, ergodicity is about the relationship between the individual and the collective. If ergodicity holds, each individual is representative of the collective. The "representative agent" of economics makes sense then.

Tuesday's Nobel Prize in Physics is - among other things - a celebration of Giorgo Parisi's contributions to the progress physicists have made in understanding ergodicity and ergodicity-breaking.

Fittingly, though no doubt by sheer coincidence, I was invited a few weeks ago... ...by Annalen der Physik - yes, the journal which publishes the Physics Nobel Lectures - to write a review article on Ergodicity Economics. So I'm using all my channels to find out what people have done.

1/8
Very roughly, why @giorgioparisi's @NobelPrize is relevant to #ErgodicityEconomics.

Giorgio Parisi's best-known work in statistical mechanics is in the area of spin glasses.
Real glasses are sort of liquids but they flow very slowly. If you look at a very old window pane.. 2/8
..in a church, say, you will see that it's thicker at the bottom. That's because the glass has flowed down. The glass wants to flow and lower its energy but its internal disordered structure makes that very hard.

Spin glasses model this. They are systems which take a very...

1/4
There used to be a clear definition of "economically rational."

This meant: maximize expected wealth.

When confronted with reality, this model fell flat on its face. People don't do it. 2/
Utility was introduced, but with it the meaning of "rational" became unclear.

Was utility a means of describing irrational behavior, or was maximizing expected utility the new rational?

Both notions exist in the literature.

1/5
The Copenhagen experiment showed that Ergodicity Economics (EE), limited to its predicted utility functions for given dynamical settings, is a better fit to human behavior than classic expected-utility theory with a freely chosen single utility function. 2/5
I don’t find this terribly interesting. Classic expected-utility theory is conceptually flawed, and science is more than data-fitting. However well or poorly it fits observations, one would have to reject expected-utility theory anyway.

1/7
Brilliant interactive animation of the coin toss.

Expected value: blue line.
Realizations: red/grey lines.

If you play for long enough, the slope of _any_ red line will point down, with mathematical certainty.

https://twitter.com/TheShubhanshu/status/1341253515608547328

2/7
Early treatments of these problems, in the 17th century, assumed that people should optimize expected wealth (blue line). If they did, they would voluntarily play this game -- the blue line points up.

But real people didn't behave this way. They declined the offer to play.

1/7
I disagree with the implicit statement by Mervyn King - wondering what @ProfJohnKay thinks - that maximizing expected utility is reasonable in the small world of a simple model.

My critique is more devastating and less palatable: it's a thought error to optimize this object. 2/
In other words, we don't need to make the model more realistic for expected utility maximization to become a bad idea. It's a priori the wrong object, namely: changes in utility are non-ergodic. Their expectation value has no physical meaning for an individual decision maker.

1/9

This feels relevant to @Twitter ...

Friedemann Schulz von Thun came up with a way of clarifying things people say.

In his scheme, any statement is dissected into four components
* factual
* self-revelation
* relationship
* appeal 2/9

The speaker, intentionally or not, sends messages on all of these levels.
The listener, intentionally or not, hears messages on all of these levels.

1/14
More on @soniasodha's Analysis program from last night.

@ReicherStephen was wonderfully clear. He says there's a "classic" view of humans now, according to which we are psychological frail, biased, faulty. We cannot cope with emergencies.
bbc.co.uk/programmes/m00… 2/
This view, he says, is contradicted by the evidence. People don't tend to panic in emergency situations but act rather soberly and sensibly.

To me, that makes perfect sense: evolution would have swiftly got rid of us if our psychology failed us whenever we needed it the most.

1/4
Like I said yesterday: it's a cliff-hanger. Let's see what @soniasodha has got for us on Monday.

My recollection: the UK's modeling at the time was catastrophically wrong - "UK 4 weeks behind Italy, and 5-6 days doubling time."
That's on the record (and it was wrong).

https://twitter.com/philipcball/status/1284094366391443456

2/4
These numbers seemed to come out of @neil_ferguson's model. Then some model assumption was changed, and estimated deaths became more realistic (500,000). No one knew why because the model code was unpublished. It seemed like robustness hadn't been checked.

1/
The generalization of this argument is instructive.

When faced with danger, do nothing to mitigate the danger, otherwise you'll feel safe and forget there's a danger.

https://twitter.com/ole_b_peters/status/1282626431818911745

2/
When it's cold, don't put on clothes, or else you might forget it's cold and die of hypothermia or slip on surprise-ice.

In a car: don't put on your seat belt, are you crazy?

Traffic lights: always cross at red to avoid that false sense of safety.