Talk:Ergodicity economics

Removal of notability and citations warning

Hi @TimothyBlue: thanks for reviewing the initial article and for your warning flags. I have removed the two flags you added after adding extensive additional material. Please, if you have time, could you check whether that is sufficient and let me know. Thanks! --Fractalfalcon (talk) 18:57, 2 January 2021 (UTC)

• Reply: Very nice first article. Best wishes from Los Angeles,   // Timothy :: talk  19:03, 2 January 2021 (UTC)

Relation to classic decision theory section

The basic mainstream economic model isn't accurately characterised by the article. It is not the change of utility that is maximised, but the sum of each period's utility. Further, consumption, not wealth, is the argument; people are assumed to get utility from consuming a loaf of bread, not having a dollar in the bank.

Of course, consumption is facilitated by wealth. Specifically, in each time period, wealth is either consumed or saved, at least in a simple model. The previous sentence is captured mathematically by the following period budget constraint: $y_{t}+x_{t}=c_{t}+x_{t+1}$, where $y_{t}$ is an income endowment received in period t, $c_{t}$ is consumption in period t, and $x_{t}$ is wealth at the start of period t (and $x_{t+1}$ is wealth at the start of period t+1, so the amount saved in period t is $\Delta x_{t+1}$).

So, the formula might be changed to: $\max _{\{c_{t}\}}\sum _{t=0}^{T}E(u(c_{t}))$ subject to the constraint $y_{t}+x_{t}=c_{t}+x_{t+1}$, along with some endpoint conditions. That is, maximise the sum of expected utility from consumption, but remember that increasing one period's utility requires you to decrease some other period's utility. The agent cares about wealth, but not for its own sake; rather, only insofar as wealth facilitates consumption. Equivalently, using the budget constraint to substitute out for consumption: $\max _{\{x_{t}\}}\sum _{t=0}^{T}E(u(y_{t}-\Delta x_{t+1}))$.

For a fuller example of the basic economic model of intertemporal choice, including the solution for consumption in each period, see https://en.wikipedia.org/wiki/Permanent_income_hypothesis#Simple_model

I didn't make the change myself because the commentary depends on it, and I still don't understand ergodicity economics well enough to explain its differences relative to mainstream economics. I hope this helps others to correct the article in due course. — Preceding unsigned comment added by Michael98743 (talk • contribs) 06:11, 20 October 2021 (UTC)

More fringe?

I'm not comfortable with the recent edits by @BenjaminSkjold. They don't solve the issues that were raised in the Wikipedia:Fringe_theories/Noticeboard/Archive_95#Ergodicity_economics discussion.

Describing 'Ergodicity economics' as an established approach 'yielding alternative solutions to classic problems in economics', apart from sounding like a fringe theory, is entirely unsourced. The text that was added and restored appears to be partly an interpretation of WP:PRIMARY sources not supported by them explicitly and partly unreferenced entirely.

If there are secondary sources that come to same conclusions, they should be referenced. If such sources don't exist, I can't see it as anything other than original research aimed at promoting a theory. PaulT2022 (talk) 03:34, 18 November 2023 (UTC)

I feel that the page in its current state makes it hard to find out what the actual content of ergodicity economics is. The current sections are

1. opening paragraph

2. Background

3. Coverage in the wider media

4. Criticism

I think a few simple explicit examples would be useful, and I propose to insert a section after "background" where the following content would be worked out:

• Ergodicity breaking can be nicely illustrated with the multiplicative coin toss. It's immediately recognizable as a classic gambling problem, and it would be natural to use something like this to first clarify what ergodicity means and why it is interesting in an economic context. The example has appeared in lectures, papers, blog posts, and books.
• The cooperation problem is an example of something that can be solved by considering the long-time limit instead of the expected value (i.e. by exploiting the ergodicity concept). Marc Elsberg writes about it in his book Greed, using the very accessible Farmer's fable.
• The mapping between wealth maximization over time and expected-utility maximization can be used to clarify the relationship between ergodicity economics and classic decision theory (classic as in: 18th and 19th century, not all modern forms of expected-utility theory can be mapped to ergodicity economics).

Any objections to this? I don't know when I will have time to do it, but I'm happy to give it a try. I can post here on the talk page first and see if anyone has comments before putting it on the live page. Aretwodeetwo (talk) 16:12, 26 March 2024 (UTC)

Did any secondary sources that describe ergodicity economics from this angle appear? If the suggestion is to 'work out the content' based on lectures, WP:PRIMARY papers and a book by a professor of storytelling, I don't see how this complies with WP:PSTS, WP:RS and WP:SYNTH. --PaulT2022 (talk) 20:10, 26 March 2024 (UTC)

I know the primary literature better than the secondary literature, but the coin toss and the cooperation problem have appeared in secondary sources. I'm not sure about the third example. It has been independently discovered, so there are two different forms of it by independent authors (basically continuous and discrete).

The idea with listing a few concrete examples of what has been done under this label is to avoid any kind of subjective evaluation. The examples I've chosen are simple mathematical statements which numerate readers can verify for themselves, and there are plenty of online code snippets and apps available where they are visualized and illustrated.

An evaluation should be kept separate from this exposition. It can go in the Criticism section, for instance.

How about I try something, and you tell me if anything subjective, evaluative, or inappropriate sneaks in? Aretwodeetwo (talk) 09:01, 28 March 2024 (UTC)

Below is an idea for adding the coin-toss example. I can run a simulation and add a figure to this to make it clearer. Any comments most welcome. There are many ways of presenting this, and I went for one that requires minimal mathematical knowledge.

==Example==

The concept of ergodicity and non-ergodicity in economic decision-making can be illustrated with a repeated multiplicative coin toss. It demonstrates how the assumptions underpinning traditional economic models, particularly those related to expected utility and risk assessment, can lead to misconceptions about real-world outcomes when analyzing stochastic processes.

=== Repeated Coin Toss ===

In this thought experiment, a person participates in a simple game where they toss a fair coin.

If the coin lands heads, the person gains 50% on their current wealth.

If the coin lands tails, the person loses 40% of their current wealth.

The game is designed to show the difference between the expected value of an investment, or bet, and the time-average or real-world outcome of repeatedly engaging in that bet over time.

==== Calculation of Expected Value: ====

The expected value of the gambler's wealth following one toss is calculated as follows.

Denoting current wealth by $x(t)$, and the time when the payout is received by $t+\delta t$, we find that wealth after one round is given by the random variable $x(t+\delta t)$, which takes the values $1.5x(t)$ (for heads) and $0.6x(t)$ (for tails), each with probability $p_{\text{H}}=p_{\text{T}}=1/2$. The expected value of the gambler's wealth after one round is therefore

${\begin{aligned}::::E[x(t+\delta t)]&=&p_{\text{H}}\times 1.5x(t)+p_{\text{T}}\times 0.6x(t)\\::::&=&1.05x(t).::::\end{aligned}}::::$

By induction, after $T$ rounds expected wealth is $E[x(t+T\delta t)]=1.05^{T}x(t)$, increasing exponentially at 5% per round in the game.

This calculation shows that the game is favorable in expectation -- its expected value increases with each round played.

==== Time-Average Performance: ====

However, the time-average growth of wealth yields different insights. Wealth in this game is a non-ergodic process, and its expected value does not indicate what happens with probability one over time. The expected value is the average over all possible outcomes. In physical terms, it would be realized if an infinitely large ensemble of gamblers were to play independently, pool their wealth after playing T rounds and divide it equally.

The time-average performance, on the other hand, indicates what happens to the wealth of a single gambler who plays repeatedly.

After $T$ rounds, this wealth will be

$x(t+T\delta t)=\prod _{\tau =1}^{T}r_{\tau }x(t),$

where we have written $r_{\tau }$ to denote the realized random factor by which wealth is multiplied in the $\tau ^{\text{th}}$ round of the game (either $t_{\tau }=r_{\text{H}}=1.5$ for tails; or $t_{\tau }=r_{\text{H}}=0.6$, for tails). Averaged over time, wealth has grown per round by a factor

$::::{\bar {r}}_{T}=\left({\frac {x(t+T\delta t)}{x(t)}}\right)^{1/T}::::$

Introducing the notation $n_{\text{H}}$ for the number of heads in a sequence of coin tosses we re-write this as

$::::{\bar {r}}_{T}=\left(r_{\text{H}}^{n_{\text{H}}}r_{\text{T}}^{T-n_{\text{H}}}\right)^{1/T}=r_{\text{H}}^{n_{\text{H}}/T}r_{\text{T}}^{(T-n_{\text{H}})/T}.::::$

For any finite $T$, the time-average per-round growth factor, ${\bar {r}}_{T}$ is a random variable. To arrive at a characteristic scalar which can be compared with the per-round growth factor of the expected value, we take the long-time limit by letting the number of rounds diverge, $T\to \infty$. The proportion of heads tossed then converges to the probability of heads (namely 1/2), and we find

$::::\lim _{T\to \infty }{\bar {r}}_{T}=\left(r_{\text{H}}r_{\text{T}}\right)^{\frac {1}{2}}\approx 0.95.::::$

We now see the effect of broken ergodicity: over time, with probability one, wealth decreases by about 5% per round, in stark contrast to the increase by 5% of the expected value.

=== Numerical Illustration ===

=== Implications and Importance ===

The repeated coin toss is important because it challenges the common assumption that decisions should be made based on maximizing expected utility. In scenarios like this, where outcomes are non-ergodic, the expected utility does not align with what most participants will actually experience over time. This discrepancy arises because losses have a more significant impact on the final wealth due to their compound nature, a factor not accounted for by simply calculating the expected value.

The thought experiment highlights the need for economic theories and decision-making models to consider the dynamics of wealth and the potential non-ergodic nature of economic processes. Aretwodeetwo (talk) 15:01, 2 May 2024 (UTC)

I agree that the Ergodicity Economics page does seem stripped from content at the moment and it would be nice to have some kind of explanation why ergodicity economists think time averages are important. Other economics pages usually have sections like 'main features' or 'main models' and maybe the coin-toss example could take this role. However, I think the text needs some editing. I have four issues: First, the text lacks references. Second, the text comes across as biased towards the theory as opposed to mainstream theory. Third, I think it's too long, a shorter explanation would be better. Fourth, it is not clear what the coin-toss has to do with utility. Tove-88 (talk) 15:42, 2 May 2024 (UTC)

Thank you for your comment. This is, of course, only a first draft, so happy to modify.

You seem to have two conflicting objectives. One: "it would be nice to have some kind of explanation why ergodicity economists think time averages are important." And two: "the text comes across as biased."

I think the way to deal with this is to remove any discussion of importance, why something may or may not be interesting etc. from the technical exposition of the example. I would even leave out the "implications and importance" section for now. Perhaps you can add a section on that (your point one).

It's also not necessary to relate the analysis to utility. So any references to that can be removed. What may be useful on the page itself is a section on "what is ergodicity."

As for shortening: always a good idea, but maybe that's too tricky to discuss on the talk page -- I could post a modified version of this on the live page, and if you have a good way of shortening it, go ahead. Aretwodeetwo (talk) 15:59, 2 May 2024 (UTC)

Many thanks again for your comments and suggestions. I have tried to incorporate all of them and uploaded my attempt. Please have a look and modify as you see fit. Aretwodeetwo (talk) 08:27, 3 May 2024 (UTC)

Overall I think the new version looks pretty good. Still a little long - maybe some of the steps towards finding the time average could be omitted? I edited the text a little.

Would you mind if I also change the time notation a bit? I think the notation with δt is unnecessarily complicated, and I don't see a reason for starting the time at t instead of 0.

It should be possible to explain why ergodicity economists thinks this specific property of economic processes is so interesting in a completely neutral way... Tove-88 (talk) 13:14, 3 May 2024 (UTC)

If you can think of ways to shorten it, that would be helpful, of course. I have no opinion on notation. Maybe something similar to the original articles so readers can identify what is what? But I didn't pay attention to that. If you can improve, please do. Aretwodeetwo (talk) 20:42, 5 May 2024 (UTC)

Criticisms of EE section

I think this section could be updated and made more specific. There are several important criticisms that are missing. Namely the reply to the Peters article in Nature Physics, by Doctor et al has several important criticisms that could be highlighted beyond what is specified here. There is also the Ford and Kay critique which recently appeared in Econ Journal Watch. Both of these specifically criticise the theory and the experimental evidence. The experimental criticism could be elaborated a little by explaining what the experiments did and claim to show, and how the criticisms apply to this, otherwise it seems vacuous to just say that they were criticised. Finally the criticisms of the experiment currently listed is just a blog post by Adam Goldstein, but the same paper was also released as a researchers.one article which is a journal/preprint repository. I would propose change to the more formal version. NotChomsky (talk) 11:35, 3 May 2024 (UTC)

I think this is a good idea. The Doctor et al paper is already cited, but the details about the criticism are very limited. Currently, the there is not much information about the core propositions of ergodicity economics, and it will probably be hard to discuss the details without first stating those, like the relation to expected utility theory which seems to be a central theme... Tove-88 (talk) 11:55, 3 May 2024 (UTC)

Sounds great! If you know more about these criticisms, I think it would be very useful to be more explicit and concrete here. Aretwodeetwo (talk) 20:39, 5 May 2024 (UTC)