I looked through the first two pages of Google Scholar for economics papers that cite Peters’ work on ergodicity. There were a lot of citations but almost none of the papers were about economics. The top relevant(ish) papers on Google Scholar (excluding other papers by Peters himself) were:
Economists’ views on the ergodicity problem, a short opinion piece which basically says Peters misrepresents mainstream economics, e.g. that expected utility theory doesn’t implicitly assume ergodicity (which is what I said I thought in my parent comment). They have a considerably longer supplemental piece with detailed explanations of their claims, which I mostly did not read. They gave an interesting thought experiment: “Would a person ever prefer a process that, after three rounds, diminishes wealth from US$10,000 to 0.5 cents over one that yields a 99.9% chance of US$10,000,000 and otherwise US$0? Ergodic theory predicts that this is so because the former has a higher average growth rate.” (This supplemental piece looks like the most detailed analysis of ergodicity economics out of all the articles I found.)
‘Ergodicity Economics’ is Pseudoscience (Toda 2023) which, uh, takes a pretty strong stand that you can probably infer from the title. It says “[ergodicity economics] has not produced falsifiable implications” which is true AFAICT (edit: actually I don’t think this is true). This paper’s author admits some confusion about what ergodicity economics prescribes and he interprets it as prescribing maximizing geometric growth rate, which wasn’t my interpretation, and I think this version is in fact falsifiable, and indeed falsified—it implies investors should take much more risk than they actually do, and that all investors should have identical risk tolerance, which sounds pretty wrong to me. But I read the Peters & Gell-Mann article as saying not to maximize geometric growth rate, but to maximize a function of the observable that has the ergodic property (and geometric growth of wealth is one such function). I think that’s actually a worse prescription because there are many functions that can generate an ergodic property so it’s not a usable optimization criterion (although Peters claims it provides a unique criterion, I don’t see how that’s true?). Insofar as ergodicity economics recommends maximizing geometric growth rate, it’s false because that’s not a good criterion in all situations, as discussed by Samuelson linked in my previous comment (and for a longer, multi-syllabic treatment, see Risk and Uncertainty: A Fallacy of Large Numbers where Samuelson proves that the decision criterion “choose the option that maximizes the probability of coming out ahead in the long run” doesn’t work because it’s intransitive; and an even longer take from Merton & Samuelson in Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods. Anyway that was a bit of a tangent but the Toda paper basically says nobody has explained how ergodicity economics can provide prescriptions in certain fairly simple and common situations even though it’s been around for >10 years years.
A comment on ergodicity economics (Kim 2019) claims that, basically, mainstream economists think ergodicity ergonomics is silly but they don’t care enough to publicly rebut it. It says Peters’ rejection of expected utility theory doesn’t make sense because for an agent to not have a utility function, it must reject one of the Von Neuman-Morgenstern axioms, and it is not clear which axiom Peters rejects, and in fact he hasn’t discussed them at all. (Which I independently noticed when I read Peters & Gell-Mann, although I didn’t think about it much.) And Kim claims that none of Peters’ demonstrative examples contradict expected utility theory (which also sounds right to me).
Ergodicity Economics and the High Beta Conundrum says that ergodicity economics implies that investors should invest with something like 2:1 leverage, which is way more risk than most people are comfortable risk. (This is also implied by a logarithmic utility function.) The author appears sympathetic to ergodicity economics and presents this as a conundrum; I take it as evidence that ergodicity economics doesn’t make sense (it’s not a definitive falsification but it’s evidence). This is not a conundrum for expected utility theory: the solution is simply that most investors don’t have logarithmic utility, they have utility functions that are more risk-averse than that.
A letter to economists and physicists: on ergodicity
economics (Kim, unspecified date). Half the text is about how expected utility theory is unfalsifiable, I think the thesis is something like “we should throw out expected utility theory because it’s bad, and it doesn’t matter whether ergodicity economics is a good enough theory to replace it”. The article doesn’t really say anything in favor of or against ergodicity economics.
What Work is Ergodicity Doing in Economics? (Ford, unspecified date), which I mostly didn’t read because it’s long but it appears to be attempting to resolve confusion around ergodicity. Ford appears basically okay with ergodicity as the term is used by some economists but he has a long critique of Peters’ version of it. I only skimmed the critique, it seemed decent but it was based on a bunch of wordy arguments with not much math so I can’t evaluate it quickly. He concludes with:
Peters makes a similar mistake to Davidson by making ergodicity the centre of his work, rather than a supporting concept where relevant. The metaphysical baggage accompanying EE [ergodicity economics] is supposed to clarify the problem. In practice it has obscured the observation that EE is essentially no more than a mechanical claim that stochastic processes, when iterated many times, are very likely to give certain outcomes. One does not have to accept [expected utility theory] as a good model of decision making to see that it is nonetheless more reasonable than EE.
So basically, I found a few favorable articles but they were shallow, and all the other articles were critiques. Some of the critiques were harsh (calling ergodicity pseudoscience or confused) but AFAIK the harshness is justified. From what I can tell, ergodicity economics doesn’t have anything to contribute.
You might be interested to know that I also wrote a paper with John Kay critiquing EE, which was published with Econ Journal Watch last year. ‘What Work is Ergodicity Doing in Economics?’ was an earlier and more general survey for a seminar, and as you note was quite wordy! The EJW paper is targeted at EE, more mathematical, generally tighter, and introduces a few new points. Peters and some other coauthors responded to it but didn’t really address any of the substantive points, which I think is further evidence that the theory’s just not very good.
Your ability and patience to follow Peters’ arguments is better than mine, but his insistence that the field of economics is broken because its standard Expected Utility Theory (axioms defined by von Neumann, who might just have thought about ergodicity a little...) neglected ergodic considerations reminds me of this XKCD. Economists don’t actually expect rational decision makers to exhibit zero risk aversion and take the bet, and Peters’ paper acknowledges the practical implementation of his ideas is the well-known Kelly criterion. And EA utilitarians are unusually fond of betting on stuff they believe is significantly +EV in prediction markets without giving away their entire bankroll each time (whether using the Kelly criterion or some other bet-sizing criteria), so they don’t need a paradigm shift to agree that if asked to bet the future of the human race on 51/49% doubling/doom game, the winning move is not to play.
afaik the only EA to have got “on the train to crazytown” to the point where he told interviewers that he’d definitely pick the 51% chance of doubling world happiness at the 49% risk of ending the world is SBF, and that niche approach to risk toleration isn’t unlinked to his rise and fall. (It’s perhaps a mild indictment of EA philosophers’ tolerance of “the train to crazytown” that he publicly advocated this as the EA perspective on utilitarianism without much pushback, but EA utilitarianism is more often criticised for having the exact opposite tendencies: longtermism being extremely risk averse. Not knowing what the distribution of future outcomes actually looks like is a much bigger problem than naive maximization)
(Sorry this comment is kind of rambly)
I looked through the first two pages of Google Scholar for economics papers that cite Peters’ work on ergodicity. There were a lot of citations but almost none of the papers were about economics. The top relevant(ish) papers on Google Scholar (excluding other papers by Peters himself) were:
Economists’ views on the ergodicity problem, a short opinion piece which basically says Peters misrepresents mainstream economics, e.g. that expected utility theory doesn’t implicitly assume ergodicity (which is what I said I thought in my parent comment). They have a considerably longer supplemental piece with detailed explanations of their claims, which I mostly did not read. They gave an interesting thought experiment: “Would a person ever prefer a process that, after three rounds, diminishes wealth from US$10,000 to 0.5 cents over one that yields a 99.9% chance of US$10,000,000 and otherwise US$0? Ergodic theory predicts that this is so because the former has a higher average growth rate.” (This supplemental piece looks like the most detailed analysis of ergodicity economics out of all the articles I found.)
The influence of ergodicity on risk affinity of timed and non-timed respondents, which is about economics but it’s a behavioral experiment so not super relevant, my main concern is that the theory behind ergodicity doesn’t seem to make sense.
‘Ergodicity Economics’ is Pseudoscience (Toda 2023) which, uh, takes a pretty strong stand that you can probably infer from the title. It says “[ergodicity economics] has not produced falsifiable implications”
which is true AFAICT(edit: actually I don’t think this is true). This paper’s author admits some confusion about what ergodicity economics prescribes and he interprets it as prescribing maximizing geometric growth rate, which wasn’t my interpretation, and I think this version is in fact falsifiable, and indeed falsified—it implies investors should take much more risk than they actually do, and that all investors should have identical risk tolerance, which sounds pretty wrong to me. But I read the Peters & Gell-Mann article as saying not to maximize geometric growth rate, but to maximize a function of the observable that has the ergodic property (and geometric growth of wealth is one such function). I think that’s actually a worse prescription because there are many functions that can generate an ergodic property so it’s not a usable optimization criterion (although Peters claims it provides a unique criterion, I don’t see how that’s true?). Insofar as ergodicity economics recommends maximizing geometric growth rate, it’s false because that’s not a good criterion in all situations, as discussed by Samuelson linked in my previous comment (and for a longer, multi-syllabic treatment, see Risk and Uncertainty: A Fallacy of Large Numbers where Samuelson proves that the decision criterion “choose the option that maximizes the probability of coming out ahead in the long run” doesn’t work because it’s intransitive; and an even longer take from Merton & Samuelson in Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods. Anyway that was a bit of a tangent but the Toda paper basically says nobody has explained how ergodicity economics can provide prescriptions in certain fairly simple and common situations even though it’s been around for >10 years years.Ergodicity Economics in Plain English basically just rephrases Peters’ papers, there’s no further analysis.
A comment on ergodicity economics (Kim 2019) claims that, basically, mainstream economists think ergodicity ergonomics is silly but they don’t care enough to publicly rebut it. It says Peters’ rejection of expected utility theory doesn’t make sense because for an agent to not have a utility function, it must reject one of the Von Neuman-Morgenstern axioms, and it is not clear which axiom Peters rejects, and in fact he hasn’t discussed them at all. (Which I independently noticed when I read Peters & Gell-Mann, although I didn’t think about it much.) And Kim claims that none of Peters’ demonstrative examples contradict expected utility theory (which also sounds right to me).
Ergodicity Economics and the High Beta Conundrum says that ergodicity economics implies that investors should invest with something like 2:1 leverage, which is way more risk than most people are comfortable risk. (This is also implied by a logarithmic utility function.) The author appears sympathetic to ergodicity economics and presents this as a conundrum; I take it as evidence that ergodicity economics doesn’t make sense (it’s not a definitive falsification but it’s evidence). This is not a conundrum for expected utility theory: the solution is simply that most investors don’t have logarithmic utility, they have utility functions that are more risk-averse than that.
A letter to economists and physicists: on ergodicity economics (Kim, unspecified date). Half the text is about how expected utility theory is unfalsifiable, I think the thesis is something like “we should throw out expected utility theory because it’s bad, and it doesn’t matter whether ergodicity economics is a good enough theory to replace it”. The article doesn’t really say anything in favor of or against ergodicity economics.
What Work is Ergodicity Doing in Economics? (Ford, unspecified date), which I mostly didn’t read because it’s long but it appears to be attempting to resolve confusion around ergodicity. Ford appears basically okay with ergodicity as the term is used by some economists but he has a long critique of Peters’ version of it. I only skimmed the critique, it seemed decent but it was based on a bunch of wordy arguments with not much math so I can’t evaluate it quickly. He concludes with:
So basically, I found a few favorable articles but they were shallow, and all the other articles were critiques. Some of the critiques were harsh (calling ergodicity pseudoscience or confused) but AFAIK the harshness is justified. From what I can tell, ergodicity economics doesn’t have anything to contribute.
You might be interested to know that I also wrote a paper with John Kay critiquing EE, which was published with Econ Journal Watch last year. ‘What Work is Ergodicity Doing in Economics?’ was an earlier and more general survey for a seminar, and as you note was quite wordy! The EJW paper is targeted at EE, more mathematical, generally tighter, and introduces a few new points. Peters and some other coauthors responded to it but didn’t really address any of the substantive points, which I think is further evidence that the theory’s just not very good.
Thanks for linking your paper! I’ll check it out. It sounds pretty good from the abstract.
Your ability and patience to follow Peters’ arguments is better than mine, but his insistence that the field of economics is broken because its standard Expected Utility Theory (axioms defined by von Neumann, who might just have thought about ergodicity a little...) neglected ergodic considerations reminds me of this XKCD. Economists don’t actually expect rational decision makers to exhibit zero risk aversion and take the bet, and Peters’ paper acknowledges the practical implementation of his ideas is the well-known Kelly criterion. And EA utilitarians are unusually fond of betting on stuff they believe is significantly +EV in prediction markets without giving away their entire bankroll each time (whether using the Kelly criterion or some other bet-sizing criteria), so they don’t need a paradigm shift to agree that if asked to bet the future of the human race on 51/49% doubling/doom game, the winning move is not to play.
afaik the only EA to have got “on the train to crazytown” to the point where he told interviewers that he’d definitely pick the 51% chance of doubling world happiness at the 49% risk of ending the world is SBF, and that niche approach to risk toleration isn’t unlinked to his rise and fall. (It’s perhaps a mild indictment of EA philosophers’ tolerance of “the train to crazytown” that he publicly advocated this as the EA perspective on utilitarianism without much pushback, but EA utilitarianism is more often criticised for having the exact opposite tendencies: longtermism being extremely risk averse. Not knowing what the distribution of future outcomes actually looks like is a much bigger problem than naive maximization)