Peters (2019) made a splash criticizing the theory of expected utility on the grounds that it implicitly assumes ergodicity where this is unwarranted. He stated this applies widely in economics, to the point of making the whole field suspect:

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 also proposed a fix of the theory based on maximizing time-average growth rate.

Doctor et al. (2020) responded stating that Peters essentially missed the target. Economists are aware of the problem (and have been for a while) and as a rule do not apply the theory of expected utility in the naive way that Peters suggests they do (though of course there are exceptions, as everyone tends to make a mistake every now and then). Briefly, what Peters got right is not new, while what is new is not right.

Peters (2020) responded that he does not see much disagreement between what he originally said and what Doctor et al. (2020) state.

Among some other reactions, Andreozzi (2021) and Kim (undated, a; undated, b) were largely skeptical of Peters.

So there is the original paper and the subsequent exchange with Doctor et al., and a couple of other responses. There must also have been some reactions of economists in, say, blogs and other spaces, given the publicity the original paper has received. Do we have a consensus among economists regarding the merit (relevance, validity) of Peters' critique?

This is not a question of opinion. I am trying to objectively gauge the consensus in the profession, i.e. has the matter become clear to most and has the majority opinion converged on anything concrete. References to back up an answer would be most appreciated.

The question is motivated by a discussion in the comments of "Why are utility functions typically assumed to be concave?"


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    $\begingroup$ I've heard economists mention it as an example of utter trash coming from econophysics. I doubt you get more "consensus" on this, clearly the author is ignorant of even the most basic decision theory. $\endgroup$ Commented Aug 3, 2021 at 7:06
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    $\begingroup$ @MichaelGreinecker, thank you! Links to such examples would be appreciated. $\endgroup$ Commented Aug 3, 2021 at 7:08
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    $\begingroup$ This is a paper in a physics journal stating nonsense about economics without even quoting any economic research. I doubt you will find much public information. Time is scarce. $\endgroup$ Commented Aug 3, 2021 at 8:42
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    $\begingroup$ I still haven't met any economit who takes Peters seriously. You can take this as evidence for economists' arrogance if you want to. $\endgroup$
    – Bayesian
    Commented Aug 3, 2021 at 12:10
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    $\begingroup$ Overblown claims of this kind are almost surely incorrect. $\endgroup$
    – PatrickT
    Commented Aug 3, 2021 at 23:11

3 Answers 3


Well there is no opinion poll among economists on specifically this problem, but what can be judged from reaction of economists the consensus is that the Ole Peters paper is misguided and irrelevant at best. I think the economists' consensus was already very well and succinctly summed up by Doctor, Wakker and Wang you cite (and is an example of this phenomena).

For starters, on twitter R. Thaler (Nobel Prize) called it hogwash, if a Nobel Prize winner for work on decision making and behavioral economics so readily dismisses your idea about how humans make decision under uncertainity its a red flag. This work was also criticized by other notable economists such as Farmer.

However, even more can be judged by the non-reaction of economists. The Ole Peters paper was so widely circulated that it is safe to assume that majority of economists know about (I would bet that if you will ask at your university department about "that ergodicity paper" most of them will know what you are talking about). It is unbelievable but this paper got so much free press that it should an case study in marketing (it was covered and uncritically cited by major media outlets such as Bloomberg and it even got a TED talk).

So it is safe to assume at very least most economists are aware of the Peter's work existence. Yet, if you look at which articles cite the Peters work, you will see most are either A) criticisms, B) not even in the field of economics and C) save for the criticisms most are not published in any reputable journal.

The Peters work is now already 2 years old, given that it is so widely known, and given that the work basically claims that our whole expected utility framework even in its general and behavioral applications is both wrong and not useful, you would expect that people would jump at the idea and start widely applying it, or at least testing it.

This is because expected utility is widely used workhorse model, and even though one can criticize it on a behavioral grounds it remains useful, the same way as Newtonian Physics, remains useful in presence of general relativity. In the areas where it is not useful we have behavioral models that still build upon the idea of expected utility or alternative theories that do not require ergodicity (e.g. like prospect theory etc., see Kahneman Thinking Fast and Slow for discussion).

Yet we do not see people at mass abandoning either expected utility or other more generalized concepts amass. Rather the paper was met by a silence occasionally interrupted by cricket's chirp.

Now either there is some conspiracy going on in our profession, or simply most economists do not even consider the paper worth while to respond to or engage with. Given how large our profession is conspiracy is unlikely (given that likelihood of keeping conspiracy secret declines drastically with number of people involved in e.g. see work of Grimes 2016 on this). So really the most straightforward explanation for the utter lack of influence of the paper on profession is that the general consensus is that it is not even worth discussing.

One could also argue that the idea is being suppressed by the 'old guard'. There are several historical examples of new ideas in a field being suppressed, for some time, by established scientists e.g. like this example. While it is not impossible that is happening to the ergodicity idea as well, one has to remember that for any good idea that is too eagerly suppressed by the 'old guard' there is always a large number of ideas that were dismissed by the old guard and actually also turned out to be bad or irrelevant. A good example are ideas like EM drive or think of all the 'theories' like ancient astronaut theory. So while it could turn out that ergodicity is being suppressed, it is more likely that it is actually not.

Of course, an important caveat is that absence of evidence is not necessary evidence of absence. Ideally, you would want some poll among economists, or at least well known economists. This being, said the evidence and lack of thereof that we currently have strongly points toward the conclusion that the consensus is that Peters work is irrelevant.

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    $\begingroup$ "Now either there is some conspiracy going on in our profession, or simply most economists do not even consider the paper worth while to respond to or engage with." This does not seem to consider that EU experts have little incentive to admit if EU is not useful in models - rendering their previous work obsolete - even without coordination. I make no claims about EU, but your argument is not very insightful. As Peters also critices behavioralism, Thaler is similarly lacking in incentives to embrace him. $\endgroup$
    – Giskard
    Commented Aug 3, 2021 at 10:17
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    $\begingroup$ @1muflon1 I think you pretty much hit the nail on the head. The only thing I might recommend adding are perhaps specific examples of nonEU theories being used (rank dependent utility being used to model insurance markets, for example, or Cumulative Prospect Theory being used to model the impacts of defaults and dominated options in choice lists). You could also make the analogy to Newtonian physics--we know conclusively that classical physics models are wrong, but they're really easy to use and model most "normal" situations with incredible accuracy. $\endgroup$
    – AndrewC
    Commented Aug 3, 2021 at 11:59
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    $\begingroup$ that comic is brilliant $\endgroup$
    – duckmayr
    Commented Aug 3, 2021 at 22:01
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    $\begingroup$ Thanks! Not realizing you had already done so, I also linked to the same comic at the other question. $\endgroup$
    – Giskard
    Commented Aug 4, 2021 at 9:14
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    $\begingroup$ @Giskard great minds think alike ;) $\endgroup$
    – 1muflon1
    Commented Aug 4, 2021 at 9:33

I’am the guy who wrote the short note that was mentioned in the original question. You can reach the note here.


I got interested in Peter's paper because of my interest in evolutionary games, where the question of whether the equilibrium selection process is or is not ergodic plays a crucial role. I agree that most economists find Peters' contribution irrelevant. However, by reading Peters’ original paper and Wakker e.a. reaction to it, a casual reader may get the impression that Peters has a point after all, but that he tends to oversell his results. The same impression one gets by reading other informal contributions written online by economists, including the present discussion.

In my note, I provide a pedantic presentation of Peters' running example and prove a very simple proposition, which, if correct, may put the entire matter at rest. This proposition says that in Peters’ example no subject who obeys the axioms of EU would accept the lottery unless he has an unbounded utility for money. In this respect, Peters' example is just a more involved instance of the St. Petersburg paradox and can be solved the way K. Menger solved the original one in 1934: the paradox only arises because we let utility for money be unbounded. Notice that it is easy to be fooled on this matter: risk-aversion will not do the trick, just as Menger proved in 1934.

The reactions to my result have been mixed. O. Peters was extremely polite, but he said that he receives way too many contributions to ergodicity economics to evaluate them all. No follower of ergodicity economics has shown any interest.

I had a brief mail exchange with P. Wakker, and he alerted me about the difference of opinion between K. Arrow (who believed unbounded utility to be a violation of EU) and P. Samuelson (who held the opposite view). In the end, he convinced me to side with Samuelson, although I still think Arrow's position may be defended. In any case, my result proves that Peters provided a very small contribution to a literature that in economics is half a century old. (In fact, you can find Samuelson’s view on Peters’ example in a PNAS paper published in 1971.)

I had some encouragement from some respected decision theorists, but most economists were not interested. From a prominent game theorist, I got a reply that rang something like: “nice work, but I have no patience for this matter”. Finally, the note has been downloaded more than 100 times, but none has sent me an email for a comment or for any other reason. I concluded that the profession is so busy that even a moderately complex result as mine is seen as overkill for ergodicity economics.

Anyway, any comment is welcomed!


PS If you have a bent for philosophical digressions, my note also discusses Peters’ claim that, when facing a compound lottery, EU assumes that a decision-maker experiences all alternative histories. In this case, Peters’ argument collides with the fact that EU is based on the independence axiom, which forces a DM to consider only the branch of the tree she happens to visit. In fact, just the opposite of what Peters claims is true.

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    $\begingroup$ How cool it is to hear from the author himself (I mean you)! Thank you so much! I would love to be able to contribute to the debate, but I only have rudimentary knowledge of decision theory, game theory and ergodicity. I nevertheless find the topic interesting and your paper helpful and illuminating! $\endgroup$ Commented Aug 11, 2021 at 7:21
  • $\begingroup$ Have a look at amazon.co.uk/Prediction-Learning-Games-Nicolo-Cesa-Bianchi/dp/… and I think Chapter 9. Universal portfolios etc. Worst case learning bounds. This stuff is quite fundamental and economists have no idea. I have yet to see a derivation of DCF from a control/decision/RL framework point of view. Would be interested if anyone knows. $\endgroup$
    – safetyduck
    Commented Dec 2, 2022 at 13:49
  • $\begingroup$ Not sure I understand this comment. That book is a very long exposition of topics developed in the 50s by obscure scientists working on the then-new field of game theory (Hannan and Blackwell mostly). The relevance of these results was discovered decades later with fundamental papers published (in top journals in Econ) by Adreeu-Mas Collell and Sergiu Hart, Fudenberg and Levine, and a few others. Maybe economists do have a clue. $\endgroup$ Commented Dec 6, 2022 at 20:58

Junior econ professor here. I saw Ole Peter's work and I was intrigued, so I actually looked into it to see if there was something original/insightful for me to learn. I even run a little simulation of what he calls the "St. Petersburg Paradox", to make sure I understood what the guy is actually talking about.

Just to be clear, I didn't spend days looking into this. I "only" spent a few hours, until I was confident that I had an informed opinion. I eventually came to the conclusion that his point has actually little to do with the ergodicity of stochastic processes, which is a well-defined concept that (i agree) most economists are probably not familiar with. However, most time-series econometricians are definitely familiar with it


His point has instead a lot to do with what's called Jensen's inequality, something that most economists learn by end of year 1 of grad school


What settled it for me was going online, and finding out that a much more senior colleague of mine (who unlike me is a published expert on time series) had - completely independently - reached a similar conclusion:


So I initially thought "well the poor guy [Peters] is just being naive: he thinks he's made a discovery and literally he's just struggling with Jensen's inequality". That is until I saw his Ted Talk and looked into his background (he works at a Climate Change/Social Justice center).

Now I'm not so sure he's being naive. I think more likely he's muddying the waters on purpose. He is giving this "stuff" (calling it a theory is too much of a stretch in my view) the pompous name of "ergodicity" so that he can sound smart and go around pontificating about inequality, climate change etc. and argue for extreme policies that would be rejected by traditional economists, because (so goes his argument) they don't understand how randomness and time interact.

That's a very old trick: you come up with some pseudo-scientific mumbo-jumbo full of technical jargon from different disciplines that most people can't understand, and then you use that to put yourself forward as an "expert", and advance ideological positions as if they were based on hard science.

Now what to make of the fact that this "ergodicity" stuff got published in Nature Physics? Well we should note that in this case the editors went out of their way and published an article about economics, which is outside of their field of expertise - with predictable consequences. That is why we have specialized journals for different disciplines.

Now if you don't believe me and you suspect that we are biased because we are "traditional economists", of course that's a possibility. Then my encouragement is: do what I did. Go ahead and figure it out for yourself. Read his paper, read the two wiki articles I linked, pick up a statistics textbook. And if you do figure out something interesting out of this, come back and do let me know. I'm happy to be proven wrong.

  • $\begingroup$ Thank you for a hands-on perspective. $\endgroup$ Commented Aug 6, 2021 at 2:54
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    $\begingroup$ The en.wikipedia.org/wiki/St._Petersburg_paradox was analyzed by Nicolas Bernoulli in 17-something and is thus much older than Ole Peters. Already back then he suggested utility functions and that is why these concave function $u$ that we use are called Bernoulli utility functions. $\endgroup$
    – Bayesian
    Commented Aug 6, 2021 at 10:25
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    $\begingroup$ I find this answer very interesting, for a couple of reasons. To begin with, Jensen’s inequality is usually taught to first-year maths undergrads, so it’s perhaps not as closely-guarded a secret of classically-trained economists as is hinted at here. But secondly, your Wikipedia link about ergodicity itself acknowledges that econometrics and signal processing use a different definition of ergodicity (which uses a temporal sample) than that used in physics (which uses a spatial sample at a single instant). Are you sure you’re talking about the same thing Peters is? $\endgroup$
    – JCW
    Commented Aug 9, 2021 at 6:07
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    $\begingroup$ Never hinted at nor thought that Jensen's inequality was an economists' secret. With respect to the definition of ergodicity, my conclusion was not dependent a particular definition of ergodicity. My point in fact is that you don't need any notion of ergodicity (neither physical nor econometric) to explain the phenomenon that OP is concerned with. And even if ergodicity had anything to do with it (remains to be proven) OP's unsubstantiated claim that, as a consequence of that, we should change the way we model income inequality in economics is a non-sequitur. $\endgroup$
    – bbecon
    Commented Aug 10, 2021 at 1:46

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