[HN Gopher] The Ergodicity Problem in Economics
___________________________________________________________________
The Ergodicity Problem in Economics
Author : ali92hm
Score : 139 points
Date : 2021-03-07 07:01 UTC (16 hours ago)
(HTM) web link (www.nature.com)
(TXT) w3m dump (www.nature.com)
| Pyramus wrote:
| This is a fascinating example of 'if you have a hammer, all you
| see is nails'. It seems odd that this has been published at all -
| but then again, it is most likely to be published in journal that
| is not domain-specific.
|
| The author seems to miss that "economics" is a vast field
| spanning the whole spectrum from applied economics, over
| theoretical economics, mathematical finance, financial
| mathematics, to pure mathematics (with physicists working along
| the whole spectrum, so this is not a consequence of the author's
| background per se).
|
| He fails to engage at the right level. From a theoretical
| mathematician's point of view all models are wrong - they are
| just deductions from assumptions. From an applied economist's
| point of view are models are right - they explain some observed
| phenomena.
|
| Ergodicity is not a niche topic, most intermediate courses on
| stochastic processes will cover it. Will loosening an assumption
| about the properties of stochastic processes yield different,
| potentially better models? Maybe. Will it lead to a revolution in
| economic theory? Unlikely.
|
| Again, odd that this has been peer-reviewed.
|
| See also the reply here, which is rather damning [1]
|
| And the author's reply to the reply. [2]
|
| [1] https://www.nature.com/articles/s41567-020-01106-x
|
| [2] https://www.nature.com/articles/s41567-020-01108-9
| xapata wrote:
| While I am sympathetic to the author's claims, I was surprised
| to see that the author didn't "strong man" the prevailing
| economics views. Anyone trying to keep up with recent
| macroeconomics research could randomly sample papers and
| probably half would analyze only the equilibrium growth path as
| if it were a certainty that the equilibrium were stable.
| [deleted]
| javitury wrote:
| Thanks for sharing the economics' reply, I found it very
| interesting. All the good stuff is in the supplement.
|
| They argue that Peters' model produces extreme risk aversion in
| lotteries with (near) zero payoffs, and such risk aversion is
| not backed by empirical work or even by intuition.
|
| "Would a person ever prefer a process [A] that, after three
| rounds, diminishes wealth from US$10,000 to 0.5 cents over one
| [B] that yields a 99.9% chance of US$10,000,000 and otherwise
| US$0? Ergodic theory predicts [A] [... but] [v]irtually
| everyone will prefer B"
|
| That is, growth models don't behave well at or near zero.
|
| Personally, I enjoyed reading Peters solution to the St.
| Petersburg paradox and how the ergodicity framework is applied
| to economics in such a concise and intuitive manner.
|
| But I am reluctant to think that this ergodicity framework will
| completely remove the "psychological" aspects of economics. The
| utility of agents still needs to be accounted for. The
| ensembles that Peters describes are heterogeneous, and agents
| can derive different amounts of utility even if wealth or
| growth rates are equal. Think about insurance.
| Xcelerate wrote:
| Could someone summarize what everyone in the comments is arguing
| about in less technical terms? I don't have a background in
| economics but do have a background with physics.
| ReflectedImage wrote:
| Economists have been using ensemble average where they should
| of being using time average.
|
| Using the wrong type of average mildly screws up everything in
| very subtle ways as you can imagine.
|
| A lot of the important results in the field including one that
| got a nobel prize turn out to be wrong.
|
| The economists are responding to this in a very mature way and
| have told Ole Peters "he can go kick a rock".
| H8crilA wrote:
| It's some hilarious turf/flame war.
|
| The paper itself is pretty interesting if you know some maths
| and haven't thought about non-linear utility functions. You can
| also read that "original" paper by Bernoulli, he has some
| simple examples there (for example why does it make sense to
| buy insurance despite it having negative expected payoff, he
| brings the example of ship cargo insurance but it applies to
| any kind of insurance really).
|
| EDIT: Daniel Bernoulli's paper:
| https://www.semanticscholar.org/paper/Exposition-of-a-New-Th...
| rmbeard wrote:
| Exactly.
| fallingfrog wrote:
| I think what's going on is that "hard sciences" people in
| physics etc have a strong feeling that most of economics (and
| behavioral science and psychology) is bunk, given that
| economists in particular seem to have all sorts of mutually
| contradictory theories, are always making predictions that turn
| out to be wildly wrong, and seem to disagree with one another
| on basic facts. This paper gives them ammunition to support
| these feelings that the emperor has no clothes.
|
| I am not qualified to judge whether those feelings are correct
| however.
| sjg007 wrote:
| I see the stock market as an interesting non-linearity that can
| decouple the value of a company from its monetary performance.
| Then there is the idea of technology and transformation which can
| happen in a short amount of time and be bigger than you expect.
| The market, like the Universe continues to expand and I guess
| smaller ones go through collapse from time to time but unlike
| physics we don't have universal forces defining trajectories.
| QuesnayJr wrote:
| I don't get what people find so exciting about his papers, which
| I find borderline troll-ish. We know that people in general don't
| reason the way he says he does. If people only cared about log of
| wealth, they would take much more risks than they do. If everyone
| did it, the return on stocks would be much lower than it is,
| because everyone would regard stocks as a great deal despite the
| volatility.
| kgwgk wrote:
| You may have seen this already: https://arxiv.org/abs/1101.4548
|
| Funny stuff. They predict that in aggregate 100% of the wealth
| is invested in stocks and investing more than that would be
| suboptimal: the optimal leverage is 1.
|
| They "submit the hypothesis to a rigorous test" and find that
| the optimal leverage for the S&P 500 is around 1, given its
| volatility.
|
| There is a small problem with their rigorous test. They forgot
| to include dividends: "a real investment in the S&P500 outgrew
| federal deposits at only 2.0% p.a".
|
| Including dividends would bring the optimal leverage to 2 or 3.
| But that's ok. It's close enough to 1 for them, apparently.
|
| Even better: ignoring dividends was not so wrong anyway because
| the S&P 500 overestimates the return of a real equity
| investment due to survivorship bias.
|
| "The S&P500 is an index of five hundred large companies, listed
| publicly in the United States. We use it as a proxy for a
| generic diversified investment in US stocks, but we note some
| caveats. Firstly, the index does not account for dividends paid
| to stockholders. This means it will tend to underestimate the
| performance of a real investment. Secondly, the index suffers
| from survivorship bias, representing a portfolio of the largest
| and most successful companies in the US, in which less
| successful companies are routinely replaced. This acts in the
| opposite direction to the first caveat."
| QuesnayJr wrote:
| I hadn't seen that. Thanks.
| fraserphysics wrote:
| Chapter 6 of "Elements of Information Theory" by Cover and Thomas
| is "Gambling and data compression". It explains that maximizing
| expected utility almost always leads to ruin. I didn't believe it
| when I first read it. Of course it is exactly correct. I
| reccomend it.
| [deleted]
| drdeca wrote:
| I feel that this downplays the justification for theories of
| expected utility too much? But I still want to keep reading to
| see where they're going with this. Ok, like, it says that
| modeling people as trying to maximize expected utility, is like
| assuming something as if one is interacting with paralell
| universe copies of onseself. But, surely the author must be
| familiar with the Von Neumann-Morgenstern utility theorem?
|
| It complains that when people fail to act according to the
| theories, that the people are considered to be irrational, rather
| than amending the theories. While it is of course true that
| theories need to be made to account for how people actually
| behave, it seems to me that people failing to satisfy the vNM
| axioms, really is a way in which people fail to live up to the
| correct ideal of a rational agent. Well, maybe for it to make
| sense, instead there should be a formalization of like, a
| compute-limited approximation of following the vNM axioms, maybe
| throw in a dash of sub-agent stuff, and a few things along those
| lines.
|
| Hmm.
|
| Ok, well, if this makes better predictions of how people behave,
| that is valuable. Though, it would raise the question of "why?".
| zwaps wrote:
| It's really mind boggling if you know the original proofs my
| Neumann-Morgenstein or Savage for that matter.
|
| In his article, Peters immediately rushes into the time domain,
| whereas the time domain doesn't exist at all in EUT.
|
| I feel like Peters could have made a valid point about the
| application of dynamic EUT, but he severely over-claims the
| problem he sees.
|
| To refute EUT, Peters had to start with one set of EUT axioms.
| He clearly doesn't want to do that. We can guess why.
| ReflectedImage wrote:
| Ole Peters has addressed this. He had a study of real people
| done, which shows that real people make decisions using the
| time domain.
|
| The behaviour of real people matches Ole Peters maths but not
| EUT. This means that EUT does not apply to the real world,
| which makes EUT a pointless theory.
| QuesnayJr wrote:
| Even that isn't new. There are hundreds of experiments that
| point out the limitations of EU. If you're looking for a
| reason to reject EU, you didn't need to wait until now.
| Allais published his paradox in 1953.
|
| If Peters wants to propose an alternate theory, he needs to
| explain all of this existing evidence. For example, he
| needs to explain why historically the return on stocks is
| so high. If people only cared about the logarithm of
| wealth, they would hold almost entirely stocks and very
| little bonds. They would take their weekly paycheck and
| deposit it directly into their Robinhood account. (And
| everyone would have a brokerage account.)
| ReflectedImage wrote:
| Ole Peters doesn't have to show things, he isn't
| claiming.
|
| "people only cared about the logarithm of wealth" But
| that isn't what Ole Peters is claiming.
| kgwgk wrote:
| That's not correct.
|
| "Multi-period Expected Utility Theory Predicts Zero Risk
| Aversion in Copenhagen Experiment, Same as Ergodicity
| Economics."
|
| https://medium.com/@aa_goldstein/multi-period-expected-
| utili...
| rmbeard wrote:
| One could always use Choquet expected utility to get around any
| behavioral objections to the von Neumann or Savage
| axiomatizations of expected utility theory. Unfortunately this
| ergodic paper by Peters is simply not a constructive
| contribution to the debate but rather a red herring.
| irotatori wrote:
| Reactions/rebuttals by economists here:
|
| https://old.reddit.com/r/badeconomics/comments/kcmtce/guy_wi...
| ReflectedImage wrote:
| The issue is that the rebuttals are wrong. They have just
| objected for the sake of objecting.
| ilaksh wrote:
| Is there a field that is similar to economics but is empirical
| and about building working systems rather than just theories, and
| incorporates recent high tech advances, and accounts for
| sustainability by incorporating things like finite resource
| tracking?
|
| Personally I think almost all of it is outdated and have no
| respect for economists. To back systems that perpetuate such
| gross inequity it seems most must have a very dated and
| reductionist Social Darwinist mindset.
|
| The first thing we need is to start to incorporate technology
| into society, such as by comprehensively tracking resources.
| Things like distributed technologies are the best starting point
| for this. Then when we use point systems for distributing control
| over resources (money) that should be a high tech system that is
| integrated with resource tracking and regulation.
|
| The way the current system works is kind of like if someone built
| an MMORPG and only included one stat --- money. Then, instead of
| server code for managing things, the powerful Economic Cult
| characters estimated what was happening and tried to regulate
| everything by controlling the spawn of gold coins.
| ReflectedImage wrote:
| FinTech hires Maths PhDs for this sort of thing.
| dash2 wrote:
| > Is there a field that is similar to economics but is
| empirical and about building working systems rather than just
| theories, and incorporates recent high tech advances, and
| accounts for sustainability by incorporating things like finite
| resource tracking?
|
| Yes.
|
| It's called "economics".
|
| Empiricism is absolutely central to modern economics. Here's
| the latest AER, the top journal.[1] 7 out of 8 articles are
| empirical. 4 out of 8 actually use the word "Evidence" in the
| title; by now this is practically a meme.
|
| Incorporates high tech advances: interested in machine
| learning? Here's an overview for you:
| https://www.nber.org/system/files/chapters/c14009/c14009.pdf
|
| Accounting for sustainability? First, environmental economics
| is an entire subfield. William Nordhaus won the Nobel prize[2]
| for estimating the costs of global warming, oh, and have you
| heard of the Stern Review? More broadly, the field of economics
| was famously _defined_ as "Economics is the science which
| studies human behaviour as a relationship between ends and
| _scarce means_ which have alternative uses " (my italics).
| Sounds like it might be relevant to finite resource tracking.
|
| Lastly, I'm not sure why you think economists support the
| current level of inequality. I'd wager most don't. Maybe you've
| heard of _Capital in the 21st Century_ , which put inequality
| squarely back on the political agenda. It's by Thomas Piketty,
| an economist.
|
| [1] https://www.aeaweb.org/issues/625
|
| [2] I beseech you not to tell me how It's Not Really The Nobel
| Prize. Everyone knows. Nobody cares.
| smitty1e wrote:
| From undergraduate Control Systems theory those decades ago, the
| point of Ergodicity seems to be that, as long as we reach a
| steady state, we can ignore the transients.
|
| Which seems a great simplifying assumption where applicable.
| penstroma wrote:
| I love reading critiques of articles by Hacker News readers in
| their fields of expertise, and finally feel I may be able to make
| a small contribution to the community.
|
| Below are some of my thoughts after a glance through the paper:
|
| 1. The critique of the article by Doctor et al. (linked from Ben
| Golub's Twitter) summarizes my thoughts succinctly. I am left
| wondering: if everyone used "ergodicity" as the basis of their
| decisions, doesn't this imply that, given some scenario with
| risk, everyone would make the same decision? But this is
| certainly not true. The author mentions that different people
| might care about "additive growth" vs. "geometric growth", but
| this is equivalent to using different functional forms of utility
| (e.g. CARA vs CRRA). Perhaps the author is saying that his
| ergodicity-derived decisions are "optimal"? But in what sense? It
| seems to me that his maximization of the growth rate is
| equivalent to using log utility. This result is well-known (see
| the Kelly criterion).
|
| 2. Ergodicity is covered in first-year graduate econometrics (at
| least where I was taught). See Hayashi Chapter 2. Perhaps not
| everyone reads it this way, but the tone of the article seems to
| suggest that this topic is completely foreign to economics.
|
| 3. There is a rich economics literature in decision theory.
| Savage's work on subjective expected utility shows that under a
| certain set of axioms of rationality, the decisions that a person
| makes can be completely captured by a subjective probability
| distribution and a personal utility function. The sentence
| "expected utility theory implicitly assumes that individuals can
| interact with copies of themselves, effectively in parallel
| universes" is completely misguided.
|
| 4. There are a number of well-known documented violations of
| expected utility (e.g. the Allais paradox). These represent
| challenges to the axioms of rationality. Nevertheless, the point
| of using expected utilities is to model human behavior, even if
| it is only approximate. From Rubinstein's great book "Economic
| Fables": "I remember the moment as a student when I realized that
| the models in economic theory do not assume that the decision
| maker consciously tries to maximize his preferences, but only
| assume that the behavior of a decision maker can be described _as
| if_ he had maximized some objective function " (emphasis mine).
|
| 5. It is true that time-separable utility (usually with constant
| relative risk aversion, or CRRA) is often assumed for many
| mainstream models for tractability reasons. However, in recent
| years substantial progress has been made in extending utility to
| recursive preferences, e.g. Epstein-Zin. In fact, Epstein-Zin is
| essentially as tractable as the conventional time-separable CRRA
| utility, and allows for the separation of elasticities between
| risk and time. I expect that these more sophisticated preferences
| will soon be the norm. There are even stranger preferences in
| use, for example hyperbolic discounting. A whole field
| (behavioral economics) is founded on the notion that humans are
| not rational. The point is, lots of work has been done on
| generalizing utility functions.
|
| 6. I am not exactly sure what point the author is trying to make
| with Figure 2. This appears to be nothing more than a
| demonstration of Ito's Lemma (the convexity adjustment necessary
| for solving stochastic differential equations). In fact, the
| author mentions as much in the last paragraph of the third
| section.
|
| 7. My (ungenerous) interpretation of the experiment section:
| "Look, experiments calibrate the coefficient of relative risk
| aversion to be about 1 (log utility). And there doesn't seem to
| be much heterogeneity in risk aversions across people. This is
| consistent with my ergodicity-derived decisions, which is
| essentially log utility. Hence my model is supported!" (For
| reference, the usual calibrations I encounter for CRRA range from
| 1 to 5.)
|
| 8. Finally, the "Outlook" section. This section definitely rubbed
| me the wrong way. The author patronizes the entire field of
| economics, boasts of the ingenuity of his invention, and claims
| to somehow link together everything from the equity premium of
| the stock market to optimal monetary policy. It sounds too
| overconfident of itself and dismissive of others. References to
| works I expect to see are absent, and self-citations are
| abundant.
|
| After reading this paper, I was gently reminded of Baez's
| "Crackpot Index". I imagine that what I am feeling is similar to
| what a physics professor might feel after reading an idea for a
| perpetual motion machine. There is a mixture of correctness and
| sophistry, with a dash of illusions of grandeur. It is
| comprehensible enough to understand and reasonable-sounding
| enough to require some effort to criticize. Looking back, writing
| such a lengthy critique might not have been the best use of my
| time.
|
| I am rather surprised this paper was published. I am not familiar
| with Nature Physics, but based on this article alone, my regard
| for it is not high. In my opinion, this paper would not be sent
| out for refereeing, let only pass the referees, at any reputable
| economics or finance journal.
| kgwgk wrote:
| Thanks for taking the time to write this. I wish I could upvote
| multiple times.
| conformist wrote:
| Thank you for the insightful comment! Nature physics is a
| reputable journal for physics, but it seems to struggle finding
| good reviewers for economics topics. It's unclear why they
| would even accept economics papers.
|
| Some thoughts on this: Peters has published with Gell-Mann, so
| physicists might be unreasonably impressed. My feeling based on
| interacting with theoretical physicists at university is that
| there is a good portion of them who have little knowledge about
| and interest in other quantitative disciplines. They sometimes
| have a tendency to like to feel superior to "less rigorous"
| disciplines, so it's not unlikely that the particular reviewers
| were attracted to this?
|
| Peters probably submits his papers to all kinds of journals,
| and probably very similar papers many times over. His more
| recent papers are kind of mono-thematic. The maths is not
| actually incorrect and easy to check, so once in a while they
| might get through the review process. Maybe that's the
| "ergodicity approach to publishing"?
| penstroma wrote:
| Thanks for explaining, and after reflection I must apologize
| for implying Nature Physics was disreputable. I understand it
| is not a mainstream economics or finance journal, so the
| domain of papers it reviews and accepts will be different. I
| also believe Peters is well-regarded in whatever is his area
| of expertise, but this doesn't appear to be economics.
| ReflectedImage wrote:
| The paper mathematically disproves Prospect theory, which won
| a nobel prize. It belongs in Nature.
| kgwgk wrote:
| > once in a while they might get through the review process
|
| He talks about a paper that has been "rejected by 14
| economics journals, if I've counted correctly, for
| questioning the ergodic hypothesis."
|
| I've not looked at that paper. I don't know how bad it is.
| But I suspect that "questioning the ergodic hypothesis" may
| not be the only reason.
|
| https://twitter.com/ole_b_peters/status/1294216181159796736
| ReflectedImage wrote:
| 1. non-ergodicity not ergocitity. "everyone would make the same
| decision?" No, in fact it explains why rational actors make
| different decisions when faced with the same rewards and risk.
|
| 2. You clearly don't understand it. Ole Peters is claiming that
| the ergodicity assumption is wrong and purposing a non-
| ergodicity version of economics to fix it.
|
| 3. "expected utility theory implicitly assumes that individuals
| can interact with copies of themselves, effectively in parallel
| universes" is completely correct. EUT implies that is true as
| one of it's implicit assumptions.
|
| 4. Which raises the question of why has no one but Ole Peters
| has come up with a new theory to fix the violations? It's poor
| show by the field of economics. Our theories don't work, let's
| just sit on our broken theories.
|
| Given Ole Peters work is mathematically correct and shows EUT
| to be mathematically incorrect. It's pretty pointless calling
| him a "crackpot". There is an objective right answer here and
| Ole Peters has that right answer.
| kgwgk wrote:
| What do you mean by EUT?
|
| A reference to the paper or textbook that you learnt it from,
| for example, would suffice.
|
| Even better if you can point to the specific place where
| there is something mathematically incorrect and/or an
| implicit assumption of individuals interacting with copies of
| themselves in parallel universes.
| timdaub wrote:
| Thanks for posting. I had read Antifragile in parts but I had
| never heard of Ergodicity. But it's a great technical term to
| understand!
|
| I looked online and found this post that explained it well:
| https://taylorpearson.me/ergodicity/
| hfkgktkrlfk wrote:
| Taleb did write about ergodicity:
|
| > _A central chapter that crystallizes all my work. Time to
| explain ergodicity, ruin and (again) rationality_
|
| https://medium.com/incerto/the-logic-of-risk-taking-107bf410...
| tomjakubowski wrote:
| n.b.: Taleb in this chapter cites Ole Peters, who is the
| author of the featured article.
| ReflectedImage wrote:
| Calling it Ergodicity Economics is a bit confusing. Existing
| economics is ergodicity. Ole Peters is claiming that the
| ergodicity assumption in economics is false. His corrected
| version of economics should be called Non-Ergodicity Economics.
| sn41 wrote:
| Ergodic theorist (occasional) here. Ergodic theory is basically
| studying situations in which the time average of (almost every)
| trajectory equals the space average of the system.
|
| This is a widely studied area in dynamical systems.
|
| I am squeamish about such popular accounts. An old account
| which is readable even today, is by Birkhoff [1].
|
| About Kelly-Bernoulli criterion, the readable account is the
| book [2].
|
| [1] https://doi.org/10.1080/00029890.1942.11991212
|
| [2] "Fortune's Formula" by William Poundstone.
| https://archive.org/details/fortunesformulau00poun
| bobcostas55 wrote:
| A reply by some economists: "Economists' views on the ergodicity
| problem"
|
| https://sci-hub.se/https://www.nature.com/articles/s41567-02...
| wrnr wrote:
| Talk by the same author for those that don't like to read: Time
| for a change - https://www.youtube.com/watch?v=f1vXAHGIpfc
| [deleted]
| RobertoG wrote:
| They have a webpage: https://ergodicityeconomics.com/
| dellannaluca wrote:
| Here is a short introduction to ergodicity in non-mathematical
| terms:
| https://twitter.com/DellAnnaLuca/status/1339621378765537282?...
| dools wrote:
| Microeconomics is meaningless unless everyone gets macroeconomics
| right
| offby37years wrote:
| It is easier to macro bullshit than it is to micro bullshit.
| laszlosandor wrote:
| Time to read!
| https://twitter.com/ben_golub/status/1338175642932715520?s=2...
| juskrey wrote:
| Many words about how economics is like physics, hence Peters
| makes a terrible insults to generations of respectful
| academics. And not a single word about how they are still
| missing the ruin problem, and how ergodicity is a dead simple
| and exact answer to it
| drdeca wrote:
| The main article doesn't seem to refer to "the ruin problem"
| either. What is that?
| juskrey wrote:
| Ole should repeat it on more occasions, since this is what
| it's all about: economic unit is not an average of the same
| imaginary economic units following different paths, some of
| which can end in a bankruptcy. Instead single bankruptcy
| will end the whole process, this is a ruin problem. That is
| economic unit is an average on its own timeline, not space.
| xapata wrote:
| In a pithy form, it's the fact that in the long run we are
| all dead.
| [deleted]
| nullc wrote:
| #!/usr/bin/python3 import random #100 people
| start with $100 balances=[100]*100 #They take
| 10000 bets with an _expected_ return of 1.25x. # ...
| so they should end up with ~1.2e1000 at the end...
| for i in range(10000): balances=[0 if x<=0 else
| random.choice([x*2,x//2]) for x in balances] #Yet all
| or almost all are bankrupt: print(len([x for x in
| balances if x<=0]))
| ulucs wrote:
| > # ... so they should end up with ~1.2e1000 at the
| end...
|
| Who has ever claimed this? Also, people end up with zero
| because you are doing integer division in your code (ie
| the simplified expected return is wrong). Here are my
| results with 100 bets, and 10000 bet takers. The average
| return is also on the upward trend, but not really close
| since CLT doesn't really apply to this distribution:
| >>> sum(balances)/1000000 24546192.840913434
| >>> print(len([x for x in balances if x<=100]))
| 5426 >>> print(len([x for x in balances if
| x>=100])) 5381 >>> print(len([x for x in
| balances if x>100])) 4574
| nullc wrote:
| Keeping it integer specifically was useful to avoid
| running out of precision using Python's multi-precision
| integers.
|
| You can show ruin without any flooring division:
| #!/usr/bin/sage import random
| balances=[Rational(100)]*100 for i in range(10000):
| balances=[0 if x<=0 else random.choice([x*2+2,x/2-1]) for
| x in balances] #Yet all or almost all are bankrupt:
| print(len([x for x in balances if x<=0]))
|
| The key points are that there is a state that a
| participant can't recover from (e.g. ending up bankrupt)
| and you do enough trials that are reasonably likely to
| eventually wander into it.
|
| One that is the case 100 bets with 10000 betters and
| 10000 bets with 100 betters stop being the same thing.
|
| And this is a very realistic and physical assumption
| because real investments have integerization, fees,
| overheads, etc. You can't invest a femto-cent in the
| market, and certainly not get the same relative returns
| as someone investing 100k.
| ulucs wrote:
| But that's factored in EUT anyway: you simplify the
| compound lottery and it turns out you have a huge
| probability of hitting zero. You might ask whether people
| will take the bet, and that's where the _utility_ comes
| in. Enough risk averseness, and noone will take a return
| of a million dollars with a 1% chance of happening at a
| price of 100%
| [deleted]
| davidgl wrote:
| This article linked above covers it well, highly
| recommended: https://taylorpearson.me/ergodicity/
| wazoox wrote:
| Economics is not like physics at all. It's a social science,
| rooted in many social assumptions and compromises and power
| relationships between human beings and groups. Most attempts
| to negate this are just tortuous ways to justify the current
| power structure.
| imtringued wrote:
| There is a small nugget that is as hard as physics. Namely
| the tools can be analyzed in their theoretical performance.
|
| But economics is deeply tied to politics. What type of
| economy you have is entirely dependent on current
| leadership. It's the government that sets the basic
| foundation and rules upon which the economy is built. Some
| governments decided to go to either extreme. Communism or
| capitalism. There is a price equilibrium, assuming one is
| allowed to exist, which is dependent on your government,
| but where exactly it lies is also entirely dependent on the
| laws the government set.
|
| If the government bans garbage disposal in rivers then it
| would be completely unreasonable to insist that the
| equilibrium price should stay the same.
|
| By this same logic if there is an inherent injustice or
| imbalance it exists in the laws the government created.
|
| One prominent example would be the central bank flooding
| the market in a way that benefits existing asset holders,
| one could have done the exact opposite as well or maybe
| even done a little of both. It's not a question of which is
| the right action, the question is "What kind of economy do
| you want?" and the central bank has spoken.
| wazoox wrote:
| Precisely. "What kind of economy do you want?" is a
| political question, that has no definite, scientific
| answer. And more restrictive economic questions, very
| often, also are political questions that should be
| democratically debated and decided, but are instead
| presented as "scientific" in nature, with the pretension
| that "we should do as our experts said" (whose experts
| exactly?).
| ssivark wrote:
| That Twitter thread is tautological trash, to put it politely.
| It seems more interested in protecting turf than directly
| critiquing (or even understanding) Ole Peters' central point.
|
| It is absolutely silly, bordering shitposting, to respond to a
| claim about subtle/hidden assumptions by claiming:
|
| > Expected utility theory makes 4 assumptions, which are stated
| precisely and concisely in every graduate textbook. Ergodicity
| is not among them.
|
| when the whole point is that the conventional economics
| literature might have ignored a subtlety.
| ssivark wrote:
| My comment on EE and von Neumann-Morgenstern utility turned
| out longer than expected, so I wrote a blog post here:
| http://sivark.me/blog/ergodicity-economics-and-von-
| neumann-m...
|
| (I'd also like to hold on to a copy rather than losing it
| buried in a comments thread :-)
|
| Since the larger discussion is getting side-tracked and might
| expire before we get a chance to discuss, I made a new HN
| submission to focus on this, if you prefer:
| https://news.ycombinator.com/item?id=26378454
| QuesnayJr wrote:
| It's not. You can read the proofs to see that they aren't
| missing a step. If you don't want to do that, I can give some
| indirect evidence. The "conventional economics literature"
| begins with a theorem of von Neumann and Morganstern,
| published in 1944. This is the John von Neumann of math and
| physics fame. In particular, von Neumann was one of the
| architects of ergodic theory. He proved the mean ergodic
| theorem all the way back in 1932. It would be pretty
| surprising indeed if it was von Neumann who missed the
| subtlety.
| ReflectedImage wrote:
| It would be more correct to say economists misinterpreted
| what von Neumann said.
| QuesnayJr wrote:
| They didn't, though. Look at von Neumann and
| Morganstern's "Theory of Games and Economic Behavior".
| There's nothing in there about time-series averages. It's
| a theory of games that you might play only once.
| ReflectedImage wrote:
| It's fairly obvious that in the real world time does play
| a role. This may shock you but theories advance over
| time. There isn't a holy paper which can never be
| improved on (at least not in sensible research fields).
| QuesnayJr wrote:
| Essentially all economic models of investment have a time
| dimension. I'm not sure where you're getting the idea
| that it's left out.
|
| Also, the field has gone far beyond von Neumann-
| Morganstern, so I'm not sure where you're getting that,
| either. I'm simply making the point that expected utility
| does not require ergodicity. If you read the proofs, it's
| clear. If you don't want to read the proofs, the best
| that I can do is provide indirect historical evidence.
| ReflectedImage wrote:
| "I'm simply making the point that expected utility does
| not require ergodicity."
|
| Okay well that point is wrong, as in very wrong.
|
| Ergodicity can be directly defined as it is valid to take
| the Expected Value. That's just what Ergodicity means.
|
| Expected Utility is defined on top of Expected Value.
|
| So Expected Utility assumes Ergodicity.
| QuesnayJr wrote:
| Weird, I can't reply directly.
|
| Peters (and you, I assume) are taking a strong
| philosophical stance on the meaning of probability. Lots
| of people would disagree with you. Essentially all
| Bayesians would disagree with you, for example.
| ReflectedImage wrote:
| Yeah reply seems to be a bit buggy.
|
| "strong philosophical stance on the meaning of
| probability" ???
|
| It's taken directly from thermodynamics:
| https://en.wikipedia.org/wiki/Ergodic_hypothesis
|
| You would be arguing directly with the laws of
| thermodynamics.
| dash2 wrote:
| You're suggesting that sometimes time matters. I agree.
| There's a whole subfield of economics studying the
| dynamics of decisions. However, As Wakker et al. point
| out:
|
| "Although it is true that our consumption of economic
| goods develops over time, time is not the most central
| aspect of all our decisions. For many of our decisions,
| other equally ubiquitous aspects such as risks, strategy
| and the balancing of pros and cons are more central. Just
| because something is ubiquitous, it should not be
| confused with being explanatory; for example, we can
| argue everything consists of molecules, but it is not a
| reason to think that all questions in economics,
| geography and throughout life should be answered by
| molecular dynamics.... Economists use static EU for
| static decisions, when dynamics are not central.
| Otherwise, a dynamic model is used."
| zwaps wrote:
| "Ergodicity economics" is not a new idea, as others have
| said.
|
| Peters' claims the contrary, and then claims to "destroy" a
| whole academic field with one fell swoop. That's academic
| shitposting.
|
| That EUT is based on assumptions that have nothing to do with
| time is quite crucial, and one major misunderstanding.
| However, if you read on, you see that Peters makes other
| claims that don't hold up.
|
| Look at it from this side: Here comes someone trying to carve
| out a heterodox niche (he ain't the first), but he does it
| without actually discovering something new and without the
| proper care for or understanding of economic theory.
|
| This ruffles people's feathers.
| [deleted]
| ReflectedImage wrote:
| I looked into this. The economists have really screwed up here.
|
| Basically, Expected Utility Theory (EUT) is wrong. It happens to
| give the right result by coincidence when you set the fudge
| factor U to log(wealth), which all economists do without any
| justification.
|
| Well EUT is corrected using the fudge factor, other parts of
| economics built using it are not.
|
| The nobel prize winning Prospect theory, when you correct the
| maths, dissolves away into nothing. The theory says people
| deviate away from the expected rational answer due to
| psychological reasons. It turns out people use the rational
| answer, the maths in Prospect theory is just wrong.
|
| Additionally, the famous St. Petersburg paradox isn't a paradox
| and has an exact answer.
|
| This is a pretty big blow for economics and the economists on
| social media aren't actually being mature about it.
| alimw wrote:
| Olle Peters has been pushing this for years. Economists are
| still working.
| ReflectedImage wrote:
| Well economics has never been working. 50% of all maths
| models in economics fail basic sensitivity analysis tests
| (read: they can not be correct). It's also refered to as the
| "dismal science".
|
| Ole Peters work is at least a step in the right direction.
| kgwgk wrote:
| The growth-optimality justification for using logarithmic
| utility is not new. It goes back at least to the 1950's and was
| discussed by prominent economists. See for example
| http://finance.martinsewell.com/money-management/Markowitz19...
| zwaps wrote:
| Economists have since refuted the points above:
|
| https://www.nature.com/articles/s41567-020-01106-x
|
| Read both sides!
| billfruit wrote:
| Thats behind a paywall.. any other link?
| ReflectedImage wrote:
| https://www.youtube.com/watch?v=LGqOH3sYmQA
| ReflectedImage wrote:
| I have, the economists completely failed to refute Ole
| Peters' points. As a Comp Sci PhD I'm telling you Ole Peters
| is correct.
| zwaps wrote:
| As a stats PhD, I am telling you Ole Peters is
| misunderstanding what EUT is ;-)
|
| EUT was developed by von Neumann, someone _slightly_
| familiar with ergodicity. It simply is not based on
| dynamics of out-of-equilibrium systems. Any such thing is
| an application that adds assumptions to the construct.
|
| Ergodicity is an obvious addition in the time domain, it is
| so obvious that the insight is not even new. However,
| Peters restricts the problem to a very simple dynamic
| gamble and then claims that all of economics must be wrong.
|
| The very first sentences of Peter's article already get
| this completely wrong.
|
| If you insist on his results, despite the quoted article,
| the most one can say is that the application of EUT to
| these problems is questionable.
|
| To put it in terms you may be more familiar with. It's like
| saying that Object Oriented Programming is "wrong", because
| Python doesn't work for my problem at hand.
| ReflectedImage wrote:
| "It simply is not based on dynamics of out-of-equilibrium
| systems"
|
| I think that's basically the key point. Ergodicity
| economics and the real world are both based on dynamic
| out of equilibrium systems. Where regular economics is
| not.
|
| Real people behave according to ergodicity economics
| according to Ole Peters study and also the data set used
| in Prospect's theory.
| rmbeard wrote:
| This is also not correct, it depends on which economic
| model you are looking at. Some assume equilibrium some
| study transitory dynamics to the equilibrium. You can't
| make general statements like that and expect them to be
| always true, you need to refer to a specific model not
| the field as a whole.
| ReflectedImage wrote:
| It's true for Expected Utility Theory and anything that
| has been based on top of it.
| ReflectedImage wrote:
| Sigh,
|
| "Ergodicity is an obvious addition in the time domain"
| Great, except Ole Peters if you understood his work is
| adding non-ergodicity.
|
| Ole Peters is effectively claiming that static gambles
| don't exist (outside of utterly bizarre circumstances
| like parallel universes or co-operatives).
|
| The set of problems that you can use EUT on and be
| correct is almost zero.
|
| To simplify:
|
| You must always use the Kelly's criteria even for single
| one-off gambles otherwise you have got the wrong answer.
|
| (There are other valid criteria then Kelly's that you
| could also use but you need to read Ole Peters' paper for
| them)
| throwaway98797 wrote:
| Kelly maximizes the median outcome, I think. I've yet to
| find an approach that minimize the bottom x percentile.
| If you're aware of one I'd love to learn it.
| hntrader wrote:
| I think you mean something that _maximizes_ the bottom x
| percentile (either by making the negative smaller or the
| positive bigger).
|
| It's not going to be an easy solution, because for a
| sufficiently small _x_ , the optimal strategy for a small
| number of bets is going to be to bet $0 each time (since
| the _x-th_ percentile of the terminal outcome will be a
| loss on capital, or ruin), but the optimal strategy for a
| large number of bets is going to be to bet > $0 (since
| the _x-th_ percentile of the terminal outcome will be
| positive).
|
| So we can already see that this is going to be a function
| of the number of bets, unlike with Kelly, and therefore
| is going to be a much harder problem.
| kgwgk wrote:
| > The set of problems that you can use EUT on and be
| correct is almost zero.
|
| But his theory is applicable in a strict subset of
| those...
| ReflectedImage wrote:
| No his theory is applicable to a much wider domain.
| Basically 99.5% of problems that are being solved with
| EUT should be solved with ergodicity economics. EUT
| validity is crushed down to the 0.5%.
| kgwgk wrote:
| Could you point to one example where a problem is solved
| and their solution is not equivalent to the choice of an
| utility function?
| ReflectedImage wrote:
| @kgwgk Ahh misread for a second there. Prospect theory is
| a good example. When calculated using Ole Peters method
| Prospect theory does not exist.
| [deleted]
| kgwgk wrote:
| I don't understand what you mean. Prospect theory tries
| to solve the problems with EUT. His methods are within
| the EUT framework. Whatever the problems in EUT that are
| solved by prospect theory, they also need to be solved in
| his theory.
| ReflectedImage wrote:
| His methods are a replacement to the EUT framework. When
| you attempt to do Prospect theory with Ergonomic
| Economics you get back the null result:
|
| "People behave as rational actors"
|
| Rather than the EUT's result of:
|
| "Faced with a risky choice leading to gains, individuals
| are risk-averse (concave value function).
|
| Faced with a risky choice leading to losses, individuals
| are risk-seeking(convex value function)."
|
| Basically ergonomics economics shows that Prospect theory
| is a math's error. This is one of the reasons why Ole
| Peters work is important.
| kgwgk wrote:
| > His methods are a replacement to the EUT framework.
|
| What's the solution to this problem using his methods,
| for example?
|
| https://en.wikipedia.org/wiki/Merton%27s_portfolio_proble
| m
|
| How do his methods apply to the uncountable situations
| where expected utility theory is used?
|
| A random example: https://www.researchgate.net/publicatio
| n/240488954_Risk_of_d...
| ReflectedImage wrote:
| I'm sure there are some great research papers that can be
| written by applying ergonomic economics to those
| problems.
|
| Is your point here that Ole Peters should convert all
| problems in economics to ergonomics economics all at
| once? Cause that's a bit of a silly point to make.
|
| There is also a fundamental problem with expected utility
| theory in that U can set to any formula. It's pretty
| close to just making stuff up on the fly.
| kgwgk wrote:
| What is it then?
|
| Is expected utility theory wrong and ergodicity economics
| is an alternative?
|
| Or is EUT too broad and ergodicity economics cannot
| blamed for being nothing more than a well-known way to
| pick a specific utility function within the EUT framework
| in a very constrained subset of problems?
|
| I think it's the latter.
|
| My point is that the claims of having subverted centuries
| of flawed economic thinking based on parallel universes
| are delusional.
|
| My opinion may of course improve if any of those great
| research papers is ever written. It would also improve if
| they changed their attitude and stopped saying idiotic
| things. I'm not sure what of those is more likely...
| ReflectedImage wrote:
| Expected Utility Theory (EUT) is wrong and Ergodicity
| Economics (EE) is an alternative.
|
| EUT is claiming there are parallel universes not EE. And
| your right EUT is delusional to make that claim.
|
| About your opinion:
|
| "It is difficult to get a man to understand something
| when his salary depends upon his not understanding it." -
| Upton Sinclair
| kgwgk wrote:
| > EUT is claiming there are parallel universes not EE.
|
| Can you back this up with a reference to anything not
| coming from Ole Peters (and known associates)?
|
| > "It is difficult to get a man to understand something
| when his salary depends upon his not understanding it."
|
| Helping to clear the confusion he creates in his full-
| time occupation is a just a hobby for me.
| ReflectedImage wrote:
| It's obviously true.
|
| Let's say there is a lottery L, it has a million tickets
| $1 each, it pays out 1 million and 1 dollars on the
| winning ticket.
|
| Should you buy a ticket?
|
| EE says no. EV says yes since it has a positive EV.
|
| EE says no because in 99.999999% of cases you lose $1.
|
| EV says yes because you share the 1 million and 1 dollars
| out in equal portions with versions of you living in a
| million parallel universes, one of which won.
|
| I hope that clears this up for you.
|
| ---
|
| @drdeca:
|
| Due to missing reply button I'll reply here.
|
| The claim being made is that U is a hack.
|
| When you set U = log (Wealth), EUT gives the same result
| as EE. When you set U to any other function EUT gives bad
| answers.
|
| EE has it's own set of functions that take place of U in
| EUT and all of those functions give the right result
| whereas EUT only gives the right result when you set U =
| log (Wealth)
| drdeca wrote:
| Expected utility doesn't say that you should buy a
| ticket, no. Obviously no.
|
| That would only hold if you assume that utility is either
| linear or superlinear in money (or, more precisely, that
| the marginal utility of losing a dollar, times 1-(1/1
| million), plus the marginal utility of gaining a million
| dollars, divided by 1 million, is greater than 0)
|
| If this is the sort of argument that people advocating
| for EE are making, it makes EE seem less worthy of
| attention.
|
| Oh, you said EV not EU? Ok, but no one claims that people
| maximize expected money. That would be stupid.
|
| Using EU rather than E$ isn't some hack to add a fudge
| factor, it is capturing that people have preferences
| about things in general, not merely how much money they
| have. Placing money centrally is silly; money isn't some
| universal terminal goal. It is a convergent instrumental
| goal. Depending on what I care about, the use of money to
| me will scale differently, just like how the scale of
| other things to each-other will. The idea of utility is
| to pick the quantity which I do value linearly in
| probability. However I take probability into account,
| provided I do so in a coherent way, there is a unique-up-
| to-positive-affine-transformation utility function which
| corresponds to that.
| kgwgk wrote:
| > EUT only gives the right result when you set U = log
| (Wealth)
|
| If it does give the right result why do you say elsewhere
| that "they aren't quite identical and it does make a
| difference" and you coded and ran a simulation that
| proves it?
| kgwgk wrote:
| > EE has it's own set of functions that take place of U
| in EUT
|
| If EE is just a way to choose the U in EUT how does that
| mean that EUT is incorrect?
|
| EUT is incorrect only when there is no U that can
| describe the preferences of the agent.
| ReflectedImage wrote:
| @kgwgk You are conceptually all over the place since you
| don't understand the topic.
|
| "If EE is just a way to choose the U in EUT how does that
| mean that EUT is incorrect?"
|
| EE doesn't choose the U in the EUT. EE has something
| similar to U in it's math where you can select any
| function of a certain class and plug it in.
|
| One of those function when plugged in gives out the Kelly
| criteria.
|
| "If it does give the right result why do you say
| elsewhere that "they aren't quite identical and it does
| make a difference" and you coded and ran a simulation
| that proves it?"
|
| The simulation ran the game purposed by Ole Peters where
| they give different results. Only in special games like
| the ones typically purposed by economists, do they give
| the same result.
| kgwgk wrote:
| Has it crossed your mind thay maybe it's you who doesn't
| understand the topic?
|
| EUT doesn't say what the U is. It only says that one can
| be found if the agent's preferences are rational (for
| some definition of rationality).
|
| Can you point to an example where EE provides a solution
| that cannot be represented by some utility function?
| kgwgk wrote:
| > The simulation ran the game purposed by Ole Peters
| where they give different results.
|
| I don't know if that game is related to "retirement
| portfolios", probably not.
|
| I understand then that you don't object to my claim that
| ergodicity economic formulas generate exactly the same
| portfolio as the "regular economics" approach when you
| make the same assumptions that are implicit in the
| asymptotic growth maximization (no spending, infinite
| horizon, logarithmic utility).
|
| And that you agree with Ole Peters and yours truly that
| asymptotic growth maximization of a multiplicative
| process gives the same solution as the maximization of
| logarithmic utility.
| drdeca wrote:
| > EUT is claiming there are parallel universes
|
| Nope. Unless you claim that all discussion of probability
| does the same.
|
| If an agent satisfies the vNM axioms , that is sufficient
| to conclude that the agent's actions are equivalent to
| maximizing the expectation of some function, which we
| call the utility. These axioms do not require any
| assumptions about "parallel universes" beyond simply the
| concept that "there is such a thing as probability".
| Presumably, the same idea would work even if the
| "probabilities" in question were all from logical
| uncertainty due to limited computation time, taking place
| in an entirely deterministic universe. In such a case,
| there explicitly cannot be the "alternate universes",
| because they would be logically inconsistent, but due to
| computational limits, the agent is still uncertain, and
| so it still makes sense to deal with expected utility.
| bradleyjg wrote:
| _As a Comp Sci PhD I 'm telling you Ole Peters is correct._
|
| What does being a Comp Sci PhD have to do with anything?
| ReflectedImage wrote:
| I understand the concept of modelling, something the
| economists and stats people are completely missing.
|
| This is fundamentally a modelling error. They are using
| valid maths that models the wrong scenario.
|
| Consider a group of 1,000,000 people making gambles. In
| traditional economics a rational actor will make
| decisions that maximize the SUM of the 1,000,000 rational
| actors money. In ergodicity economics a rational actor
| will make decisions that maximize it's money.
|
| A subtle distinction, but as a Comp Sci PhD I can tell
| you that small modelling error has utterly fatal
| consequences for large parts of economics.
|
| Prospect theory for example is written off.
|
| Physics PhDs also do modelling. You can see this as a
| knowledge gap in understanding of a typical economist or
| stats person, which is why they are having such
| difficultly in understanding Ole Peters work.
| bradleyjg wrote:
| The entirety of two fields don't understand modeling but
| luckily we have Computer Science, and of course Physics,
| PhDs to solve all problems in all fields.
|
| You have to be aware of how this comes off, right? This
| is all tongue in cheek?!? I mean your comment might as
| well have said "So, why does <your field> need a whole
| journal, anyway?"
| ReflectedImage wrote:
| The maths says they are wrong. There is nothing more to
| say really.
|
| https://www.youtube.com/watch?v=mGBxUNaQI1I
| bradleyjg wrote:
| In that case why the appeal to your own authority "as a
| Computer Science PhD" instead of just showing the math?
| You are trying to have your cake and eat it too---no
| credentials matter except your own.
| ReflectedImage wrote:
| Here's the maths:
|
| https://aip.scitation.org/doi/full/10.1063/1.4940236 http
| s://ergodicityeconomics.files.wordpress.com/2018/06/ergo.
| ..
| bopbeepboop wrote:
| That's a rather uncharitable interpretation.
|
| Another interpretation would be "expert in field that
| uses maths technique a lot critiques use of that
| technique in field that uses it less frequently".
|
| Empirically that's useful, eg physicists often make
| substantial contributions to economic models/math.
| ulucs wrote:
| > In traditional economics a rational actor will make
| decisions that maximize the SUM of the 1,000,000 rational
| actors money
|
| ??? Have you not heard of competitive equilibria at all?
| Is game theory outside of the realm of traditional
| economics?
|
| > Prospect theory for example is written off.
|
| Yeah, it's so written off that the authors received the
| biggest award in economics for their works in behavioral
| economics.
| bopbeepboop wrote:
| It's interesting:
|
| I spent a year developing platforms for PhD economists,
| and I would generally describe their work as "precisely
| wrong" for these reasons.
|
| We ended up starting two math research programs to try
| and keep them from building errors into our system:
|
| 1. Forcing them to actually check their math, because we
| discovered multiple math errors that drastically changed
| the results.
|
| 2. Started researching "assumption continuity" to see if
| we could define some notion of "small change in axiom ->
| small change in model" test to keep them from assuming
| "sharp" things, where if they were a little wrong the
| whole model was garbage.
|
| It's literally a research problem in industry to keep PhD
| economists from cooking the books and claiming major
| conclusions.
| dash2 wrote:
| I'm an academic in an economics department. This paper is trash.
|
| The published version of Peter Wakker et al's critique [1] is
| remarkably polite. You have to read their supplementary
| information [2] for the full, hilarious horror. Here are some
| juicy quotes to tempt you:
|
| "The EU [expected utility] value does not actually have to be
| realized or consumed in any sense.... However, Peters erroneously
| thinks that the EU value must actually be realized in some
| sense.... EU involves imagining, a priori, some outcomes that
| later may not have actually been received. This procedure
| involves imagining consequences that will never happen. But we do
| this every day, and such is the nature of every probabilistic
| decision. We do not need to believe in "parallel universes" or
| the existence of "multiverse clones"...."
|
| "A more fundamental problem in dynamic decisions is that we do
| not just maximize our entire wealth at the end of our life, but
| intermediate consumption patterns virtually always play a role.
| For nonquantitative outcomes, growth rates cannot even be
| defined. Dynamic questions as discussed here are central, for
| instance, in economic growth theory and in life-cycle consumption
| theory."
|
| "Peters suggests that economists should primarily study
| intertemporal processes, the topic of ergodic theory. For
| example, he suggests that risk attitudes and risky variance are
| not important and that interpersonal variations are not
| important, and then, in one blow, that neither is any economic
| theory."
|
| "Peters' claims that, because of the ubiquity of time, we should
| always study intertemporal growth. Similarly, a risk theorist can
| claim that we always face uncertainties and, therefore, we should
| always study risk theories.... In the annotated bibliography
| Wakker (2020), the keyword "own small expertise = meaning of
| life" gives references to other authors falling victim to this
| ubiquity fallacy.
|
| ... and then there's the experiment. Oh boy, I'd forgotten that
| part!
|
| "Meder et al. applied expected utility and prospect theory in a
| way that we call static: they applied EU and PT to each choice in
| each round separately, as if it was the only choice made and as
| if intermediate outcomes were actually received. This static
| analysis is incorrect. The intermediate outcomes are not outcomes
| received and consumed by subjects."
|
| Translation: Sorry, kid, you failed your midterm.
|
| tl:dr; This is nonsense, an embarrassment to the authors, and an
| embarrassment to physics. Yet it pops up on Hacker News from time
| to time as a Deep Mathematical Takedown of Economists by
| Physicists!!!!... No.[3]
|
| [1] https://www.nature.com/articles/s41567-020-01106-x
|
| [2] https://static-
| content.springer.com/esm/art%3A10.1038%2Fs415...
|
| [3]
| https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...
| eclat wrote:
| https://www.luca-dellanna.com/ergodicity/
|
| I found this to be an excellent overview of ergodicity and its
| implications.
| oli5679 wrote:
| (1) their insight is not novel, they have independently
| reinvented Something that started with the Kelly Criterion
|
| https://en.m.wikipedia.org/wiki/Kelly_criterion
|
| (2) Expected utility theory makes no assumptions about
| ergodicity. In intertemporal setting, portfolio allocations
| maximising expected utility will chose something close to their
| metric as well as giving some insight into the split between
| investment and consumption.
|
| https://en.m.wikipedia.org/wiki/Intertemporal_choice
|
| (3) with intertemporal analysis, the rate of discounting is
| important. This has been heavily discussed by economists and
| philosophers already. If you don't have heavy discounting, the
| future becomes much more important relative to the present than
| would be consistent with many people and government's actions.
| kgwgk wrote:
| They don't have to deal with intertemporal substitution because
| their model doesn't consider consumption at all.
|
| They care only about the limit of the rate of growth when the
| horizon grows. It's effectively a single (infinite) period
| model.
|
| At best, they just repeat a well-known argument supporting
| logarithmic utility. It's just a special case within the
| expected utility framework.
| kgwgk wrote:
| > they have independently reinvented
|
| I'm not sure it's fair to say "independently reinvented". They
| know the previous work, at least some of it. Their contribution
| is to add the word "ergodic" here and there and tell the reader
| that "Growth rate optimization is now sometimes called
| 'ergodicity economics'".
| juskrey wrote:
| Kelly here is the only way which is addressing the ruin, other
| two are (bad) tricks around initially wrong assumptions
| hntrader wrote:
| In practice, utility theory works well.
|
| Poker players adopt a utility function similar to _u(x)=x_
| and apply some very basic risk management heuristics
| (bankroll management) on top in order to handle ergodicity.
| Their whole thought process is centred on _E[u(x)]_ ( _E[x]_
| ), and they have much more affinity for expected utility
| theory than the more "correct" Kelly.
|
| Professional investors adopt a slightly risk-averse _u(x)_
| (not quite _ln(x)_ in my experience) and do just fine with
| that. Risk of ruin is managed again using simple practical
| heuristics, such as capping the maximum downside on each
| decision, and sizing up only when confident (in Kelly-like
| fashion - but very subjective).
|
| That it doesn't explicitly handle ergodicity isn't a huge
| flaw in practice. It's still a useful (although imperfect)
| mental model of what's going on in people's brains and offers
| _some_ practical usefulness.
|
| It's also not a wrong assumption technically, because it's
| not claiming to model such phenomena, its claim is to model
| the utility of a single discrete choice.
| ReflectedImage wrote:
| There are some nasty side effects of EUT through. Prospect
| theory for example shouldn't exist (when you handle the
| non-ergodicity part of the problem properly the theory
| vanishes into thin air).
|
| EUT + Hacks works but anything built upon of EUT is subject
| to sudden collapse due to unstable foundations.
|
| Ergonomic economics is able putting down stable foundations
| that other theories can be built upon of.
| [deleted]
| hntrader wrote:
| EUT should be adjusted to handle ergodicity properly. But
| the concept of expected utility needs to be the
| centrepiece of the theory.
|
| Kelly, for example, is fatally flawed because it ignores
| utility:
|
| (1) Ruin isn't an absorbing state in most contexts, due
| to bankrupticy laws, limited liability, relationships,
| and so on. Ruin _is_ an absorbing state in other
| contexts. Only utility can capture this difference.
|
| (2) Implementing Kelly requires the emotional fortitude
| of a rock. In practice, it becomes a losing strategy
| since the practitioner will collapse emotionally and make
| bad decisions whenever the distribution of the outcome is
| unknown.
|
| (3) Implementing Kelly forgets that investors will redeem
| capital if the downswing is too severe for them.
|
| (4) etc.
|
| Only a conceptual framework built around expected utility
| as a bedrock principle can handle these practical
| realities, and moreover capture those practical realities
| empirically.
| ReflectedImage wrote:
| "expected utility needs to be the centrepiece of the
| theory" Fundamentally expected utility is wrong.
|
| Kellys is fatally flawed as it's merely one of a whole
| class of functions that be used, where Kellys happens to
| be on the aggressive side of things.
|
| Ole Peters gives the entire class of the functions that
| can be used. There is obviously a whole band of less to
| more aggressive options you can take.
| hntrader wrote:
| > Fundamentally expected utility is wrong.
|
| Do you say this because EUT currently doesn't handle
| ergodicity? Why do those two things need to be mutually
| exclusive?
|
| > whole band of less to more aggressive options
|
| Right, and which option I pick will be based on utility
| preference considerations both over the lifecycle of the
| decision making process as well as over the terminal
| outcome's distribution.
|
| Expected utility is still _inextricably_ part of this.
|
| Older people are going to choose low aggression options
| on their retirement portfolio because the utility
| consequences of ruin are much different to a 20 year
| old's.
|
| Expected utility _is_ the point. Handling ergocidity just
| tells us how to get there correctly.
| ReflectedImage wrote:
| "doesn't handle ergodicity?" non-ergodicity. The
| ergodicity economics' name is confusing as it dropped the
| non- part.
|
| "Why do those two things need to be mutually exclusive?"
| EUT is basically the formula of ergodicity with slight
| changes. It doesn't retrofit.
|
| "their retirement portfolio" The ergodicity economic
| formulas generate slightly more money on average than
| their regular economics counter parts. [You can see where
| this is going...]
| hntrader wrote:
| > The ergodicity economic formulas generate slightly more
| money
|
| We're talking about a theory of humans' (financial)
| decision making.
|
| Old people make less money than young people on purpose
| because of expected utility preferences.
|
| Ignoring expected utility is therefore automatically
| fatal and a non-starter, as this single example
| demonstrates.
| ReflectedImage wrote:
| "Old people make less money than young people on purpose
| because of expected utility preferences."
|
| You need to prove this whilst keeping in mind that
| ergodicity economics takes account of factors that
| regular economics does not. You would need to show it
| wasn't one of those factors being responsible.
|
| Ole Peters has already done the studies on people
| (outsourced to a psychology department) to show they are
| following his economics model.
| hntrader wrote:
| "You need to prove this "
|
| It's already well established. Lifecycle investing is
| common practice among pension funds. "You
| would need to show it wasn't one of those factors"
|
| Firstly, I'm not the one with the burden of proof that
| has to check whether this fits the theory.
|
| Secondly, you're misunderstanding my objection. What I'm
| objecting to are the very conceptual foundations of the
| theory. Old people demonstrably accept a lower EV than
| young people because of a difference in expected utility
| over the distribution of near-term outcomes. To throw the
| concept of expected utility in the bin is therefore a
| departure from reality and as such the theory
| automatically fails on conceptual grounds.
| ReflectedImage wrote:
| The maths of Ergodicty Economics has been checked by a
| Nobel prize winning physicist. No one has been able to
| contest it.
|
| You can look all through the comment section, you won't
| find anyone claiming the maths is wrong.
|
| Ergodicty economics disproves EUT. EUT is rejected on
| solid mathematical grounds.
|
| Saying Expected Utility is correct is no different than
| claiming that 2 + 2 = 5. Though the maths involved is a
| bit more complicated.
| hntrader wrote:
| Once again, you are misunderstanding my objection.
|
| The math of EE is correct given the axioms from which it
| is deduced. Nobody anywhere is disputing that.
|
| What I'm disputing is whether it is a theory that
| explains human financial decision making, in the same way
| that some physicists dispute that string theory explains
| physical reality (despite acknowledging that the math
| behind string theory is deductively correct).
| "Saying Expected Utility is correct"
|
| It is conceptually correct, as my old vs young example
| shows. The fact that EE fails to model this is a fatal
| counterexample.
|
| Once again - the math IS deductively correct, but that
| same math fails as a theory of financial decision making
| since it doesn't explain the observed reality.
| ReflectedImage wrote:
| "I'm not talking about orthodox utility theory ("EUT"),
| and I'm not trying to say that it's currently a good
| theory, either."
|
| The reply button is missing below so I'll reply here.
|
| The issue is that the major results of economics in this
| sort of area are been effectively destroyed by EE.
| Prospect theory for example is completely gone.
|
| There may be places where people's behaviour isn't
| rational but research into that needs to be effectively
| carried out again from scratch. The main "evo psych"
| results in economists have been effectively disproven.
|
| So you might be right that people don't act rationally
| but all existing research into that area is currently
| dead in the water. It's start from square 1 again.
| hntrader wrote:
| "research ... dead in the water"
|
| There's no need for explicit research to establish the
| fact that people differ in their subjective preferences
| (utility) pertaining to outcome distributions. The
| evidence is abundant.
|
| I can go down to the casino and see this. Or I can see
| that family member A has insurance while family member B
| doesn't.
|
| You talked earlier about wanting a theory to have stable
| foundations. A theory that doesn't even recognize the
| existence of subjective expected utility is not that.
| ReflectedImage wrote:
| There are studies that show that people follow EE and not
| EUT.
|
| It's the other way around EUT fails as a theory of
| financial decision making since it doesn't explain the
| observed reality.
| kgwgk wrote:
| No. There are people who don't seem to understand what is
| EUT who claim so, though. [1]
|
| If EE just puts the U in EUT it will also fail as a
| theory of financial decision making in all the cases
| where EUT fails.
|
| [1] Did Ergodicity Economics and the Copenhagen
| Experiment Really Falsify Expected Utility Theory?
| https://researchers.one/articles/20.02.00002
| ReflectedImage wrote:
| EE does not put an U in EUT.
|
| EE stats that in EUT the U term must equal log (Wealth)
| otherwise EUT produces wrong results.
|
| EE uses a completely different formula. It has an open
| space for a (slightly restricted) function (similar to
| U). An example of EE with this open space filled is
| Kelly's criterion, which of course looks nothing like
| EUT.
| kgwgk wrote:
| > An example of EE with this open space filled is Kelly's
| criterion, which of course looks nothing like EUT.
|
| I'm not sure if I'm reading this correctly:
|
| Kelly's criterion looks nothing like EUT?
|
| Maybe I completely misunderstood what you were trying to
| say.
|
| https://en.wikipedia.org/wiki/Kelly_criterion
|
| "The Kelly bet size is found by maximizing the expected
| value of the logarithm of wealth, which is equivalent to
| maximizing the expected geometric growth rate."
| hntrader wrote:
| I'm talking about the _concept_ of expected utility. If
| EE does away with that _concept_ , then it is a failed
| theory on _conceptual_ grounds.
|
| Without this concept, tell me how EE is supposed to
| grapple with:
|
| (1) gamblers who take on negative EV bets
|
| (2) old people who shift into fixed income
|
| (3) low risk-tolerance young people who keep only cash
|
| (4) high risk-tolerance young people who put everything
| into crypto
|
| (5) why some people buy insurance and some don't, despite
| earning the same income
|
| The fact is, you can't explain this heterogeneous
| behaviour without the _concept_ of expected utility of
| outcomes.
|
| Our brains are emotional, irrational vehicles designed by
| evo psych, and you can't grapple with that reality
| without some notion of subjective preference pertaining
| to expected outcome.
| ReflectedImage wrote:
| "There's no such thing as a "correct result" because
| people's preferences (utility) varies by individual."
|
| But there are incorrect results and setting U to anything
| other than log (Wealth) results in an incorrect result.
|
| "It can also happen in other cases that EE cannot be used
| to explain the preferences of the agent while EUT is
| still applicable because a utility function (maybe
| logarithmic, maybe not) can be found which describes them
| adequately."
|
| I just told you that you can not use an utility function
| other than log (Wealth). Any other utility function you
| use will give you a mathematically incorrect result. The
| log (Wealth) term covers up the maths error, so it can't
| be changed to another term.
|
| If you want to do something like that then you need to
| use the maths from EE.
| hntrader wrote:
| "Any other utility function you use will give you a
| mathematically incorrect result."
|
| Tell that to the drunk gambler who just empirically
| falsified your fantasy theory.
| kgwgk wrote:
| What does "mathematically incorrect" mean?
|
| The role of the utility function in EUT is to represent
| the agents preferences.
|
| Preferences can be rational (i.e. consistent) and not be
| represented by the logarithm of wealth.
|
| If Mr. X has some amount to invest now to pay for his
| child's college in five years it's not "irrational" to
| opt for something less risky than taking a loan to get a
| leveraged equity investment.
|
| Mr. X may not care that his portfolio wouldn't growth at
| the optimal highest possible rate if left untouched
| forever, if that's what you mean by "mathematically
| incorrect result".
|
| Mr. X doesn't care about your idea of "correct result",
| he cares about being reasonably certain to have enough
| money available in five years.
|
| Now, you tell me to use the maths from EE to find the
| "correct" utility functions.
|
| How can I use the maths from EE to select a portfolio if
| I want to take out a certain amount of money in five
| years?
| ReflectedImage wrote:
| Okay so let me cut this down.
|
| EE shows that EUT only gives correct results when U = log
| (Wealth), that means as soon as you set U to anything
| other than log (Wealth), it is no longer giving correct
| results.
|
| So it would be fair to say EUT also has no concept of
| utility.
| hntrader wrote:
| You misunderstand the concept of subjective utility.
|
| There's no such thing as a "correct result" because
| people's preferences (utility) varies by individual.
|
| What's "correct" for a risk-seeking gambler is very
| different to what's "correct" for an investor who's
| trying to build generational wealth.
|
| That's _why_ we have a _U(x)_ to begin with. Without
| addressing this _concept_ , you're no longer attempting
| to describe reality, you're making a prescriptive
| normative assertion that everyone should follow a
| specific strategy of your choosing.
| kgwgk wrote:
| > EE shows that EUT only gives correct results when U =
| log (Wealth)
|
| You seem to think that this invalidates EUT.
|
| On the contrary, it's a vindication of EUT.
|
| In that particular case, EUT works and the preferences of
| the agent would be correctly described by that particular
| utility function. Otherwise you wouldn't say that EE and
| U=log(w) give "correct results".
|
| It can also happen in other cases that EE cannot be used
| to explain the preferences of the agent while EUT is
| still applicable because a utility function (maybe
| logarithmic, maybe not) can be found which describes them
| adequately.
| kgwgk wrote:
| How do you define "correct results"?
|
| Talking about portfolio selection, for example, the EE -
| a.k.a. U=log(wealth) - solution may be the "correct
| solution" to the "we never spend a dollar problem and we
| have an infinite horizon" problem.
|
| But EE cannot get any results, correct or otherwise, for
| many other problems that are much more interesting where
| EUT can be applied.
|
| Like investment decisions when your horizon is not
| infinite and you intend to use the money at some point.
| kgwgk wrote:
| Is there any example of ergodicity economics doing
| something other than selecting an utility function?
|
| If Expected Utility is not correct all the solutions
| proposed by Ergodicity Economics cannot be correct
| either.
| kgwgk wrote:
| > Though the maths involved is a bit more complicated.
|
| Do you claim to understand them or are you just relaying
| the claims from others?
|
| We don't even know what do you mean by EUT.
| ReflectedImage wrote:
| I've discussed this topic with several economics
| professors, thank you very much.
| kgwgk wrote:
| You're welcome. Do they agree that EUT is incorrect
| because it's about interacting with copies of yourself in
| parallel universes?
|
| Maybe they think that EUT is too limited to explain the
| world but then they won't be impressed with the more
| restrictive EE.
| ReflectedImage wrote:
| I did a 3 day conversation with them over twitter. You
| aren't going to come up with something they didn't.
| [deleted]
| kgwgk wrote:
| > "their retirement portfolio" The ergodicity economic
| formulas generate slightly more money on average than
| their regular economics counter parts.
|
| False.
|
| The ergodicity economic formulas generate exactly the
| same portfolio as the "regular economics" approach when
| you make the same assumptions that are implicit in the
| asymptotic growth maximization (no spending, infinite
| horizon, logarithmic utility).
|
| Don't you think that when people choose investments their
| objective may be to spend at least some of their money
| before the end of time?
| ReflectedImage wrote:
| @kgwgk "Because optimizing asymptotic growth and
| maximizing logarithmic utilty are mathematically
| identical."
|
| I'm afraid not. They are infact different. One includes
| the starting wealth of the gambler and the other does
| not.
| ReflectedImage wrote:
| @kgwgk "have the slightest idea of what does"
|
| On that specific problem there are other problems where
| they are not equal.
| kgwgk wrote:
| You acknowledge then that you were wrong when you said
| that "One includes the starting wealth of the gambler and
| the other does not."
|
| Good. We're progressing. You've learned something today.
| ReflectedImage wrote:
| Only how stubborn people can be.
| kgwgk wrote:
| By the way, I'm not even sure what's your misunderstading
| here.
|
| Which solution does include the starting wealth of the
| gambler, according to you, and which one doesn't?
| [deleted]
| kgwgk wrote:
| You don't have the slightest idea of what does it mean to
| maximize the expectation of logarithmic utility, do you?
|
| Will you believe it from the mouth of Ole Peters himself?
|
| This is from the Nature Physics article:
|
| "we had worked out in detail the correspondences between
| linear utility and additive dynamics; and between
| logarithmic utility and multiplicative dynamics"
|
| From "The time resolution of the St Petersburg paradox":
|
| "the time-average performance of the lottery is computed.
| The final result can be phrased mathematically
| identically to Daniel Bernoulli's resolution, which uses
| logarithmic utility"
|
| "Equation (6.10) is mathematically equivalent to
| Bernoulli's use of logarithmic utility."
| ReflectedImage wrote:
| " You acknowledge then that you were wrong when you said
| that "One includes the starting wealth of the gambler and
| the other does not."
|
| Good. We're progressing. You've learned something today.
| "
|
| No, one does include the starting wealth of the gambler
| and the other does not.
| kgwgk wrote:
| Will you believe it from the mouth of Ole Peters himself?
|
| This is from the Nature Physics article:
|
| "we had worked out in detail the correspondences between
| linear utility and additive dynamics; and between
| logarithmic utility and multiplicative dynamics"
|
| From "The time resolution of the St Petersburg paradox":
|
| "the time-average performance of the lottery is computed.
| The final result can be phrased mathematically
| identically to Daniel Bernoulli's resolution, which uses
| logarithmic utility"
|
| "Equation (6.10) is mathematically equivalent to
| Bernoulli's use of logarithmic utility."
| ReflectedImage wrote:
| True. It makes more money I've coded and run the
| simulations.
|
| The rest is just you arguing against a strawman in your
| head.
| kgwgk wrote:
| Growth-optimal portfolios are part of regular economics.
| Look it up.
|
| Maybe there was something wrong with your code? Because
| optimizing asymptotic growth and maximizing logarithmic
| utilty are mathematically identical.
| ReflectedImage wrote:
| Ergonomic Economics (EE) is a more general theory than
| Growth-optimal portfolios. Kelly's criterion is a special
| case of EE.
|
| EE doesn't suffer from the same problems as Growth-
| optimal portfolios either (Kelly's is a hyper aggressive
| form of EE).
|
| "Maybe there was something wrong with your code? Because
| optimizing asymptotic growth and maximizing logarithmic
| utilty are mathematically identical."
|
| So naive and so wrong. That's only true if you structure
| the problem to make it true. In the general case, not at
| all.
| kgwgk wrote:
| I said "generate exactly the same portfolio (...) when
| you make the same assumptions that are implicit in the
| asymptotic growth maximization".
|
| You said it was not so. That you coded and ran the
| simulations.
|
| Did you compare the asymptotic growth maximization of a
| multiplicative process with the logarithmic utility
| solution? Yes or no?
|
| Either you simulated something else or you did something
| wrong trying to simulate two problems that everyone
| agrees that are identical.
| ReflectedImage wrote:
| Yes I did.
|
| They aren't quite identical and it does make a
| difference.
|
| "that everyone agrees that are identical."
|
| Except of course the theory of thermodynamics. But now
| you are going to try to explain to me that the theory of
| thermodynamics is wrong.
|
| Hint: I won't be impressed.
| kgwgk wrote:
| Will you believe it from the mouth of Ole Peters himself?
| This is from the Nature Physics article:
|
| "we had worked out in detail the correspondences between
| linear utility and additive dynamics; and between
| logarithmic utility and multiplicative dynamics"
|
| From "The time resolution of the St Petersburg paradox":
|
| "the time-average performance of the lottery is computed.
| The final result can be phrased mathematically
| identically to Daniel Bernoulli's resolution, which uses
| logarithmic utility"
|
| "Equation (6.10) is mathematically equivalent to
| Bernoulli's use of logarithmic utility."
| kgwgk wrote:
| Seriously, this is a mathematical fact. The opinion of
| the theory of thermodynamics is irrelevant and your
| simulation cannot disprove it.
|
| It's not a matter of opinion. There is no reason to
| disagree. You don't have to take my word for it. You
| don't even have to believe Ole Peters when he says that
| asymptotic growth maximization in a multiplicate process
| is equivalent to logarithmic utility maximization.
|
| The maths are not that complex. You can derive it
| yourself of find a proof and go through it until you're
| satisfied.
|
| You insists a simulation that you coded and ran shows
| that this mathematical identity is false. I can think of
| multiple reasons. For example:
|
| - you are thinking of something other than a
| multiplicative process and the maximization of growth and
| logarithmic utility
|
| - you coded something that doesn't does what you think it
| does
|
| - the output you produced doesn't says what you think it
| says
|
| - you have fun playing dumb on the internet
| kgwgk wrote:
| Their result is not an alternative to expected utility
| maximization. It is expected (logarithmic) utility
| maximization.
| ncmncm wrote:
| This is important. It is disgraceful that economics failed to
| arrive at this result at any time in the past century.
| dataflow wrote:
| What result are you referring to, exactly?
| QuesnayJr wrote:
| And what result is that? Most of this is well-known. Ergodicity
| is a concept that's covered in econometrics classes. "When are
| time averages the averages of the underlying probability
| distribution?" is the first topic in time series.
|
| Honestly, the whole approach is a step back. People discussed
| these ideas back when Kelly first published the Kelly rule, and
| the conclusion is that most people are not that aggressive in
| their investment decisions. People still study it, though,
| (it's called the growth optimal portfolio), and its properties
| are well-known.
|
| Peters also sneaks in a second assumption, which is that the
| growth rate of wealth is ergodic. Is it? That's not clear to me
| at all.
| ReflectedImage wrote:
| "most people are not that aggressive in their investment
| decisions"
|
| That's because Kelly's criterion is a special case of Ole
| Peters, where Kelly's is a very aggressive option. There are
| other criterion that can be used, which are not so
| aggressive. Ole Peters lists the class of functions that can
| be used in his paper.
|
| So basically economics has rejected it for the wrong reason.
| QuesnayJr wrote:
| As far as I can tell, he lists wealth, and log wealth as
| the two possible criteria. If there are others, I missed
| them.
|
| If you try to match a power utility model with stock market
| data, to match prices on the stock market, you would reject
| both the additive model (eta = 0) and the multiplicative
| model (eta = 1), in favor of an eta greater than 10. This
| is known as the equity premium puzzle.
|
| The thrust of research over the past 30 years in explaining
| stock prices has been to reject both Peters' models, and
| expected utility in general. People build their entire
| careers on investigating alternatives. There are hundreds
| of experiments to explain, plus all of the real-world data.
| It turns out that explaining all of this with one unified
| model is hard.
| ReflectedImage wrote:
| Those are the EUT criteria not Ole Peters.
|
| The maths you are looking for is here: https://ergodicity
| economics.files.wordpress.com/2018/06/ergo...
| [deleted]
| tribler wrote:
| "We therefore have reason to be optimistic about the future of
| economic theory."
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