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Comment by laszlosandor | Hacker News Reader

Time to read! https://twitter.com/ben_golub/status/1338175642932715520?s=2...

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.

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.

It would be more correct to say economists misinterpreted what von Neumann said.

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.

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).

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."

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.

"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.

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.

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.

This is what I've always suspected was the subtext of this. "We're physicists, and what we learned while thinking about microcanonical ensemble is all you need to know about probability. No, we have nothing to learn from the hundreds of probabilists and statisticians on the subject of probability, or the hundred-year old debate on the meaning of probability."

There are more things in heaven and earth than dreamt of in your philosophy, Horatio: https://plato.stanford.edu/entries/probability-interpret/

There are a thing or two that they could learn from other physicists as well.

https://bayes.wustl.edu/etj/articles/theory.1.pdf

“It is concluded that statistical mechanics need not be regarded as a physical theory dependent for its validity on the truth of additional assumptions not contained in the laws of mechanics (such as ergodicity, metric transitivity, equal a priori probabilities, etc.).”

"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.

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

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

The main article doesn't seem to refer to "the ruin problem" either. What is that?

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.

  #!/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]))

> # ... 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

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.

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%

This article linked above covers it well, highly recommended: https://taylorpearson.me/ergodicity/

In a pithy form, it's the fact that in the long run we are all dead.

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.

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.

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?).

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