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Comment by zwaps | Hacker News Reader

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.

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"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.

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.

It's true for Expected Utility Theory and anything that has been based on top of it.

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)

> 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...

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%.

Could you point to one example where a problem is solved and their solution is not equivalent to the choice of an utility function?

@kgwgk Ahh misread for a second there. Prospect theory is a good example. When calculated using Ole Peters method Prospect theory does not exist.

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.

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.

> 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_problem

How do his methods apply to the uncountable situations where expected utility theory is used?

A random example: https://www.researchgate.net/publication/240488954_Risk_of_d...

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.

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...

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

> 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.

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.

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@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)

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.

> 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?

> 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.

@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.

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?

> 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.

> 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.

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.

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.

You may find this interesting: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=439400

“This paper provides an alternative behavioral foundation for an investor's use of power utility in the objective function and its particular risk aversion parameter. The foundation is grounded in an investor's desire to minimize the objective probability that the growth rate of invested wealth will not exceed an investor-selected target growth rate. Large deviations theory is used to show that this is equivalent to using power utility, with an argument that depends on the investor's target, and a risk aversion parameter determined by maximization. As a result, an investor's risk aversion parameter is not independent of the investment opportunity set, contrary to the standard model assumption.”

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