Ole Peters & why Ergodicity Econ is shite

In Economics, Income is defined as what you can spend without depleting your Wealth and Wealth is defined as the set of assets which generates your current Income. We may be indifferent between different combinations of goods and services which yield the same Utility. Subtract Depreciation of Assets used to generate Income and we have a vector which represents our Real Income. This is by no means easy to measure. When relative prices change, which happens when goods and services become more or less scarce, there is a substitution effect but, because substitutes may be imperfect, there is also an Income effect. Some may be worse off though overall prosperity seems to have increased. Sometimes, we feel the pinch because we are not used to a substitute which, later, we are more happy with. Thus, in the long run, apparent falls in Real Income turn out to be blessings in disguise because they got us to change our behavior and use new goods and services which are superior. In general, there is a 'Laspeyres bias' such that we underestimate growth in Income.

Different types of Wealth have different impact on Income. A more secure asset may generate less Income while some prestigious assets may reduce money income because of their upkeep, yet they may have a reputational effect or create a psychic benefit such that they still count as wealth.

In general, it is in our interest to prefer the Technology, indeed to prefer the Preferences (i.e. have 'meta-preferences') such that the Wealth to Income ratio is lowest.  This means we prefer cheaper and more efficient types of assets. Also we don't necessarily want an asset whose life-time is much longer than ours unless we can raise money on it or use it to give a contingent gift to family or charity etc. This is because we can die at any time. We don't want to have foregone too much consumption just for prudential reasons or because of a mental pathology like that of the miser. Furthermore, though change is difficult (especially as one grows older!), it is often a good thing in itself because it enables us to make other changes in our own attitudes and outlook. This is particularly true about changes which use new technology and which reduce depreciation and thus make development environmentally, socially and humanly sustainable.

It is important to understand that Income and Wealth- like the Utility we gain from the former, when we Consume rather than Save, or the sense of Security we gain from the latter- are finite and bounded. They involve scarce resources. They can't go to infinity. If they could, there would be no scarcity. Whoever has infinite Wealth or Income can endow everyone else with infinite Wealth or Income. Scarcity would have ceased to exist. We would be living in a Fantasy land. Economics would be empty.

All this is common sense. But not to a silly maths maven named Ole Peters who  introduces 'a montonically increasing function of wealth, which we call suggestively u(x).' This is foolish. Utility is not a function of wealth or Income. It is a function of Consumption. If I buy and eat a cake, I get utility. If I save for a cake making machine, I may end up having more cake but I get no utility till I actually eat one of the cakes, or sell one of the cakes and buy something else, produced by the cake making machine.

Ole Peters & Co claim-

we are able to interpret different utility functions as encoding different non-ergodic dynamics and remove the element of human irrationality from the explanation of basic economic behavior. 

This is very stupid goobledegook. A utility function maps consumption choices onto consumer satisfaction. It encodes facts about our physiology and our preferences which are given biologically and psychologically. It is not the case that we can change our physiology when Economic circumstances change. If this happened, we would go on splitting into different species.

Production and Asset creation could be considered to represent dynamic systems. A 'non-ergodic dynamic' means something which is 'path dependent'- i.e. current actions are governed by those which went before. In general this is irrational. We don't throw good money after bad. Just because we made a mistake last time round, we don't repeat it hoping to change the outcome. Instead we look at our options afresh- maybe glance around to see what the smart people are doing- and then make a decision. In this sense, Economics- as the science of Choice under Scarcity- is ergodic, i.e. not path dependent. Even if some people are irrational, the entry and exist of agents into markets means that ergodicity prevails at the margin. People aren't robots or meat machines following a pre-determined path.

Peters' claim is meaningless shit.

The axioms he uses are

1)  Human behavior can be understood. It follows a rationale and is in that sense rational. 

This is nonsense. Billiard balls aren't rational. We can understand their behavior. Human beings can be rational- i.e. they reason about things. However, if humans evolved on an uncertain fitness landscape, then there would be survival value in unpredictability so as to baffle a predator or parasite. Thus, there is a fallacy of composition in saying 'if humans are rational, their behavior must be predictable or deterministic'. It is perfectly possible for human rationality to involve non-deterministic algorithms. These could have 'univalent foundations' with an appropriate type theoretic class of intensional objects. In other words, it has a mathematical representation of an idiosyncratic type or one with intractably many degrees of freedom. At the 'macro' level, we can speak of 'Muth Rationality'- aggregates behave as if all agents have the 'correct' economic theory and a common information set- but this is like an Aumann correlated equilibrium with appropriate public signals.

Economics is the science of rational choice under scarcity. If there is no scarcity or rationality is not used in making the choice, Economics is out of place. There are many areas of life when it would be repugnant to be calculating in one's approach. Treating the matter as 'economic' would represent a lack of humanity. Families would break down if sexual reproduction were reduced to prostitution. National defense and Law & Order would cease to be effective if soldiers and police officers acted on the basis of a self-interested Utilitarian calculus. The Business Enterprise, which internalises externalities, would unwind into a multitude of adhesion contracts. Productivity would collapse.

All this is well known- if not blindingly obvious- yet Ole Peters & Co have this as their second axiom-

2) Humans make decisions in a manner that would optimise the time-average growth rate of wealth, were those decisions to be repeated indefinitely.

This is mad. To optimize wealth growth we should live like misers who were also immortal. In reality, if it is worthwhile, we should try to find that wealth configuration which has the lowest ratio to Real Income. Indeed, that's what happens. We prefer assets which are more efficient and less costly because they generate more Real Income.

In our treatment, decisions are choices between different stochastic processes, not choices between different random variables as is usually the case in decision theory

The problem here is that Knightian Uncertainty obtains. We don't know what stochastic processes obtain nor how they are combined.

Moreover, we don't know what is or isn't wealth, let alone what its growth rate is. This is because the future is unknown. There may be a Revolution or breakdown of Law & Order such that having a type of wealth gets you tortured or killed. Gilt edged securities could turn out to be worthless- as Tzarist bonds turned out to be worthless.

Instead of maximizing utility, the proper response to Uncertainty is 'regret minimization'- e.g. Hannan Consistent type hedging. We know that there may be a catastrophic outcome but would feel less regret if our actions were justified and prudent and had other admirable qualities such that, at the end, there is nothing we can really reproach ourselves with. We would also want to hedge our bets by not following the herd in some matters and developing non-transferable assets which are not material- things like moral character, aesthetic or intellectual distinction, piety and religious faith.

Ole Peters & Co look not at economics, which is about scarcity and real life, but 'chrematistics'- financial alchemy- which can be wholly fraudulent. However, it can has a political, or distributional, aspect. A War, a Revolution, or a hyperinflation caused by political conflict, can have a dramatic effect on 'chrematistics' while the real economy is scarcely touched. It is perfectly possible for financial wealth to disappear while the real economy grows very rapidly.

Ole Peters says he has a new approach which yields the same results as expected utility theory but which is superior because

The range of questions we can answer in this way is surprising to us. Examples are: how does an investor choose the leverage of an investment ? How can we resolve the St. Petersburg paradox ? How can we resolve the equity premium puzzle ? Why do people choose to cooperate ? Why do insurance contracts exist ? How can we make sense of the recent changes in observed economic inequality? Do economic systems change from one phase to another under different tax regimes? 

There is no St. Petersburg paradox- it is merely silly and can be resolved linguistically- or better still, it can be ignored as evidence of the imbecility of pedagogues.

 Nor is there any equity premium puzzle- it assumes something Samuel Butler noticed 150 years ago - viz. the incentive structure of the agent making the portfolio choice, not the beneficial owner, is what matters. Unfortunately, this is not empirifically verifiable. Still, only stupid academics puzzle over it. But they have a history of puzzling over utter shite.

Non Economists could already give superior answers to Academic Economists on all the other questions.

Consider the following statement from Ole Peter's blog. It is pure gobbledegook.

In the setting of decisions under uncertainty, optimizing appropriate growth rates can be mapped to Laplace’s expected utility theory, (which is worked out in Peters&Gell-Mann(2016)and inspired the Copenhagen experiment).

If decisions are made under Knightian uncertainty then we don't what possible states of the world are. We don't know if growth has occurred because we don't know whether Wealth has decreased. Thus, currently, we don't know if we really have grown our economy over the last hundred years. It may turn out that there are no substitutes of fossil fuel and that our current Global Income is not sustainable. We were actually burning through our Wealth, not growing at all.

Similarly, if an asteroid hits us in a couple of years, we would say no actual Growth occurred because we ought to have been building an anti-asteroid defense system. Failure to do so meant we were burning through our wealth- not growing at all.

As a matter of fact, Governments and Markets do get juiced about growth rates and some people may pretend to have 'optimized' them. But people also get juiced about all sorts of crazy shit. Some silly mathematicians can be relied on to turn up and talk some gobbledegook to make the thing look plausible. Since they don't have any professional qualifications, they can't be done for fraud if they talk up a Madoff.

Peters & Gell-Mann think 'a gamble' has a certain structure which, in the real world, it does not. Essentially, if a person offers a gamble with positive expected value, then it is irrational to expect that he can pay under all circumstances. Furthermore, coalitions can be formed to drive the gambler to bankruptcy. It is not the case that anyone has infinite wealth.

Consider their definition of Gamble- A gamble is a set of possible changes in monetary wealth ∆W(n) with associated probabilities pn(n), where n are integers designating events. For convenience, we order events such that ∆W(n + 1) > ∆W(n).

N is unknown. We don't know and can't even imagine all the possible events that might occur. There may even be a non zero chance that some of the money in my pocket will spontaneously turn into a rabbit. Thus, the only thing we can say about 'Gambles' is we all take them all the time but don't know what they are and have no way of ever finding out.


Peters & Gell-Mann also don't get why utility functions must be bounded. If this weren't true we'd either be immortal and/or have no need for decision theory. There would be a direct means to gain infinite utility.

Thus these two silly fellows have invented a type of economics which does not have Knightian uncertainty and either assumes immortality or so direct way to gain infinite utility not dependent on economic decisions. Notice that if utility is transferable, then one person who gains infinite utility can give infinite utility to everyone else. Economics disappears because there is no scarcity.

Why do these two idiots think any economic growth rate can 'contain' a utility function which goes to infinity? This assumes that there is some contingency such that no scarcity exists. Why not simply say 'Laplace's theory, not Bernoulli's, allows everybody to be immortal and to enjoy infinite happiness? Though no God is required for this hypothesis, yet we could be as Gods!'

Now let us turn to this 'Copenhagen Experiment'- it is merely a game with a particular structure which has no connection with the real world.

Each subject, in an experiment that spanned two days, engaged in a gambling paradigm with either additive or multiplicative wealth dynamics. At the start of each day endowed with an initial wealth of 1000DKK / ~$155 (Fig. 1a), after which they took part in a passive session during which they had an opportunity to learn, via observation, the deterministic effect of fractal stimuli on their endowed wealth (Fig. 1b). On the additive day (Day+ ) the fractals caused additive changes in wealth whereas on the multiplicative day (Day´ ) the fractals caused multiplicative changes to their endowed wealth (eqs. 1-5, Supp. Fig. 1). Having repeatedly observed these contingencies, subjects subsequently engaged in an active session during which they chose between gambles composed of the same fractals (Fig. 1c, eqs. 6-9). There were four sessions in total per subject, Passive´ and Active´ occurring on Day´ ; and Passive+ and Active+ occurring on Day+ . We adopted three complementary analysis strategies. The first is model-independent in the sense that we tested whether choice frequencies change according to gamble dynamics. The second and third approaches were model-dependent insofar as we formally compare theoretical models of utility in terms of their parameter estimates, and in terms of the predictive adequacy of each utility model.

What is this shit supposed to prove? People learn to use different strategies when the game varies. But that game captures nothing about Reality. These cretins assume something which isn't true about the world and then say 'if the world were like we say it is, then people would act the way we say they will because we can rig up an experiment where we pay people to play along for a couple of days.' The problem is that they then run out of grant money to pay their lab rats who go back to the real world and behave completely differently.

The imbecile, Ole Peters, thinks this 'Copenhagen Experiment' confirms that the-

The growth rate contains a function that we can identify with the utility function in Laplace’s theory (not in Bernoulli’s expected utility theory, which is inconsistent).

If you rig things in advance and pay people to play a game, you can prove anything you like. Laplace and Bernoulli weren't economists. They were laying the foundations of Probability theory which may be used by Decision theory but which is not itself that theory. Bernoulli was simply asserting a common sense notion of diminishing marginal utility- i.e. the notion that beyond a certain point, more of something produces smaller and smaller increments of pleasure till satiation is reached. Peters, cretin that he is, thinks this is wrong- utility can be infinite!

In other words: ergodicity economics unifies different branches of decision theory (including intertemporal discounting and expected utility theory) into one concept: growth rate maximization.

No! It is worthless gibberish.  Gell-Mann was a smart guy- in his field. In Economics he was a senile shithead. As for Peters, I suppose he is a child of his age.

Consider the following from his blog-

a null model of human behavior must be that people maximize the growth rate of their wealth.

Right! Coz people don't eat food or need to buy clothes. They just maxmize the growth rate of their wealth! Which planet does this cretin live on?

That means they do different things, depending on the dynamics. Let’s fix \Delta t for a moment. Under additive dynamics they’ll then optimize \Delta x, under multiplicative dynamics they’ll optimize \Delta \ln x, and under general dynamics \Delta u(x).

Sure. If you say 'a null model of human behavior is that they do whatever crazy shit my model says they do' then everything else follows.

So people optimize the change in a generally non-linear function of wealth… that’s utility theory, and that’s why we called the non-linear transformation u.

That's not utility theory. It is some crazy shit you cooked up. People don't want to maximize wealth. They know they will die. The plan is to have enough to enjoy your retirement and maybe leave a bit for your kids. This may mean you get a sports-car and a second wife in your fifties because that's better than being on a cruise ship with your first wife while in your seventies. People make trade-offs like this all the time. What they don't do is 'optimize the change in a generally non-linear function' which only exists in the imagination of some shithead.

Turns out, this has less to do with your idiosyncratic psychology and more to do with the dynamic to which your wealth is subjected.

Why does it turn out this way? The answer is because this shithead has a 'null model' of an utterly crazy type which says you and everybody else will always behave in an utterly crazy way.

I’ll leave the extension of this treatment to a random environment as an exercise. Hint: in a deterministic environment, growth rates are constant in time. In a random environment they are ergodic (that’s why at the London Mathematical Laboratory we don’t say “utility function” but “ergodicity mapping”).

So if this crazy bed-bug had said 'the null model is that human beings turn into werewolves at a rate which depends on the rapidity of the lunar cycle' then- in a deterministic environment, that rate will be constant- e.g. every 28 days. In a random environment, where full moons can occur at any time, the London Mathematical Laboratory would gas on about your 'ergodicity mappings' to being a werewolf.