ergodicity

What Is Ergodicity? Ergodicity In A Nutshell

Ergodicity is one of the most important concepts in statistics. Ergodicity is a mathematical concept suggesting that a point of a moving system will eventually visit all parts of the space the system moves in. On the opposite side, non-ergodic means that a system doesn’t visit all the possible parts, as there are absorbing barriers.

Understanding ergodicity

As Ole Peters, the principal investigator into ergodicity, explains:

In the 1650s, mathematicians came up with the concept of expected value and this immediately became an important concept in economics.

And he continued:

Most prominently in the pricing of financial products like life insurance in the 1700s people noticed that the concept doesn’t always work.

Sometimes the mathematical object which mathematicians had named expected value reflects what we might expect the value of some quantity to be with the everyday meaning of the word expect but sometimes the mathematical meaning and the everyday meaning don’t coincide.

And he continued:

Eexpected utility theory acknowledges that we’re all different we each value money and risk and time and anything else differently and these individual differences can account for the failure of expected value theory.

Suppose you are writing a restaurant travel guide and want to determine what the popular restaurants are in your home city.

One strategy involves taking a momentary snapshot, where you visit ten restaurants and count how many patrons are eating in each. 

Another strategy involves choosing one patron and following them for a predetermined amount of time.

For the purposes of this example, let’s say twelve months.

During this time, you observe their eating behavior and whether they dine at a particular restaurant repeatedly.

With two different strategies, you will obtain two different results. The first strategy is a statistical analysis of the entire ensemble of restaurant diners at a given moment in time. The second strategy is a statistical analysis for one person for a certain period of time. 

While the first strategy may not be representative of popular restaurants over a long period of time, the second strategy may not be representative of popular restaurants for all restaurant diners.

If both strategies determine that the same ten restaurants are the most popular in the city, the ensemble of diners is said to be ergodic.

In reality, however, most ensembles of human populations are not ergodic.

Why is ergodicity important?

Ergodicity is important in explaining how individuals make conclusions about something while having information about something else.

Fundamentally, ergodicity helps determine whether the generalizations people make are correct or incorrect. If the generalization is directed at an ergodic ensemble, there is a good chance it is correct.

To explain this concept in more detail, consider a newspaper reader. One day, the reader notices that the newspaper has printed inaccurate information.

Based on this observation, they generalize that the newspaper will print inaccurate information in the future.

This generalization is more or less ergodic and thus correct. If someone determines how many mistakes appear in one issue of a newspaper and then compares that number with how many mistakes the editor makes over time, the results are almost identical. 

Ergodicity in finance

Many theories of finance and investment assume ergodicity.

These assumptions are particularly prevalent in modern portfolio theory, aggregate macroeconomic models, and discounted cash flow (DCF) models, among others.

However, these models often fail to account for large deviations caused by debt crises, financial crises, and other systemic risks associated with the banking system.

Author Nassim Nicholas Taleb suggested finance and investment were non-ergodic since an even statistical distribution where the system returns to every possible state infinite times is simply not possible. 

The reasons for this are caused by what Taleb called absorbing states, where ruin such as bankruptcy, death, or the devolution of a country or legal regime occurs.

Ruin then results in absorbing barriers, which Taleb defines as “anything that prevents people with skin in the game from emerging from it, and to which the system will invariably trend.

Given the possibility of ruin in finance and investment, cost-benefit analyses are no longer possible and the system is non-ergodic.

In other words, traditional models based on probabilistic data fail to account for extreme, atypical scenarios that end in ruin.

To grasp this concept, you need to understand the difference between ensemble probability and time probability.

In an ensemble probability, we pretty much take all the possible outcomes from a group of people and sort of average it out.

A completely different story applies to time probability.

Source: Nassim Nicholas Taleb at The Logic of Risk Taking

As Taleb explains:

The difference between 100 people going to a casino and one person going to a casino 100 times, i.e. between (path dependent) and conventionally understood probability. The mistake has persisted in economics and psychology since age immemorial.

Ensemble probability vs. time probability

In short, modern economics, finance, and cognitive psychology often fall into the trap of mistaking time probability for ensemble probability, where an outcome is judged based on all the possible paths that the players in the system can take.

Instead of taking into account that in the real world, there is an absorbing barrier (a point o non-return and ruin), thus making most of the endevoirs “path-dependent.”

From there, we develop naturally something that Taleb would define as “BS detector,” which is a natural defense in a complex world.

Whereas instead, with the claimed “rationality,” modern psychologists want us to act against this natural tendency to avoid ruin as if we were living parallel lives altogether.

When instead, we have a natural filter to ruin, and we do understand risk in the real world.

Modern behavioral psychologists, instead, assign humans a growing list of biases, claiming the “irrationality” of individuals rather than acknowledging (as Taleb would say over and over) they do not understand the real world.

This has huge implications, as it cancels out most of the work proposed in modern financial theory and behavioral economics.

In fact, as already explained in biases and what we got wrong about them, this also invalidates many of the findings of the last decades related to behavioral economics and psychology.

Ergodicity example – Toyota

Now that we’ve established that the financial industry does not comprise an ergodic system, here is another example of how ergodicity is relevant in business.

Toyota

Toyota favors ergodicity in its production processes as part of the Toyota Production System (TPS) – a lean manufacturing framework designed to improve efficiency, reduce waste, and increase productivity. 

toyota-production-system
The Toyota Production System (TPS) is an early form of lean manufacturing created by auto-manufacturer Toyota. Created by the Toyota Motor Corporation in the 1940s and 50s, the Toyota Production System seeks to manufacture vehicles ordered by customers most quickly and efficiently possible.

The framework relies on the principles of ergodicity to optimize the production process with Toyota’s continuous improvement practices reliant on data analysis and collection.

This enables the company to analyze production line performance over time to identify and address any issues that impact the system.

In the context of the TPS, ergodicity refers to the ability of its systems to converge to a stable equilibrium state over time.

This is achieved through the use of standardized work processes, visual management systems, and continuous improvement cycles. 

Ergodicity and just-in-time (JIT) manufacturing

In a 2021 paper published in the American Journal of Operations Research, Swiss researchers referenced ergodicity in the TPS as part of a broader study of virtual elasticity and on-time delivery (OTD) in manufacturing systems.

In the paper, authors Bruno G. Rüttimann and Martin T. Stöckli noted that Toyota’s JIT system relies on a “deterministic and predefined product-mix leading to ergodic-type of processes. In addition, manufacturing batches produced in multi-product manufacturing cells (mixed model) are standardized in equal timeslots called pitches to reduce Mura (unevenness), while the production-mix is alternated using Heijunka-box levelled scheduling.

From the above quote, there are two key terms to unpack:

  1. Mura – a type of waste produced by unevenness in production that can also be caused when standards are either not followed or do not exist. 
  2. Heijunka – a lean production method where orders are processed in response to consumer demand. Heijunka-box leveled scheduling is a visualization tool used to schedule production by type or volume over a fixed period. 

Both Mura and Heijunka enable Toyota to reduce the instance of non-ergodic processes on the factory floor.

Non-ergodic processes are the result of various production bottlenecks and are a major problem for production managers since they often cause uncontrolled work-in-progress (WIP) generation.

Heijunka also protects Toyota from overburden when customer demand spikes as value is produced based on takt time (average sell rate). In other words, the company delivers value to the customer at a steady rate to better react to demand fluctuations. 

As we noted earlier, this is achieved by leveling production based on the average volume of orders or the average demand for each type of product

Ergodicity and task standardization

The definition of an ergodic system is one where the time and ensemble averages become equivalent over time.

Whilst most human systems are non-ergodic, Toyota seeks to minimize the negative aspects of human influence via task standardization and automation.

Task standardization, as we mentioned at the outset, is a key component of the TPS that maximizes efficiency and minimizes waste.

The concept of standard work increases the likelihood that all employees – regardless of skill, experience, or motivation – can perform the same task and produce an identical outcome. 

In Toyota’s case, standard work has been refined over decades with the kaizen continuous improvement approach and is thus extremely precise.

Each employee relentlessly seeks out waste to improve the efficiency of their workstation or area. Over time, this contributes to a similar trajectory for the entire employee cohort in each Toyota factory.

Ergodicity additional exampleCorporate profitability

In a 2022 study published in Management Science, researchers from the University of Bamburg revisited the somewhat perpetual debate around corporate profitability and whether the systems that governed it were ergodic.

Prior work on the subject indicated that corporate idiosyncrasies were important determinants of profitability, but this only told part of the story.

What the researchers found was that while idiosyncrasies did correlate with profitability for shorter-lived companies, there was no correlation with survivor firms whose profitability was ergodic. 

How is corporate profitability ergodic?

In this context, ergodicity was based on the inability to statistically tell the difference between the moments of the distribution of survivors’ return on assets (ROA) and the moments of their individual ROA time series.

Put another way, survivor companies were found to be equally profitable (on average) and experience equally volatile fluctuations in their profitability. 

To demonstrate this, the researchers took samples from 5,266 publicly-traded firms across the United States in almost every industry.

Banking companies were excluded because of the unique structure of their balance sheets. For all others, the focus was on annual corporate profit rate measured by the ratio of operating income to total assets.

The ergodic hypothesis

To motivate the ergodic hypothesis, the team studied the data from two perspectives that provide complimentary views on company profitability:

  1. ROA time series – which captures individual destinies over time, and
  2. Cross-sectional ROA – which clarifies the space of potential outcomes and their associated probabilities at a certain point in time.

If the time series moments differed between companies and/or related to a company’s idiosyncrasies, the cross-sectional moments would not represent individual destinies and thus be considered a non-ergodic system.

By extension, the researchers noted that the system would be ergodic only if the cross-sectional perspective could be used to draw inferences about individual trajectories.

Testing for ergodicity

To test the hypothesis that the idiosyncrasies of a corporation do not affect average volatility and profitability (conditional on survival), researchers analyzed how the ROA time series was influenced by various industrial and financial variables.

These included market share, productivity, leverage, market valuation, industry concentration, and size.

Firms were then grouped according to age such that:

  • 1,804 companies were present in the population for 10 to 17 years. 
  • 837 companies were present for 18 to 25 years, and
  • 720 companies were present for more than 26 years.

Results

Statistical analyses showed that newer firms (less than 20 years old) tended to show low or even negative profitability which was correlated with their respective idiosyncrasies. Conversely, shorter-lived companies that were highly productive or significantly large were more profitable and less volatile.

However, the statistical distribution of the 498 survivor companies (which existed for the entire study period between 1980 and 2012) was reasonably approximated. That is, profitability tended to fluctuate with equal probability beyond a certain point with the effect or impact of idiosyncrasies vanishing over time.

The key point here is that as a company grows “older”, time series movements are less dispersed across all of the companies in the study.

These movements converge toward the values obtained from the cross-sectional ROA distribution.

This means that, at least in theory, survivor companies cannot do any better (but must not do any worse) than their competitors in terms of the amount (and volatility) of their profits.

While this confirmed the researchers’ theory that profitability was an ergodic system, it countered the idea that average profitability and volatility were based on a company’s industry and idiosyncrasies. 

Since the variation is concentrated in firms under 20 years old, ergodicity is only applicable to the profitability of older, survivor companies. 

Consequences and implications

The researchers noted that the results had major implications for strategy – particularly for those businesses who valued longevity. 

But what of the mechanism for ergodicity in corporate profitability? The most obvious answer is that in search of abnormal profits, companies perpetually reallocate capital to make a sufficient return and beat the competition. 

While some companies did report profits that were deviations above the average, it was acknowledged that such profits would be impossible to maintain in an era of disruption and anti-monopolistic regulation. 

The team posited that the long-term survival of a company was thus based on maintaining a profitability level that was at least equal to peers.

In new or younger firms, it was deemed important that management understand how various idiosyncrasies impact survival probability (and not how they affect profitability itself).

Key takeaways

  • Ergodicity is a mathematical concept suggesting that a point of a moving system will eventually visit all parts of the space the system moves in.
  • Ergodicity helps explain how individuals make conclusions about something while having information about something else. More specifically, ergodicity helps determine whether the generalizations people make are correct or incorrect.
  • In finance and investing, ergodicity forms the basis of DCF and macroeconomic modeling. However, the industry is non-ergodic because of the presence of ruin events and the failure of probabilistic data models to properly account for them.

Connected Thinking Frameworks

Convergent vs. Divergent Thinking

convergent-vs-divergent-thinking
Convergent thinking occurs when the solution to a problem can be found by applying established rules and logical reasoning. Whereas divergent thinking is an unstructured problem-solving method where participants are encouraged to develop many innovative ideas or solutions to a given problem. Where convergent thinking might work for larger, mature organizations where divergent thinking is more suited for startups and innovative companies.

Critical Thinking

critical-thinking
Critical thinking involves analyzing observations, facts, evidence, and arguments to form a judgment about what someone reads, hears, says, or writes.

Biases

biases
The concept of cognitive biases was introduced and popularized by the work of Amos Tversky and Daniel Kahneman in 1972. Biases are seen as systematic errors and flaws that make humans deviate from the standards of rationality, thus making us inept at making good decisions under uncertainty.

Second-Order Thinking

second-order-thinking
Second-order thinking is a means of assessing the implications of our decisions by considering future consequences. Second-order thinking is a mental model that considers all future possibilities. It encourages individuals to think outside of the box so that they can prepare for every and eventuality. It also discourages the tendency for individuals to default to the most obvious choice.

Lateral Thinking

lateral-thinking
Lateral thinking is a business strategy that involves approaching a problem from a different direction. The strategy attempts to remove traditionally formulaic and routine approaches to problem-solving by advocating creative thinking, therefore finding unconventional ways to solve a known problem. This sort of non-linear approach to problem-solving, can at times, create a big impact.

Bounded Rationality

bounded-rationality
Bounded rationality is a concept attributed to Herbert Simon, an economist and political scientist interested in decision-making and how we make decisions in the real world. In fact, he believed that rather than optimizing (which was the mainstream view in the past decades) humans follow what he called satisficing.

Dunning-Kruger Effect

dunning-kruger-effect
The Dunning-Kruger effect describes a cognitive bias where people with low ability in a task overestimate their ability to perform that task well. Consumers or businesses that do not possess the requisite knowledge make bad decisions. What’s more, knowledge gaps prevent the person or business from seeing their mistakes.

Occam’s Razor

occams-razor
Occam’s Razor states that one should not increase (beyond reason) the number of entities required to explain anything. All things being equal, the simplest solution is often the best one. The principle is attributed to 14th-century English theologian William of Ockham.

Lindy Effect

lindy-effect
The Lindy Effect is a theory about the ageing of non-perishable things, like technology or ideas. Popularized by author Nicholas Nassim Taleb, the Lindy Effect states that non-perishable things like technology age – linearly – in reverse. Therefore, the older an idea or a technology, the same will be its life expectancy.

Antifragility

antifragility
Antifragility was first coined as a term by author, and options trader Nassim Nicholas Taleb. Antifragility is a characteristic of systems that thrive as a result of stressors, volatility, and randomness. Therefore, Antifragile is the opposite of fragile. Where a fragile thing breaks up to volatility; a robust thing resists volatility. An antifragile thing gets stronger from volatility (provided the level of stressors and randomness doesn’t pass a certain threshold).

Systems Thinking

systems-thinking
Systems thinking is a holistic means of investigating the factors and interactions that could contribute to a potential outcome. It is about thinking non-linearly, and understanding the second-order consequences of actions and input into the system.

Vertical Thinking

vertical-thinking
Vertical thinking, on the other hand, is a problem-solving approach that favors a selective, analytical, structured, and sequential mindset. The focus of vertical thinking is to arrive at a reasoned, defined solution.

Maslow’s Hammer

einstellung-effect
Maslow’s Hammer, otherwise known as the law of the instrument or the Einstellung effect, is a cognitive bias causing an over-reliance on a familiar tool. This can be expressed as the tendency to overuse a known tool (perhaps a hammer) to solve issues that might require a different tool. This problem is persistent in the business world where perhaps known tools or frameworks might be used in the wrong context (like business plans used as planning tools instead of only investors’ pitches).

Peter Principle

peter-principle
The Peter Principle was first described by Canadian sociologist Lawrence J. Peter in his 1969 book The Peter Principle. The Peter Principle states that people are continually promoted within an organization until they reach their level of incompetence.

Straw Man Fallacy

straw-man-fallacy
The straw man fallacy describes an argument that misrepresents an opponent’s stance to make rebuttal more convenient. The straw man fallacy is a type of informal logical fallacy, defined as a flaw in the structure of an argument that renders it invalid.

Streisand Effect

streisand-effect
The Streisand Effect is a paradoxical phenomenon where the act of suppressing information to reduce visibility causes it to become more visible. In 2003, Streisand attempted to suppress aerial photographs of her Californian home by suing photographer Kenneth Adelman for an invasion of privacy. Adelman, who Streisand assumed was paparazzi, was instead taking photographs to document and study coastal erosion. In her quest for more privacy, Streisand’s efforts had the opposite effect.

Heuristic

heuristic
As highlighted by German psychologist Gerd Gigerenzer in the paper “Heuristic Decision Making,” the term heuristic is of Greek origin, meaning “serving to find out or discover.” More precisely, a heuristic is a fast and accurate way to make decisions in the real world, which is driven by uncertainty.

Recognition Heuristic

recognition-heuristic
The recognition heuristic is a psychological model of judgment and decision making. It is part of a suite of simple and economical heuristics proposed by psychologists Daniel Goldstein and Gerd Gigerenzer. The recognition heuristic argues that inferences are made about an object based on whether it is recognized or not.

Representativeness Heuristic

representativeness-heuristic
The representativeness heuristic was first described by psychologists Daniel Kahneman and Amos Tversky. The representativeness heuristic judges the probability of an event according to the degree to which that event resembles a broader class. When queried, most will choose the first option because the description of John matches the stereotype we may hold for an archaeologist.

Take-The-Best Heuristic

take-the-best-heuristic
The take-the-best heuristic is a decision-making shortcut that helps an individual choose between several alternatives. The take-the-best (TTB) heuristic decides between two or more alternatives based on a single good attribute, otherwise known as a cue. In the process, less desirable attributes are ignored.

Bundling Bias

bundling-bias
The bundling bias is a cognitive bias in e-commerce where a consumer tends not to use all of the products bought as a group, or bundle. Bundling occurs when individual products or services are sold together as a bundle. Common examples are tickets and experiences. The bundling bias dictates that consumers are less likely to use each item in the bundle. This means that the value of the bundle and indeed the value of each item in the bundle is decreased.

Barnum Effect

barnum-effect
The Barnum Effect is a cognitive bias where individuals believe that generic information – which applies to most people – is specifically tailored for themselves.

First-Principles Thinking

first-principles-thinking
First-principles thinking – sometimes called reasoning from first principles – is used to reverse-engineer complex problems and encourage creativity. It involves breaking down problems into basic elements and reassembling them from the ground up. Elon Musk is among the strongest proponents of this way of thinking.

Ladder Of Inference

ladder-of-inference
The ladder of inference is a conscious or subconscious thinking process where an individual moves from a fact to a decision or action. The ladder of inference was created by academic Chris Argyris to illustrate how people form and then use mental models to make decisions.

Goodhart’s Law

goodharts-law
Goodhart’s Law is named after British monetary policy theorist and economist Charles Goodhart. Speaking at a conference in Sydney in 1975, Goodhart said that “any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes.” Goodhart’s Law states that when a measure becomes a target, it ceases to be a good measure.

Six Thinking Hats Model

six-thinking-hats-model
The Six Thinking Hats model was created by psychologist Edward de Bono in 1986, who noted that personality type was a key driver of how people approached problem-solving. For example, optimists view situations differently from pessimists. Analytical individuals may generate ideas that a more emotional person would not, and vice versa.

Mandela Effect

mandela-effect
The Mandela effect is a phenomenon where a large group of people remembers an event differently from how it occurred. The Mandela effect was first described in relation to Fiona Broome, who believed that former South African President Nelson Mandela died in prison during the 1980s. While Mandela was released from prison in 1990 and died 23 years later, Broome remembered news coverage of his death in prison and even a speech from his widow. Of course, neither event occurred in reality. But Broome was later to discover that she was not the only one with the same recollection of events.

Crowding-Out Effect

crowding-out-effect
The crowding-out effect occurs when public sector spending reduces spending in the private sector.

Bandwagon Effect

bandwagon-effect
The bandwagon effect tells us that the more a belief or idea has been adopted by more people within a group, the more the individual adoption of that idea might increase within the same group. This is the psychological effect that leads to herd mentality. What in marketing can be associated with social proof.

Moore’s Law

moores-law
Moore’s law states that the number of transistors on a microchip doubles approximately every two years. This observation was made by Intel co-founder Gordon Moore in 1965 and it become a guiding principle for the semiconductor industry and has had far-reaching implications for technology as a whole.

Disruptive Innovation

disruptive-innovation
Disruptive innovation as a term was first described by Clayton M. Christensen, an American academic and business consultant whom The Economist called “the most influential management thinker of his time.” Disruptive innovation describes the process by which a product or service takes hold at the bottom of a market and eventually displaces established competitors, products, firms, or alliances.

Value Migration

value-migration
Value migration was first described by author Adrian Slywotzky in his 1996 book Value Migration – How to Think Several Moves Ahead of the Competition. Value migration is the transferal of value-creating forces from outdated business models to something better able to satisfy consumer demands.

Bye-Now Effect

bye-now-effect
The bye-now effect describes the tendency for consumers to think of the word “buy” when they read the word “bye”. In a study that tracked diners at a name-your-own-price restaurant, each diner was asked to read one of two phrases before ordering their meal. The first phrase, “so long”, resulted in diners paying an average of $32 per meal. But when diners recited the phrase “bye bye” before ordering, the average price per meal rose to $45.

Groupthink

groupthink
Groupthink occurs when well-intentioned individuals make non-optimal or irrational decisions based on a belief that dissent is impossible or on a motivation to conform. Groupthink occurs when members of a group reach a consensus without critical reasoning or evaluation of the alternatives and their consequences.

Stereotyping

stereotyping
A stereotype is a fixed and over-generalized belief about a particular group or class of people. These beliefs are based on the false assumption that certain characteristics are common to every individual residing in that group. Many stereotypes have a long and sometimes controversial history and are a direct consequence of various political, social, or economic events. Stereotyping is the process of making assumptions about a person or group of people based on various attributes, including gender, race, religion, or physical traits.

Murphy’s Law

murphys-law
Murphy’s Law states that if anything can go wrong, it will go wrong. Murphy’s Law was named after aerospace engineer Edward A. Murphy. During his time working at Edwards Air Force Base in 1949, Murphy cursed a technician who had improperly wired an electrical component and said, “If there is any way to do it wrong, he’ll find it.”

Law of Unintended Consequences

law-of-unintended-consequences
The law of unintended consequences was first mentioned by British philosopher John Locke when writing to parliament about the unintended effects of interest rate rises. However, it was popularized in 1936 by American sociologist Robert K. Merton who looked at unexpected, unanticipated, and unintended consequences and their impact on society.

Fundamental Attribution Error

fundamental-attribution-error
Fundamental attribution error is a bias people display when judging the behavior of others. The tendency is to over-emphasize personal characteristics and under-emphasize environmental and situational factors.

Outcome Bias

outcome-bias
Outcome bias describes a tendency to evaluate a decision based on its outcome and not on the process by which the decision was reached. In other words, the quality of a decision is only determined once the outcome is known. Outcome bias occurs when a decision is based on the outcome of previous events without regard for how those events developed.

Hindsight Bias

hindsight-bias
Hindsight bias is the tendency for people to perceive past events as more predictable than they actually were. The result of a presidential election, for example, seems more obvious when the winner is announced. The same can also be said for the avid sports fan who predicted the correct outcome of a match regardless of whether their team won or lost. Hindsight bias, therefore, is the tendency for an individual to convince themselves that they accurately predicted an event before it happened.

Read Next: BiasesBounded RationalityMandela EffectDunning-Kruger EffectLindy EffectCrowding Out EffectBandwagon Effect.

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