Ergodicity - what it is and how it impacts us!

Updated: Jul 2

Most human systems are non-ergodic. This is code for most human systems may lead to ruin.

What is Ergodicity?

In layman terms, ergodicity is where system probability outcomes are the same, regardless of whether many system participants engage the system simultaneously or whether one participant engages the system over time. For statistically oriented people, think of comparing the difference between cross sectional and time series analyses.

For Example:

A coin flipping game (with a fair coin and consistent flipping conditions) is ergodic. Regardless if 100 people flipped a coin at the same time or 1 person flipped a coin 100 times, the outcome is expected to be approximately a 50% probability of heads or tails.

A Russian roulette game (with a fair bullet chamber) is non-ergodic. If 100 people play Russian roulette at once, 1/6th (or 17%) of them will likely die. If I alone try to play Russian roulette 100 times, there is an almost 100% chance I will be dead long before I get to 100 attempts.

Investing is a good example of where the ergodicity confusion can create significant risk.

Most companies eventually fail. Credit Suisse and CNBC demonstrate the average life of companies is shortening, down from an average of 60 years in 1958 to an average of 20 years in 2012. The trend seems to be shortening as technology continues to disrupt older companies. So investing in one company, no matter how good it is today, may at some point lead to a loss of value. To manage this risk, a good practice is to invest in portfolios of companies and periodically rebalance holdings. This recognizes that investing, by its very nature, is a non-ergodic activity. If investing was ergodic, we would only need to invest in one company.

Also, companies that promote their own employee stock ownership plans may expose their employees to undesired risk. A company, because it is likely to fail at some point, is non-ergodic. As such, stock ownership plans are very risky. Just look at what happened to the GSEs (the Government Sponsored Enterprises, Fannie Mae and Freddie Mac), resulting from the Financial Crisis and Great Recession. After they went bankrupt and were ordered into conservatorship, the employees lost ALL their company stock value. The employees of the GSEs had accumulated stock via various company stock ownership plans. At the time, the GSEs were backed by an implied guarantee of the U.S. Government. So if GSE employees and retirees lost value on their company stock ownership plans, imagine the risk of companies without the backing of the U.S. Government!

To be clear, I’m certainly not suggesting company stock ownership plans are bad. My concern is a lack of diversification. Single company stock ownership should only be considered in the context of a well diversified investment portfolio. Complicating the considerations, some companies provide significant incentives for their employee, especially executives, to participate in employee stock ownership plans. For executives, SEC public disclosure requirements may create a disincentive to divest employee stock.

Ergodicity as related to economics and physics

Economics: See the following link for a good explanation concerning ergodicity in the context of economics.

“Much of classical economics assumes that human behaviour is founded on the expected average outcome of the group (see Expected Utility Theory). This works under the assumption that most environments or situations are ergodic, when in fact this is not the case.”

This statistical mechanics approach works well when describing gases and entropic behavior. However, in the world of human affairs, very few activities are ergodic. So the underlying assumption of ergodicity in the Paul Samuelson branch of economics is problematic and is the basis of the behavioral economics revolution to improve the formulations with the ergodicity assumption. (E.g., Expected Utility Theory, Efficient Market Hypothesis)

Physics: Relating to entropy, if entropy is the ultimate definition of ruin, then perhaps the human struggle against entropy is actually a search for ergodic systems. At least, the human struggle against entropy relates to building resilience into known non-ergodic systems.

See the following link for a nice article on ergodic systems and economics in Nature:

Birkhoff’s Ergodicity equation:

Basically, an individual performs the same activity over time (left side of the equation) has the same probabilistic outcome as many individuals performing the same activity at the same time. (Right side of equation). This is an ergodic system.

Also, a gas being released from a closed container would have an ergodic relationship to its surroundings. Meaning the gas would have an equal distribution across the new container. In effect, time becomes meaningless as a descriptor of the gas distribution in the new space. The gas would have a uniform distribution after the initial transition.

The key here is the gas movement to the new space is aligned with the Second Law of Thermodynamics (entropy). The gas outcome (I.e., a uniform distribution in the new space) is the expected entropic outcome.

Most people want to avoid ruin. (that is, entropy) As such, many human activities that are non-ergodic, if properly managed, can avoid ruin.


As a suggested reading: NN Taleb, in his book Skin In The Game, does a nice job applying Ergodicity principles.

In Richard Dawkins’ book, The Selfish Gene, the author uses a probability based evolution comparison example that misses the mark from an ergodicity standpoint.

"At some point a particularly remarkable molecule was formed by accident. We will call it the replicator. It may not necessarily have been the biggest or the most complex molecule around, but it had the extraordinary property of being able to create copies of itself. This may seem a very unlikely sort of accident to happen. So it was. It was exceedingly improbable. In the lifetime of a man, things that are that improbable can be treated for practical purposes as impossible. That is why you will never win a big prize on the football pools. But in our human estimates of what is probable and what is not, we are not used to dealing in hundreds of millions of years. If you filled in pools coupons every week for a hundred million years you would very likely win several jackpots."

As it relates to ergodicity, the football pool / evolution probability comparison is like comparing apples and oranges:

  • A football pool is non ergodic. Eventually the pool player will run out of money. Thus, there is a different probability of ruin the longer the game is played.

  • A natural system like earth and evolution is ergodic. In effect, the probabilistic evolution game can be played forever with little impact to probability.

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