Ergodicity Is Not Intuitive

Ergodicity is a nice word. It includes the Latin root “ergo” meaning “therefore” but is derived from the Greek Ergod meaning work. It is a fundamental concept in statistics and people who understand it seldom apply it incorrectly. Some statistical analysis is ergodic.

Ergodic, adjective MATHEMATICS
relating to or denoting systems or processes with the property that, given sufficient time, they include or impinge on all points in a given space and can be represented statistically by a reasonably large selection of points.

Actuaries use an ergodic population when estimating the likelihood of the death rate for various ages. They know with near certainty what will happen in general but know nothing about a specific member of the group. Individuals are non-ergodic.

Here’s how ergodicity works.

Suppose I want to do a traffic survey. I am interested in intersections at 9 A.M. particularly and to do the survey I have choices.

  1. I could take a snapshot of each intersection and count the cars in and near it. That would give me an idea of the congestion and I would likely get a pretty good estimate of the problem intersections. This is the ensemble study. It implicitly includes all the people but may not represent the intersections over time.
  2. Alternatively I could pick someone or maybe a few people and follow them for a year and see what intersections they passed through. I would get a statistical view of congestion from that sample too and it might be similar or it might be dissimilar to the ensemble study I did earlier. This one includes a long time but not all the people.

Ensemble studies tend to be ergodic. Any other one I did would look much like the average of all of them.

People studies are non-ergodic because people are different. Studying one of them will tell you something about how all may behave but it is unreliable.


People make mistakes using statistics. Suppose I said of all crime black people commit proportionally more than white people. An ensemble study. A tendency from that is to assume all black people are criminals. Yet I know that if I pick a single p[person who is black, the chances are very high they are not a criminal. Individual behaviour is not necessarily predictable from the general nature of the ensemble study.

An error we see today is the excess of the radical Black Lives Matter movement. BLM relies on the misconception that all white people use an ensemble statistic regarding Blacks. Do they lump all black people together and pay them no respect. If instead they used particular statistics, they would find that is untrue. Many if not most white people treat black people respectfully, but that truth would not make for a very good movement. No emotion there.

Ensemble thinking is found in many political situations and is exploited.


In investing there is a tendency to think ensemble sometimes and that leads to bubbles. The bubble being the best example. Not all online businesses will succeed even though some will. Most investors realize that the ensemble of carmakers and its opportunities tells you too little about the future of Ford.

The takeaway

It is usually a mistake to rely on ensemble ideas when dealing with people or investments. Opinion can be an ensemble statistic too. Mark Twain had the idea a hundred years ago. “Whenever you find yourself on the side of the majority, it is time to pause and reflect.”

Some ensemble ideas will have validity, but should be thought of as only directionally accurate. They may give you hints about reality but be sure the reality is thought through carefully when you make it specific.

You might enjoy the 170 year old book, Extraordinary Popular Delusions and the Madness of Crowds by Charles MacKay. It is available on line and it deals with how the personality of crowds is different form the individual personality of every one of its members.

Think specific and mistrust ensemble statistics unless you clearly define their particular purpose.


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