You don´t establish an agile organization forcing company employees to hold hands and sing Kumbaya around the kicker table.
For the problem-solving design of agile organizations we are guided by the model with two distinct types of decisions, and two distinct classes of randomness.
Because every perfect solution for a wrongly described problem is wrong!
Which skills, terms, techniques, theories, methods, tools are suitable for which quadrant?
How to introduce them?
The complete text The Fourth Quadrant: A Map of the Limits of Statistics is an extract from the book Black Swan by Nassim Nicholas Taleb.
Two distinct types of decisions:
The first type of decisions is simple, "binary", i.e. you just care if something is true or false. Very true or very false does not matter. Someone is either pregnant or not pregnant. A statement is "true" or "false" with some confidence interval. (I call these M0 as, more technically, they depend on the zeroth moment, namely just on probability of events, and not their magnitude —you just care about "raw" probability). A biological experiment in the laboratory or a bet with a friend about the outcome of a soccer game belong to this category.
The second type of decisions is more complex. You do not just care of the frequency—but of the impact as well, or, even more complex, some function of the impact. So there is another layer of uncertainty of impact. (I call these M1+, as they depend on higher moments of the distribution). When you invest you do not care how many times you make or lose, you care about the expectation: how many times you make or lose times the amount made or lost.
Two distinct classes of probability structures:
There are two classes of probability domains—very distinct qualitatively and quantitatively. The first, thin-tailed: Mediocristan, the second, thick tailed Extremistan.
The Map for agile Management
Simple binary decisions, in Mediocristan: Statistics does wonders. These situations are, unfortunately, more common in academia, laboratories, and games than real life—what I call the "ludic fallacy". In other words, these are the situations in casinos, games, dice, and we tend to study them because we are successful in modeling them.
Simple decisions, in Extremistan: some well known problem studied in the literature. Except of course that there are not many simple decisions in Extremistan.
Complex decisions in Mediocristan: Statistical methods work surprisingly well.
Complex decisions in Extremistan: Welcome to the Black Swan domain. Here is where your limits are. Do not base your decisions on statistically based claims. Or, alternatively, try to move your exposure type to make it third-quadrant style ("clipping tails").
Have you already described the dynamics in the environment of your company or your project?