Risk and Uncertainty: Understanding Small Worlds, Large Worlds

JD Solomon
1 hour ago
3 min read

Real decisions rarely unfold in the tidy models we prefer. Most of the time, we operate in “small worlds,” where the boundaries are known, the variables are manageable, and experience gives us confidence. The trouble comes when we unknowingly step into “large worlds,” where assumptions break down, data thins out, and the consequences of being wrong grow quickly. Understanding the difference is essential for anyone charged with making decisions that stand up to scrutiny.

Large Worlds

Large worlds are environments where measurement is difficult and key input variables are interdependent, making accurate prediction challenging. Their defining feature is complexity, leading to persistent uncertainty.

Small Worlds

Small worlds are environments where measurement is feasible. Inputs are separable and often treated as independent, allowing for accurate estimation of input-output relationships and calculable risks. Their hallmark is predictability.

We Try to Decompose into Small Worlds

From systems engineering to business analytics, we tend to decompose large worlds into small worlds. Creating small worlds, or measurable states, is an appropriate analytical approach for making complexity more understandable. Decomposition of larger states into more discrete components can be powerful.

Decomposition Misses Larger Uncertainties

The one big issue with decomposition is that re-aggregating the smaller states and understanding their risks does not usually explain the uncertainties of the larger state. In many cases, the larger world may have natural or constructed “layers of protection” that protect the system from risk in the smaller, decomposed states.

Specialists often waste much time and money trying to fully resolve their small states when a decision maker really needs a better understanding of the larger one. And, of course, many of the inter-relationships and dependencies that create uncertainty in the larger state cannot be measured or may not be totally understood.

Example: The Manhattan Project

Jimmie Savage, the statistician of the Manhattan Project, understood a lot about small worlds, large worlds, risk, and uncertainty. When you are working on a team to create the world’s first nuclear bomb, you tend to understand much about large worlds and uncertainty.

Savage understood that in small worlds, debates related to math and statistics were more justified. In large worlds, the debate is largely irrelevant because much is not understood or cannot be measured.

In large worlds, the best we can do is probably more akin to the Bayesian, who views probability as a "degree of belief" that changes as new evidence becomes available. In other words, they learn as they go.

Most Big Decisions Are In Large Worlds

Most of us work in small worlds and are not the decision makers in the large world. We often lose sight of that as we banter about who has a better approach or a better methodology. In small worlds, where we can quantify risk and there is limited uncertainty, these things matter. In large worlds, full of less measurable uncertainty, the bantering just creates unhelpful noise.

Applying Small Worlds and Large Worlds

Context matters. Effective decision making depends on knowing when we’ve moved beyond the comfort of small worlds and into the uncertainty of larger ones. Models and decomposition help only to a point; after that, judgment and awareness matter more than precision. Staying alert to that shift is what keeps our decisions grounded and credible in the real world.

Credit for the concept of Small Worlds and Large Worlds to Leonard “Jimmie” Savage in his 1954 classic book, The Foundations of Statistics. And don’t let the title fool you – the book is more about decision making than about statistics. I prefer the 1972 Second Edition.

This article was first published by JD Solomon on LinkedIn.

Solomon, J. D. (2018, September 26). Risk and uncertainty: Understanding small worlds, large worlds. LinkedIn. https://www.linkedin.com/pulse/risk-uncertainty-understanding-small-worlds-large-jd-solomon

JD Solomon writes and consults on decision-making, reliability, risk, and communication for leaders and technical professionals. His work connects technical disciplines with human understanding to help people make better decisions and build stronger systems. Learn more at www.jdsolomonsolutions.com and www.communicatingwithfinesse.com.