Why “Good Enough” Models Beat Perfect Ones: Insights from Economics & Weather

The opening sentence comes from the renowned economist John Maynard Keynes, who emphasized that when discussing economic decisions, precision is not always realistic or necessary in a complex real world, especially when it can be misleading; a "roughly correct" approach is more practical and useful.

The core of mathematical modeling is using mathematical tools to explain and predict complex real‑world problems. This process is like creating a "compressed package" of reality: we cannot capture every detail, but by grasping the key points we can obtain useful answers. Statistician George Box famously summed up the essence: All models are wrong, but some are useful. The emphasis is on usefulness —models need not be perfect; as long as they help us understand and make decisions, they have achieved their purpose.

Model Simplification and Assumptions

The real world is immensely complex, and attempting to build an infallible mathematical model is often impossible and even futile. Take weather forecasting as an example: even modern meteorological models consider countless variables yet cannot predict long‑term weather accurately because weather systems are inherently chaotic —a tiny error can lead to vastly different outcomes. In such cases, increasing model complexity can amplify errors.

Therefore, modelers frequently make bold simplifications and assumptions, such as treating fluids as incompressible or assuming rational behavior in economics. Although these assumptions do not match reality, they allow us to extract key information from complex problems and reach roughly correct conclusions instead of getting lost in endless details. As Ockham’s razor states, "Do not multiply entities beyond necessity." Simplification often makes a model more useful.

Complexity and Uncertainty

When modeling, we must consider not only complexity but also uncertainty. For instance, the epidemiological SIR model assumes uniform behavior and a fixed infection rate. While this simplification is unrealistic, it provided effective guidance for public‑health decisions during the early COVID‑19 outbreak. In contrast, more complex agent‑based models (ABM) may be more precise but often require excessive data and computational resources, making timely, practical predictions impossible.

Thus, a roughly correct model can reveal overall trends, whereas striving for absolute precision may trap us in unavoidable errors. For example, probabilistic weather forecasts do not claim certainty about rain but instead convey the likelihood of precipitation, offering more useful information than an exact but potentially erroneous prediction.

Philosophically, mathematical modeling embodies a pragmatic mindset and reflects an attitude toward the world: we do not seek "perfect" answers but aim for "useful" solutions. Especially when facing uncertainty, simplification and approximation enable us to capture the essential aspects rather than obsess over minute details.