Decision trees

Decision trees support choices between two or more courses of action. By displaying decisions, uncertain events, outcomes, probabilities and values in one structure, they make the assumptions behind risk and reward explicit.

When to use it

• Use a tree when a decision is complex enough that laying out every material option and outcome will improve judgement.
• Use it when decision makers need to compare the expected costs and benefits of alternative paths transparently.

Origins

Tree-like reasoning has existed for centuries, and Bayes’ theorem provided an early formal basis for updating probabilities. Modern decision-tree analysis became widespread with operations research, decision theory and computer programming during the nineteen fifties. The same visual logic later became important in machine-learning classification, although a managerial decision tree represents choices and uncertainty rather than merely predicting a class.

What it is

A decision tree is a graphical model of a sequence of choices and uncertain events. It allows decision makers to attach probabilities, costs and benefits to each path and then compare the expected values. Standard symbols distinguish what management controls from what it cannot control:

Decision nodes

, drawn as squares, mark a choice among mutually exclusive alternatives.

Decision branches

extend from a decision node and should collectively cover the feasible alternatives.

Event nodes

, drawn as circles, mark uncertainty resolved outside the decision maker’s control.

Event branches

show the possible results of an uncertain event.

Terminal nodes

, often drawn as triangles, contain the final value or outcome of a complete path.