Use of Decision Trees in Decision Making

What a decision tree is

This is the quantitative cousin of the decision analysis you met in Foundations. Where that lesson introduced expected monetary value, the decision tree gives it a structure for real, multi-stage choices: a visual model of how a decision unfolds through chance and further decisions, evaluated systematically rather than by feel.

How a decision tree is solved

You build the tree left-to-right (the order events happen) and solve it right-to-left — a process called rolling back:

Decision tree calculator

A classic one-stage choice: a risky option (A) with a good and a bad outcome, vs a sure option (B). Adjust the odds and payoffs to see the expected value and the recommended choice:

Using decision trees well

Reach for a decision tree when a choice has uncertain outcomes you can put probabilities on, and especially for sequential decisions where today's choice depends on what you learn later. Keep the tree as simple as the decision allows, source the probabilities and payoffs honestly (a tree built on guessed inputs just dresses up a guess), and present the recommended path with its expected value and the key risks.

Ten things to remember

1. A decision tree maps choices, chance events, and payoffs as branches.
2. It's decision analysis made concrete — EMV given a structure.
3. Decision nodes (squares) you control; chance nodes (circles) you don't.
4. Build left to right, solve right to left ("rolling back").
5. At chance nodes take EMV; at decision nodes pick the best branch.
6. EMV(A) $52k beats sure $40k at the defaults — but A risks a $20k loss.
7. EMV informs; risk tolerance still has a vote — mind the catastrophic downside.
8. Best for sequential decisions — it values future flexibility a flat EMV can't.
9. Garbage probabilities, garbage tree — ground the inputs and test sensitivity.
10. Keep it as simple as the decision allows — and present the path, EMV, and risks.