Decision Tree
A visual of sequential decisions with probabilities and payoffs; fold back to compute expected value.
Author
Decision analysis (Howard Raiffa, Ronald A. Howard); machine-learning variants (CART, ID3)
Model type
About
A decision tree is a visual, quantitative way to choose under uncertainty. Squares show decisions, circles show chance events, and triangles/end nodes show outcomes/payoffs. By assigning probabilities and payoffs, you can compute expected values, compare strategies, and see where extra information would change the choice. In data science, trees are learned from data; in decision analysis, you design the tree to structure the decision.
How it works
Nodes & branches
- Decision node (■) – choose one branch.
- Chance node (○) – nature picks an outcome with stated probabilities (sum to 1).
- Terminal node (▲) – payoff (money, time, utility, risk points).
Rollback (fold-back) – compute expected value at each chance node and “roll back” towards the start; at decision nodes pick the branch with the higher EV (or higher utility if risk-averse).
Value of information – compare EV with and without new info (test, pilot) to get EVPI/EVSI; buy info only if it exceeds cost and delay.
Sensitivity – vary probabilities/payoffs; identify breakpoints where the preferred branch flips.
Pruning – collapse dominated or irrelevant branches; keep the tree readable.
Updating – if evidence arrives, update probabilities (Bayes) and rerun the rollback.
Use-cases
Product & GTM – feature launch vs pilot; channel tests; price experiments.
Operations – make/buy, supplier selection, maintenance vs replace.
Risk & compliance – controls investment vs breach cost; incident playbooks.
Clinical / troubleshooting – test-and-treat pathways; diagnostic flows.
Legal / negotiations – settle vs litigate, offer ladders and expected outcomes.
Data science – CART/GBTs for prediction when you have labelled data.
Step-by-step
Define the decision – objective, options, horizon, and payoff unit (e.g., £EV, hours saved, utility).
Sketch the tree – decisions first, then uncertainties; avoid duplicating subtrees by re-using structure.
Assign probabilities – use data, expert judgement, or ranges; ensure each chance node sums to 1.
Assign payoffs – include costs, delays, risks; use present values if timing differs.
Rollback – compute EVs from right to left; select the highest-EV branch at each decision node.
Test sensitivity – vary key probabilities/payoffs; mark thresholds where the choice would change.
Check information value – calculate EVPI/EVSI for tests/pilots; only buy information that pays.
Decide & document – record inputs, EVs, breakpoints, and triggers to revisit (e.g., if p(success) < 0.35).
Pitfalls & Cautions
False precision – spurious decimals on weak assumptions; show ranges and breakpoints.
Omitted paths – leaving out realistic options or failure modes biases EV.
Probability errors – branches that don’t sum to 1; mixing conditional and unconditional probs.
Double counting – the same cost added on multiple branches.
Static view – not revisiting after new evidence; schedule an update trigger.
Utility blind – EV in £ ignores risk attitudes; use expected utility for large, risky stakes.
Related Mental Models
Click below to learn other mental models
Regret Minimalisation Framework
Project yourself to the decision horizon and choose the option that you will regret least. Weight omissions heavily, and treat reversibility as a key lever.
Combinations vs Permutations
Order matters → permutations. Order doesn’t → combinations. Adjust for with/without replacement.
Margin of Safety
Deliberately leave room for error—buy below value, build above load, plan beyond the optimistic case—so mistakes and volatility don’t cause ruin.