Decision Tree

Activate when: user says 'help me choose between two options with different risks', 'I need to map out what could happen if we go with X', 'we have a sequential decision — first we do A then depending on results we do B', 'what is the expected value of this investment given uncertain demand'. Do NOT activate when: the decision is a one-shot choice with no sequential stages (use simple EV instead); probabilities cannot be estimated even roughly and uncertainty is too deep to quantify.

Overview

A decision tree maps a multi-stage decision: decision nodes (squares) for choices you control, chance nodes (circles) for outcomes you don't, probabilities on every branch, payoffs at the leaves — then rollback right-to-left to get expected value at the root. First systematized by John F. Magee (HBR, 1964); formalized by Howard Raiffa (1968). Its biggest value: converting "I feel we should expand" into "what probability do you assign to high demand?" — making every assumption explicit and contestable.

Composes with expected-value-and-kelly (EV scaffold + bet sizing), probabilistic-thinking (calibration per node), inversion (rollback = working outcomes backward), mece (branches must be MECE so probabilities sum to 1.0).

When to Use

• Decision has sequential stages (decide → learn → decide again)
• Outcomes uncertain; probabilities can be estimated (even roughly)
• Payoffs quantifiable (NPV, revenue, cost, lives saved)
• Multiple stakeholders need a shared visual model to align on assumptions

Not when: one-shot choice with no stages; probabilities unestimable; payoffs purely qualitative; branch set too large (use scenario planning instead).

Coaching Novices (Adaptive Front Door)

• Engine mode: user has a concrete multi-stage decision → run The Process directly.
• Coach mode: user is unfamiliar or has no concrete case → guide step by step.

In Coach mode, respond one step at a time. Each [WAIT] is a hard stop — output only that step's question, then stop.

1. One-line: a decision tree converts "I feel" into "what probability do you assign?" — making assumptions explicit so they can be argued about.
2. Check fit. Sequential stages? Uncertain outcomes? Quantifiable payoffs? If yes to all three, a tree applies.
3. Elicit their real case. What's the initial choice? What uncertain outcomes follow? What payoffs result?

[WAIT — do not advance until user responds]

4. Run The Process one step at a time with their input — draw structure, assign probabilities, assign payoffs, roll back.

[WAIT — do not advance until user responds]

5. Close by naming the insight: the threshold at which the recommendation flips, and whether to gather more data.

[WAIT — do not advance until user responds]

The Process

Step 1 — Root: Define the decision (options, timeline, decision-maker). Draw a square; each option is a branch.

Step 2 — Chance nodes: For each branch, identify uncertain events → draw circles. Branches at each circle must be MECE; probabilities must sum to 1.0.

Step 3 — Probabilities: Assign a number (0.0–1.0) + documented basis to every branch. Reject "50/50" without justification.

Step 4 — Payoffs: Assign consistent-unit payoffs (NPV, revenue, etc.) to every terminal leaf.

Step 5 — Rollback: Right to left — EV at each circle = Σ(p × value). At each square, keep highest EV branch; mark losers //.

Step 6 — Sensitivity + stop-rule: Find the probability threshold where the optimal choice switches. Compute EVPI = EV(perfect info) − EV(best decision now). If EVPI < cost of data: decide now. If EVPI > cost: gather data first. Stop refining when the leading option's EV advantage exceeds the value of further analysis.

Output Template

text

Decision Tree: <topic>
Options: A / B  |  Timeline:
Tree: [node-by-node description]
Probabilities: Node | Branch | p | Basis
Payoffs: Path | Value | Unit
Rollback: Option A EV= / Option B EV= / Optimal=
Sensitivity: flips when p([key branch]) > [threshold]  |  EVPI=
Recommendation: [option] — holds if [condition]; flips if [condition]

→ Method in Action: Magee 1964 — Chemical Plant Investment (HBR)

Pack: Decision Tree by Domain

Domain	Root Decision	Key Uncertainty	Payoff	Watch For
Capital investment	Large vs. small plant	Demand scenarios	NPV	Overconfident demand p
R&D portfolio	Fund vs. kill	Technical success; adoption	Revenue × p	Ignoring base-rate failure
Litigation	Settle vs. litigate	Win/lose; damages	Expected settlement	Anchoring on best case
Product launch	Now vs. delay	Market reception; competitor	Revenue per scenario	Missing competitor-first branch
M&A	Acquire vs. pass	Integration; synergy	Post-acquisition EV	Paying for performance peak

Applying It Well

• Draw before calculating — structure surfaces hidden assumptions
• Assign probabilities before revealing your preferred option
• Run sensitivity before concluding; find the switchover threshold and EVPI
• Audit missing branches explicitly: "what did we leave out?"

→ Primary sources: references/sources.md

Common Rationalizations

[D] = designed upfront | [O] = observed in real use. [O] entries are more valuable.

Rationalization (Fake Move)	Reality
[D] "This is strategic — we don't need numbers."	Without numbers the tree is just a picture. Force strategic disagreements to become numerical ones.
[D] "We can't estimate probabilities."	Even rough estimates beat implicit zero/one assumptions. Every un-numbered branch already has an implicit probability.
[D] "The tree chose A — we're done."	Holds only at assigned probabilities. Sensitivity analysis is mandatory before concluding.
[D] "We enumerated all branches."	Trees are always simplifications. Ask explicitly: what branches are missing?
[D] "It's 50/50 — we just don't know."	50/50 is a claim requiring justification. What base rate supports it?
[D] "My gut says B even though the tree says A."	Gut = implicit tree with different probabilities. Find which number your gut is using and put it in.
[D] "The tree gave a recommendation — it must be right."	GIGO: garbage probabilities produce garbage recommendations. Calibrate inputs first.
→ Add [O] entries here after each real use — paste the actual failure pattern	What went wrong and why

Red Flags

• Probabilities verbal only — no numbers written | Chance-node probabilities don't sum to 1.0
• No sensitivity analysis performed | Terminal payoffs in mixed units across branches
• Probabilities assigned post-hoc to justify a pre-decided conclusion | No missing-branch audit

Verification

• Root decision defined; all options enumerated
• All chance nodes MECE; probabilities sum to 1.0 at each node
• Every probability has documented basis
• All terminal payoffs in same unit and discount rate
• Rollback verified numerically at every node
• Sensitivity complete — switchover threshold identified
• EVPI calculated; data-gathering decision made
• Missing-branch audit performed; recommendation states conditions it holds and flips

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