Decision Trees

Decision Trees — Structured Decision-Making

Decision tree analysis: a visual tool for making decisions with probabilities and expected value.

When to Use

✅ Good for:

• Business decisions (investments, hiring, product launches)
• Personal choices (career, relocation, purchases)
• Trading & investing (position sizing, entry/exit)
• Operational decisions (expansion, outsourcing)
• Any situation with measurable consequences

❌ Not suitable for:

• Decisions with true uncertainty (black swans)
• Fast tactical choices
• Purely emotional/ethical questions

Method

Decision tree = tree-like structure where:

• Decision nodes (squares) — your actions
• Chance nodes (circles) — random events
• End nodes (triangles) — final outcomes

Process:

1. Define options — all possible actions
2. Define outcomes — what can happen after each action
3. Estimate probabilities — how likely is each outcome (0-100%)
4. Estimate values — utility/reward for each outcome (money, points, utility units)
5. Calculate EV — expected value = Σ (probability × value)
6. Choose — option with highest EV

Formula

EV = Σ (probability_i × value_i)

Example:

• Outcome A: 70% probability, +$100 → 0.7 × 100 = $70
• Outcome B: 30% probability, -$50 → 0.3 × (-50) = -$15
• EV = $70 + (-$15) = $55

Classic Example (from Wikipedia)

Decision: Go to party or stay home?

Estimates:

• Party: +9 utility (fun)
• Home: +3 utility (comfort)
• Carrying jacket unnecessarily: -2 utility
• Being cold: -10 utility
• Probability cold: 70%
• Probability warm: 30%

Tree:

Decision
├─ Go to party
│  ├─ Take jacket
│  │  ├─ Cold (70%) → 9 utility (party)
│  │  └─ Warm (30%) → 9 - 2 = 7 utility (carried unnecessarily)
│  │  EV = 0.7 × 9 + 0.3 × 7 = 8.4
│  └─ Don't take jacket
│     ├─ Cold (70%) → 9 - 10 = -1 utility (froze)
│     └─ Warm (30%) → 9 utility (perfect)
│     EV = 0.7 × (-1) + 0.3 × 9 = 2.0
└─ Stay home
   └─ EV = 3.0 (always)

Conclusion: Go and take jacket (EV = 8.4) > stay home (EV = 3.0) > go without jacket (EV = 2.0)

Business Example

Decision: Launch new product?

Estimates:

• Success probability: 40%
• Failure probability: 60%
• Profit if success: $500K
• Loss if failure: $200K
• Don't launch: $0

Tree:

Launch product
├─ Success (40%) → +$500K
└─ Failure (60%) → -$200K

EV = (0.4 × 500K) + (0.6 × -200K) = 200K - 120K = +$80K

Don't launch
└─ EV = $0

Conclusion: Launch (EV = +$80K) is better than not launching ($0).

Trading Example

Decision: Enter position or wait?

Estimates:

• Probability of rise: 60%
• Probability of fall: 40%
• Position size: $1000
• Target: +10% ($100 profit)
• Stop-loss: -5% ($50 loss)

Tree:

Enter position
├─ Rise (60%) → +$100
└─ Fall (40%) → -$50

EV = (0.6 × 100) + (0.4 × -50) = 60 - 20 = +$40

Wait
└─ No position → $0

EV = $0

Conclusion: Entering position has positive EV (+$40), better than waiting ($0).

Method Limitations

⚠️ Critical points:

1. Subjective estimates — probabilities often "finger in the air"
2. Doesn't account for risk appetite — ignores psychology (loss aversion)
3. Simplified model — reality is more complex
4. Unstable — small data changes can drastically alter the tree
5. May be inaccurate — other methods exist that are more precise (random forests)

But: The method is valuable for structuring thinking, even if numbers are approximate.

User Workflow

1. Structuring

Ask:

• What are the action options?
• What are possible outcomes?
• What are values/utility for each outcome?
• How do we measure value? (money, utility units, happiness points)

2. Probability Estimation

Help estimate through:

• Historical data (if available)
• Comparable situations
• Expert judgment (user experience)
• Subjective assessment (if no data)

3. Visualization

Draw tree in markdown:

Decision
├─ Option A
│  ├─ Outcome A1 (X%) → Value Y
│  └─ Outcome A2 (Z%) → Value W
└─ Option B
   └─ Outcome B1 (100%) → Value V

4. EV Calculation

For each option:

EV_A = (X% × Y) + (Z% × W)
EV_B = V

5. Recommendation

Option with highest EV = best choice (rationally).

But add context:

• Risk tolerance (can user handle worst case)
• Time horizon (when is result needed)
• Other factors (reputational risk, emotions, ethics)

Application Examples by Domain

Trading & Investing

Position Sizing:

• Options: 5%, 10%, 20% of capital
• Outcomes: Profit/loss with different probabilities
• Value: Absolute profit in $

Entry Timing:

• Options: Enter now, wait for -5%, wait for -10%
• Outcomes: Price goes up/down
• Value: Opportunity cost vs better entry price

Business Strategy

Product Launch:

• Options: Launch / don't launch
• Outcomes: Success / failure
• Value: Revenue, market share, costs

Hiring Decision:

• Options: Hire candidate A / candidate B / don't hire
• Outcomes: Successful onboarding / quit after X months
• Value: Productivity, costs, opportunity cost

Personal Decisions

Career Change:

• Options: Stay / change job / start business
• Outcomes: Success / failure in new role
• Value: Salary, satisfaction, growth, risk

Real Estate:

• Options: Buy house A / house B / continue renting
• Outcomes: Price increase / decrease / personal situation changes
• Value: Net worth, monthly costs, quality of life

Operations

Capacity Planning:

• Options: Expand production / outsource / status quo
• Outcomes: Demand increases / decreases
• Value: Profit, utilization, fixed costs

Vendor Selection:

• Options: Vendor A / Vendor B / in-house
• Outcomes: Quality, reliability, failures
• Value: Total cost of ownership

Calculator Script

Use scripts/decision_tree.py for automated EV calculations:

python3 scripts/decision_tree.py --interactive

Or via JSON:

python3 scripts/decision_tree.py --json tree.json

JSON format:

{
  "decision": "Launch product?",
  "options": [
    {
      "name": "Launch",
      "outcomes": [
        {"name": "Success", "probability": 0.4, "value": 500000},
        {"name": "Failure", "probability": 0.6, "value": -200000}
      ]
    },
    {
      "name": "Don't launch",
      "outcomes": [
        {"name": "Status quo", "probability": 1.0, "value": 0}
      ]
    }
  ]
}

Output:

📊 Decision Tree Analysis

Decision: Launch product?

Option 1: Launch
  └─ EV = $80,000.00
     ├─ Success (40.0%) → +$500,000.00
     └─ Failure (60.0%) → -$200,000.00

Option 2: Don't launch
  └─ EV = $0.00
     └─ Status quo (100.0%) → $0.00

✅ Recommendation: Launch (EV: $80,000.00)

Final Checklist

Before giving recommendation, ensure:

• ✅ All options covered
• ✅ Probabilities sum to 100% for each branch
• ✅ Values are realistic (not fantasies)
• ✅ Worst case scenario is clear to user
• ✅ Risk/reward ratio is explicit
• ✅ Method limitations mentioned
• ✅ Qualitative context added (not just EV)

Method Advantages

✅ Simple — people understand trees intuitively ✅ Visual — clear structure ✅ Works with little data — can use expert estimates ✅ White box — transparent logic ✅ Worst/best case — extreme scenarios visible ✅ Multiple decision-makers — can account for different interests

Method Disadvantages

❌ Unstable — small data changes → large tree changes ❌ Inaccurate — often more precise methods exist ❌ Subjective — probability estimates "from the head" ❌ Complex — becomes unwieldy with many outcomes ❌ Doesn't account for risk preference — assumes risk neutrality

Important

The method is valuable for structuring thinking, but numbers are often taken from thin air.

What matters more is the process — forcing yourself to think through all branches and explicitly evaluate consequences.

Don't sell the decision as "scientifically proven" — it's just a framework for conscious choice.

Further Reading

• Decision trees in operations research
• Influence diagrams (more compact for complex decisions)
• Utility functions (accounting for risk aversion)
• Monte Carlo simulation (for greater accuracy)
• Real options analysis (for strategic decisions)