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:

```bash
python3 scripts/decision_tree.py --interactive
```

Or via JSON:

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

JSON format:

```json
{
  "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)