Risk vs uncertainty — the fundamental distinction
Decision trees — drawing, calculating expected values (EV), choosing optimal paths
Scientific vs intuitive decision-making — when to use each
Influence diagrams and the role of data in reducing uncertainty
Limitations of quantitative decision tools
Stakeholder influence on decisions
Decision trees appear frequently in Paper 1 and Paper 2 — often as 9-mark quantitative Qs
You must be able to: draw, calculate EV, identify the best option, AND evaluate limitations
Risk — outcome is unknown but probability can be estimated from data or experience
Uncertainty — outcome is unknown AND probability cannot be meaningfully estimated
Example of risk: "30% chance of rain" — historical weather data makes this quantifiable
Example of uncertainty: launching a product in a brand new market with no precedent
Decision trees work under risk — they need probability estimates
Under pure uncertainty, intuitive/heuristic approaches are often more appropriate
Pretending uncertainty is risk (making up probabilities) can be dangerous
□ Square node — decision point (the manager chooses which branch)
○ Circle node — chance node (probability determines the outcome)
Each branch from a circle node has a probability (must sum to 1.0)
Each outcome has a payoff (usually profit or revenue in £000s)
Always draw the tree LEFT to RIGHT — decisions come first, outcomes come last
Probabilities on chance branches must sum to 1
Payoffs are shown at the END of each branch (rightmost)
Costs of decisions are usually subtracted from payoffs (e.g. development costs)
EV = Σ (Probability × Payoff)
Calculate EV at each chance node by multiplying each outcome by its probability and summing
Then subtract any upfront costs to get the net expected value
| Outcome | Probability | Payoff (£000) | EV (£000) |
|---|---|---|---|
| Success | 0.6 | +500 | +300 |
| Failure | 0.4 | −200 | −80 |
| EV at chance node | +220 | ||
| Less: launch cost | −80 | ||
| Net EV (Launch) | +140 | ||
| Net EV (Don't launch) | 0 | ||
▸ Decision: Launch — net EV of £140k > £0
Real decisions often involve stages: test → evaluate → launch (or not)
Multi-stage trees: a chance node can lead to another decision node
Always calculate from RIGHT to LEFT — roll back the tree
Roll back: if test positive → launch (£140k); if negative → abort (£0)
EV(Test path) = 0.7×140 + 0.3×0 − 20 = 98 − 20 = £78k
EV(Skip test) = £140k — so skip test in this case
Data-driven; uses quantitative models
Systematic: define problem → gather data → evaluate options → decide
Reproducible and auditable
Best when: data exists, time available, decision is reversible
Gut feel; pattern recognition from experience
Fast; works under time pressure or data scarcity
Can embed unconscious bias
Best when: expert experience relevant, novelty high, speed critical
Most good decisions blend both — data-informed but leadership-validated
Jeff Bezos: "Most decisions should be made with 70% of the information you wish you had"
Waiting for certainty = lost opportunity; acting recklessly = unnecessary risk
Probabilities are estimates — small errors cascade through the calculation
Payoffs are estimates — actual outcomes rarely match projections
Ignores correlation — outcomes aren't always independent
Can't capture all options — only the branches you draw are considered
EV is an average — it does not reflect risk attitude of the decision-maker
A risk-averse firm may prefer a lower but more certain outcome
Ignores non-financial factors: brand, staff morale, ethics, relationships
Gives false precision — creates an illusion of certainty from uncertain data
"Decision trees are a useful starting point but should be used alongside qualitative judgement. The quality of the output depends entirely on the accuracy of the probability and payoff estimates, which are themselves uncertain."
Risk neutral — chooses option with highest expected value regardless of spread
Risk averse — prefers lower but more certain outcome; will sacrifice EV for certainty
Risk seeking — prefers high variance options; willing to gamble for chance of big upside
Financial position: a cash-strapped firm cannot afford to fail — risk averse
Market position: a dominant firm may be more willing to take risks
Entrepreneur vs manager: founders often more risk-seeking than salaried managers
Stakeholder expectations: shareholders may demand different risk tolerance than creditors
Maximin — choose the option with the best worst-case outcome (risk averse)
Maximax — choose the option with the best best-case outcome (risk seeking)
Market research reduces uncertainty by giving better probability estimates
Test markets: launch in one region first to gather real-world data
Scenario planning: model "what if" — best, base, and worst cases
Sensitivity analysis: how much would the answer change if probabilities changed by ±10%?
Worth spending on research if it changes the decision AND the payoff gap is large
Not worth it if: time is too short, or the decision is low-stakes
Diminishing returns: at some point, more data adds little insight but delays action
Map the key variables that influence an outcome and their relationships
Less precise than decision trees but better for complex, multi-factor decisions
Useful for identifying which uncertainties matter most — focus research there
Decisions aren't made in a vacuum — they're made within stakeholder relationships
Mendelow's Matrix: map stakeholders by power and interest to prioritise engagement
High power / high interest = manage closely — they can block or derail decisions
Shareholders: push for short-term returns → may discourage risky long-term investments
Banks/creditors: covenant restrictions → limit risk appetite
Workers: industrial action threat → influences restructuring decisions
Government: regulation or subsidy → changes cost-benefit calculation
Customers: changing preferences → force strategic pivots
Stakeholder pressure can change probabilities (e.g. government signals support → success more likely)
Or change payoffs (e.g. union agreement changes labour cost assumptions)
A firm is considering launching a new product. There is a 0.7 probability of success, generating £400,000, and 0.3 probability of failure, generating −£100,000. The launch cost is £50,000. What is the net expected value of launching?
A risk-averse manager is choosing between two options. Option A has an expected value of £150,000 with outcomes ranging from £50,000 to £300,000. Option B has an expected value of £120,000 with outcomes ranging from £100,000 to £160,000. Which option will the risk-averse manager most likely choose, and why?
Which of the following is the most significant limitation of using decision trees in business decisions?