## **Learning Outcomes**

On completing this article, you will be able to explain and apply decision criteria under uncertainty for management decisions. You will distinguish between risk, uncertainty, and ambiguity, describe the impact of managerial risk attitudes on decision-making, and assess the role of utility theory. You will learn how expected value, maximin, maximax, and minimax regret criteria operate, and how utility theory and subjective judgement may influence the selection of a strategy.

## **ACCA Advanced Performance Management (APM) Syllabus**

For ACCA Advanced Performance Management (APM), you are required to understand decision-making under uncertainty and the role of risk and utility in management appraisal. Revision should focus on:

- The differences between risk, uncertainty, and ambiguity in management decision environments
- Key quantitative and qualitative decision criteria under uncertainty (expected value, maximax, maximin, minimax regret)
- The influence of managerial risk attitudes and utility theory on choices
- How professional judgement and risk appetite of stakeholders affect recommendations and reporting of performance

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. Which decision rule is appropriate for a manager who is risk-averse?
   a) Maximax
   b) Maximin
   c) Expected value
   d) Minimax regret

2. Briefly explain the main limitation of using the expected value criterion in a one-off decision.

3. Define “utility” in the context of decision-making under uncertainty.

4. An investment yields a possible gain of \$50,000 (probability 0.6) or a loss of \$10,000 (probability 0.4). Calculate the expected value.

5. Give one example of managerial judgement affecting decision-making under uncertainty.

## **Introduction**

Organisational decisions often take place where outcomes are uncertain and probabilities of events may be unknown or difficult to estimate. Selecting the best course of action requires not just technical analysis, but careful consideration of risk attitudes, utility, and subjective judgement. For ACCA Advanced Performance Management (APM), it is essential to apply a structured approach to decision-making under uncertainty, to recognise the motivation behind preferences, and to incorporate the broader context of risk appetite and organisational objectives.

> **Key Term: risk**
> The possibility that future events will differ from expected outcomes, with known or estimable probabilities.
>
> **Key Term: uncertainty**
> A situation where the range of possible outcomes is known, but their probabilities are not.
>
> **Key Term: risk attitude**
> An individual or organisation's predisposition toward accepting or avoiding risk in decision-making.
>
> **Key Term: utility theory**
> A model that assesses the value (utility) a decision-maker places on different outcomes, reflecting personal preferences and attitudes toward risk.

## DECISION CRITERIA UNDER UNCERTAINTY

Decision criteria provide structured methods to select action when outcomes are not certain. The main types used in performance management are:

### Expected Value (EV)

The EV criterion identifies the option with the highest average outcome, weighted by probabilities. It is mathematically optimal for repeated decisions and is suitable for risk-neutral decision-makers.

- **Formula:**  
  $EV = \sum (Probability_i \times Payoff_i)$

**Limitations:** EV is less relevant for one-off, large or personally significant decisions, as it does not reflect risk preferences.

> **Key Term: risk-neutral**
> A decision-maker who is indifferent to risk, focusing only on average expected outcome.

### Maximax, Maximin, and Minimax Regret Criteria

These criteria are applied when probabilities are unknown or ignored:

- **Maximax:** Selects the option with the highest possible return. Suits risk-seeking or optimistic managers.
- **Maximin:** Selects the option with the best of the worst possible outcomes. Suits risk-averse or pessimistic managers.
- **Minimax regret:** Aims to minimise the maximum regret (opportunity loss) from making the wrong decision. Appeals to those who want to avoid making a poor choice relative to what could have been achieved.

> **Key Term: regret**
> The loss incurred by not choosing the best outcome in hindsight.

### **Worked Example 1.1**

**Scenario:**  
A manager must choose between launching Product X or Product Y. The future market could be "Strong" or "Weak" (equal chance, probabilities unknown). Payoffs (profit in \$000):

|           | Strong | Weak |
| --------- | ------ | ---- |
| Product X | 40     | 10   |
| Product Y | 70     | -20  |

**Apply maximin, maximax, and minimax regret decision criteria.**

> **Answer:**
>
> - **Maximax:** Choose Y (highest possible = 70).
> - **Maximin:** Choose X (worst = 10 for X, -20 for Y; X's minimum is higher).
> - **Minimax regret:** Calculate regret table:
>   - For Strong: X: 70-40 = 30; Y: 0
>   - For Weak: X: 0; Y: 10-(-20) = 30
>   - Maximum regret: X = 30; Y = 30
>   - Both choices have same maximum regret, so either may be chosen.

## MANAGERIAL RISK ATTITUDE AND UTILITY

### Risk Attitude in Decision-Making

Managerial preferences strongly affect which criterion is chosen, especially when outcomes have substantial downside:

- **Risk-averse:** Favors security; may accept lower average returns to avoid losses (maximin).
- **Risk-seeking:** Chases highest possible gain; willing to accept large downside (maximax).
- **Risk-neutral:** Focuses on expected values; indifferent to risk.

Organisational policy, performance evaluation systems, and stakeholder priorities can shape or constrain individual manager's risk attitudes.

> **Key Term: managerial judgement**
> The use of personal experience, intuition, and subjective assessments by managers in making decisions under uncertainty.

### Utility Theory

Traditional quantitative methods assume monetary outcomes are the only relevant factor. In reality, people assign different values ("utilities") to gains and losses:

- **Utility functions** represent how satisfaction changes with wealth or outcomes.
- A risk-averse manager's utility curve increases at a decreasing rate (diminishing marginal utility).
- Utility theory enables assigning values to uncertain outcomes that reflect true preferences, not just monetary value.

### **Worked Example 1.2**

**Scenario:**  
A divisional manager is offered a 50:50 chance to win a \$40,000 bonus or nothing (expected value: \$20,000), versus a guaranteed \$16,000 bonus. She prefers the certain \$16,000.

> **Answer:**
>
> This is risk aversion: the utility of a certain outcome outweighs the higher expected value of the gamble.

### The Role of Managerial Judgement

In practice, managers must overlay formal analysis with their own experience. For example, they may:

- Discount improbable estimates, even if assigned probabilities suggest otherwise.
- Consider strategic fit, stakeholder perceptions, and long-term impacts not captured by models.
- Reject choices that statistically "should" be taken if the risk of loss is unacceptable on personal or corporate grounds.

In high-uncertainty environments or where reputational risk is a concern, subjective judgement carries greater weight. Effective managers combine quantitative criteria with clear communication of risk, rationale, and non-quantifiable factors.

### **Worked Example 1.3**

**Scenario:**  
A board must choose between a safe but low-return project, and a high-return but high-risk project that could lead to significant losses if unsuccessful. The shareholders support maximising long-term value, but key staff bonuses depend on short-term profits.

**Discuss how managerial judgement and risk attitudes may influence the decision.**

> **Answer:**
>
> Managers may favour the safe project if their rewards are tied to short-term goals, even if it is not best for long-term shareholder value. If they are risk-averse, they will avoid the riskier project despite its higher potential return. A risk-seeking manager or a performance system focused on long-term value may support the riskier choice.

### **Exam Warning**

Be alert in exam questions for scenarios where quantitative analysis (e.g. expected value) contradicts what a risk-averse manager or organisation might choose. You must recommend an approach consistent with the specific risk attitude of the decision-maker and justify your reasoning.

## **Summary**

Managers select between decision criteria under uncertainty based on organisational context, their own risk preferences, and stakeholder priorities. Expected value is mathematically sound but insufficient on its own for one-off or high-impact decisions. Maximin, maximax, and minimax regret approaches address uncertainty and risk attitude. Utility theory enables decisions that better reflect real preferences. Professional judgement is required to assess qualitative factors and justify selected approaches.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain the distinctions between risk, uncertainty, and ambiguity
- Apply expected value, maximax, maximin, and minimax regret criteria to decisions under uncertainty
- Identify how managerial risk attitudes (risk-seeking, risk-neutral, risk-averse) affect choices
- Use utility theory to reflect individual or stakeholder preferences for risk
- Recognise the importance of managerial judgement in uncertain environments
- Advise on the alignment of decision criteria with organisational objectives and stakeholder risk appetite

## **Key Terms and Concepts**

- risk
- uncertainty
- risk attitude
- utility theory
- risk-neutral
- regret
- managerial judgement

Decision criteria under uncertainty - Utility risk attitude and managerial judgement