Decision making under Uncertainty: Criteria of Maximax, Maximin, Maximax Regret
Decision Making Under Uncertainty: Key Criteria
Decision-making under uncertainty involves making choices without knowing the probabilities of various outcomes. Several criteria help decision-makers navigate this uncertainty by providing different approaches to evaluate potential decisions. Here are the main criteria:
1. Maximax Criterion
Concept:
- The Maximax criterion is an optimistic approach where the decision-maker focuses on the maximum possible payoff for each decision and then chooses the decision with the highest of these maximum payoffs.
Steps:
- Identify the maximum payoff for each decision alternative.
- Select the decision with the highest maximum payoff.
Example: If a company is considering three projects with potential profits (in thousands) as follows:
| Decision/Project | Outcome 1 | Outcome 2 | Outcome 3 |
|---|---|---|---|
| Project A | 100 | 200 | 300 |
| Project B | 150 | 250 | 200 |
| Project C | 200 | 100 | 400 |
- Maximum payoffs:
- Project A: 300
- Project B: 250
- Project C: 400
- Chosen Decision: Project C (because 400 is the highest maximum payoff).
Pros:
- Encourages risk-taking and high rewards.
- Useful when the decision-maker is highly optimistic.
Cons:
- Can lead to high-risk decisions.
- Ignores potential negative outcomes.
2. Maximin Criterion
Concept:
- The Maximin criterion is a pessimistic approach where the decision-maker focuses on the minimum payoff for each decision and then chooses the decision with the highest of these minimum payoffs.
Steps:
- Identify the minimum payoff for each decision alternative.
- Select the decision with the highest minimum payoff.
Example: Using the same table:
- Minimum payoffs:
- Project A: 100
- Project B: 150
- Project C: 100
- Chosen Decision: Project B (because 150 is the highest minimum payoff).
Pros:
- Ensures a safer choice.
- Useful for risk-averse decision-makers.
Cons:
- May lead to overly conservative decisions.
- Ignores potential high rewards.
3. Minimax Regret Criterion
Concept:
- The Minimax Regret criterion aims to minimize the maximum regret, where regret is the difference between the payoff of the chosen decision and the best possible payoff for each outcome.
Steps:
- Create a regret table by calculating regrets for each decision in each outcome.
- Identify the maximum regret for each decision alternative.
- Select the decision with the smallest maximum regret.
Example: Regret table derived from the initial table:
| Decision/Project | Outcome 1 | Outcome 2 | Outcome 3 |
|---|---|---|---|
| Project A | 100 | 50 | 100 |
| Project B | 50 | 0 | 200 |
| Project C | 0 |
- Maximum regrets:
- Project A: 100
- Project B: 200
- Project C: 150
- Chosen Decision: Project A (because 100 is the smallest maximum regret).
Pros:
- Balances optimism and pessimism.
- Reduces the impact of poor decisions.
Cons:
- Can be complex to calculate.
- May still involve significant regrets.
4. Laplace Criterion
Concept:
- The Laplace criterion assumes that all outcomes are equally likely and selects the decision with the highest average payoff.
Steps:
- Calculate the average payoff for each decision alternative.
- Select the decision with the highest average payoff.
Example: Averages for each project:
- Project A: (100 + 200 + 300) / 3 = 200
- Project B: (150 + 250 + 200) / 3 = 200
- Project C: (200 + 100 + 400) / 3 = 233.33
- Chosen Decision: Project C (because 233.33 is the highest average payoff).
Pros:
- Treats all outcomes equally.
- Useful when probabilities are unknown.
Cons:
- Assumes equal likelihood which may not be realistic.
- Ignores variance in outcomes.
5. Hurwicz Criterion
Concept:
- The Hurwicz criterion is a compromise between the Maximax and Maximin criteria, using a coefficient of optimism (α) to weigh the best and worst payoffs.
Steps:
- Choose a coefficient of optimism (α), where 0 ≤ α ≤ 1.
- Calculate the weighted average of the maximum and minimum payoffs for each decision: α * (maximum payoff) + (1 - α) * (minimum payoff).
- Select the decision with the highest weighted average.
Example: Assuming α = 0.6:
- Project A: 0.6 * 300 + 0.4 * 100 = 220
- Project B: 0.6 * 250 + 0.4 * 150 = 210
- Project C: 0.6 * 400 + 0.4 * 100 = 280
- Chosen Decision: Project C (because 280 is the highest weighted average).
Pros:
- Flexibility in balancing optimism and pessimism.
- Decision-maker can adjust α based on their risk preference.
Cons:
- Requires subjective selection of α.
- Sensitivity to the chosen value of α.
Conclusion
Each of these criteria provides a unique approach to decision-making under uncertainty. The choice of criterion depends on the decision-maker's risk tolerance, optimism, and the specific context of the decision. By understanding and applying these criteria, decision-makers can better navigate uncertainty and make more informed choices.