Decision Making Under Certainty, Risk, and Uncertainty
This calculator helps evaluate decision alternatives using various criteria for different decision environments:
Expected Value: ∑(Probability × Outcome)
Maximax: Maximum of maximum payoffs (optimistic)
Maximin: Maximum of minimum payoffs (pessimistic)
Hurwicz: α × (Best) + (1-α) × (Worst)
Laplace: Average of all payoffs (equal probability)
Maximax: Maximum of maximum payoffs (optimistic)
Maximin: Maximum of minimum payoffs (pessimistic)
Hurwicz: α × (Best) + (1-α) × (Worst)
Laplace: Average of all payoffs (equal probability)
Results
Practical Examples
Example 1: Product Launch (Risk)
Alternatives: Launch now, Improve then launch, Don't launch
States: Strong demand (0.3), Moderate demand (0.5), Weak demand (0.2)
Payoffs (in $M): [50, 20, -10], [40, 30, 5], [0, 0, 0]
Expected Values: 22, 27.5, 0 → Best: Improve then launch
Example 2: Vendor Selection (Uncertainty)
Alternatives: Vendor A, Vendor B, Vendor C
States: Best case, Average case, Worst case
Payoffs (in days): [5, 7, 10], [6, 6, 8], [8, 8, 8]
Maximin: 7, 6, 8 → Best: Vendor C (guarantees ≤8 days)
Example 3: Investment (Hurwicz Criterion)
Alternatives: Stocks, Bonds, Savings
States: Boom, Normal, Recession
Payoffs (in % return): [15, 5, -5], [8, 6, 4], [3, 3, 3]
With α=0.7: 9, 7.2, 3 → Best: Stocks (optimistic investor)
Decision Criteria Guidelines
| Criterion | Best Used When | Advantages | Limitations |
|---|---|---|---|
| Expected Value | Probabilities are known (Risk) | Mathematically sound, considers all outcomes | Requires accurate probabilities |
| Maximax | Optimistic outlook, low risk aversion | Seeks best possible outcome | Ignores potential losses |
| Maximin | Pessimistic outlook, high risk aversion | Protects against worst case | May miss good opportunities |
| Hurwicz | Balance between optimism and pessimism | Adjustable risk preference | Subjective α selection |
| Laplace | No probability information (Uncertainty) | Simple, treats all states equally | May not reflect reality |