Assignment Choice under Uncertainty
Task
We have four alternatives A1, A2, A3, and A4 to choose from. There are also four situations S1, S2, S3, and S4 that cause different pay-offs for each alternative. Furthermore, the probability of occurrence of those four situations is unknown.
S1 | S2 | S3 | S4 | |
A1 | 10 | 10 | 5 | 8 |
A2 | 9 | 10 | 12 | 8 |
A3 | 15 | 3 | 2 | -2 |
A4 | 14 | 4 | 3 | 0 |
What alternative should you select under the following decision rules:
- LaPlace rule?
- Maxmin-rule
- Maximax rule
- Range rule (lowest rank = 1)
- Minimax regret rule
- Hurzwicz rule (optimism parameter a = 0.3)
Solution
S1 | S2 | S3 | S4 | LaPlace | Maximin Rule | Maximax rule | Range rule | Minimax Regrett | Hurwicz | |
A1 | 10 | 10 | 5 | 8 | 8.25 | 5 | 10 | 7 | 7 | 6.5 |
A2 | 9 | 10 | 12 | 8 | 9.75 | 8 | 12 | 7 | 6 | 9.2 |
A3 | 15 | 3 | 2 | -2 | 4.5 | -2 | 15 | 11 | 10 | 3.1 |
A4 | 14 | 4 | 3 | 0 | 5.25 | 0 | 14 | 9 | 8 | 4.2 |
The bold numbers show the choice for each rule.