Decision Theory and Expected Value
This domain tests choice under uncertainty using payoff tables, expected monetary value, decision trees and the value of information. You must separate the decision criterion from the probabilities.
Core rules
- EMV of an alternative = Σ(probability × payoff) across states of nature.
- Maximax chooses the highest possible payoff (optimistic); maximin chooses the highest of the worst payoffs (pessimistic).
- Minimax regret chooses the alternative with the smallest maximum opportunity loss.
- EVPI = expected payoff with perfect information − best EMV without it.
- A decision tree works backwards from terminal payoffs, folding back at chance nodes by EMV and choosing the best branch at decision nodes.
- Probabilities at each chance node must sum to 1.
Worked example
States S1 and S2 have probabilities 0.6 and 0.4. Alternative A pays 100 in S1 and 20 in S2; B pays 60 in both. EMV(A) = 0.6×100 + 0.4×20 = 68. EMV(B) = 60. Choose A. With perfect information the payoff is 100 in S1 and 60 in S2: EV = 0.6×100 + 0.4×60 = 84. EVPI = 84 − 68 = 16. That is the maximum worth paying for a perfect forecast, not the cost of the forecast itself.
Traps
- Confusing maximax with maximin.
- Computing EVPI as the best payoff minus the chosen payoff rather than expected values.
- Using EMV when the decision-maker is risk-averse or the decision is one-off.
- Including sunk costs in payoffs.