359. Decision Criteria

Five classical criteria for decisions under uncertainty when probabilities are unknown or deeply uncertain (probability estimates aren’t trustworthy). Used when EMV doesn’t apply.

359.1. Setup

Acts , states , payoff matrix . No probabilities. How to choose?

Five rules give five different answers, reflecting different attitudes toward uncertainty.

359.2. Maximin (pessimist)

Worst-case thinking. For each act, find the worst possible payoff. Pick the act with the best worst case:

Very conservative — wars, safety-critical systems, fiduciary obligations.

359.3. Maximax (optimist)

Best-case thinking. For each act, find the best possible payoff. Pick the act with the best best case:

Aggressive — startup founders, venture capital, lottery players.

359.4. Minimax regret (Savage)

Avoid kicking-yourself thinking. For each (act, state), compute the regret — how much better you’d have done with the best act for that state:

Then minimize the maximum regret:

Used when retrospective comparison is the bigger concern than absolute outcome — diplomatic / political decisions.

359.5. Hurwicz criterion (compromise)

Linear combination of optimism and pessimism. Coefficient of optimism :

: maximax. : maximin. : balanced.

Calibrate to the decision-maker’s risk attitude (or context: high in opportunity-rich environments, low in threat-heavy ones).

359.6. Laplace (insufficient reason)

Pretend each state is equally likely (uniform prior), then apply EMV:

Equivalent to Bayesian decision under uniform prior. The first thing to try when you have no information about state probabilities.

359.7. Comparison example

Payoffs:
Maximin Maximax Min Regret Hurwicz () Laplace
(regret table needed)

Different criteria, different winners — picks (Maximin) vs (Maximax / Hurwicz / Laplace).

359.8. Which to use?

No single right answer — depends on:

359.9. See also