Minimax Regret, explained.
Minimax regret chooses an action whose largest opportunity loss across possible states is smallest, where loss is measured relative to the best action in each state.
Why it happens
Café pays 4 in sun and rain; Park pays 10 or 0; Hall pays 7 or 3. Worst payoffs are 4,0,3; worst regrets are 6,4,3. Choose a criterion, commit a venue and inspect both weather outcomes without assigning probabilities.
Minimax regret chooses an action whose largest opportunity loss across possible states is smallest, where loss is measured relative to the best action in each state.
Read the result
Worst payoff and worst regret have different reference points. Inspect the state-specific best outcome before treating a shortfall as regret.
A worked example
A venue under unknown weather probabilities
Compare Café's payoffs four and four with Park's ten and zero and Hall's seven and three.
Maximin chooses Café with worst payoff four; minimax regret chooses Hall with worst shortfall three relative to each weather state's best venue.
Commit a venue and inspect both weather outcomes to see how the two criteria evaluate the same payoff table.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Café pays 4 in sun and rain; Park pays 10 or 0; Hall pays 7 or 3. Worst payoffs are 4,0,3; worst regrets are 6,4,3. Choose a criterion, commit a venue and inspect both weather outcomes without assigning probabilities.
Where this idea is useful
A practical use
A decision with unknown probabilities can be compared under different conservative rules rather than an unstated expected-value calculation.
A common misconception
“The most conservative rule must recommend the same action every time.”
Conservatism can mean protecting an absolute floor or limiting missed opportunity. Those are different judgments and can produce different recommendations.
What this explanation leaves out
- Payoffs and states are authored, no probabilities are implied, and numerical opportunity loss is not emotional regret. The criteria embody different judgments rather than one universally correct decision rule.
Does a high opportunity-loss number measure how upset I should feel?
No. Regret is a technical payoff comparison here. It does not measure emotional regret or prescribe a psychological response to the outcome.
Are you trying to protect a minimum result or avoid falling far behind the best action in hindsight?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.