Minimax Regret Criterion

The Minimax Regret Criterion is a technique used to make decisions under uncertainty. The context of a decision making process under uncertainty, a decision maker is faced to uncertain states of nature and a number of decision alternatives that can be chosen. The decision made and the final state of nature (which the decision maker does not know beforehand) determines the payoff.

Under this Minimax Regret Criterion, the decision maker calculates the maximum opportunity loss values (or also known as regret) for each alternative, and then she chooses the decision that has the lowest maximum regret.

The regret or opportunity loss for a specific alternative, at a given state of nature, is how much we lose by choosing that alternative and not the optimal alternative, given that state of nature (if the current alternative IS the optima alternative, then the opportunity loss for that alternative, given the state of nature, is 0).

The Minimax Regret Criterion is not the only strategy to make decisions under uncertainty. Depending on the risk stance and whether or not the probability of the states of nature are known, there are other alternatives, such as the Maximax criterion (the optimistic criterion) , the Maximim criterion (the pessimistic criterion) , Hurwicz's Criterion Method , the EOL method , or the Expected Monetary Value Criterion , just to mention a few.