**Instructions:** This calculator allows you to use the Expected Opportunity Loss criterion (also known as EOL criterion) to make a decision under uncertainty. Please first indicate the number of decision alternatives and states of nature. Then type the corresponding payoff matrix, the probabilities associated to the states of nature and optionally the name of the decision alternatives and states of nature in the form below

## EOL Criterion

The Expected Opportunity Loss (EOL) Criterion, is a technique used to make decisions under uncertainty, under the assumption that the probabilities of each state of nature is known. 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 EOL criterion, the decision maker calculates the expected value of the opportunity loss values for each alternative, and then she chooses the decision that has the minimum EOL.

For decision alternative \(i\), the expected opportunity loss is

\[ EMV_i = \sum_{j=1}^k p_j \times OL_{ij}\]where the 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 EOL 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 Minimax Regret Method, or the Expected Monetary Value Criterion, just to mention a few.

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