**Instructions:** This calculator allows you to use the Expected Monetary Value criterion (also known as EMV 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

## EMV Criterion

The Expected Monetary Value (EMV) 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 EMV criterion, the decision maker calculates the expected value of the payoff for each alternative, and then she chooses the decision that has the maximum weighted average.

For decision alternative \(i\), the expected monetary value is

\[ EMV_i = \sum_{j=1}^k p_j \times M_{ij}\]The EMV 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 Opportunity Loss Methods, just to mention a few.

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