# Decision theory: the decision criteria

Posted by: carkod on: October 5, 2008

## Decision criteria

Choosing something is just like a lottery, but to make it less random, we should follow some selection criteria in order to choose among the alternatives helpings us to compare and of course make our decision.

### The minimum and maximum criteria

This trick is pretty easy, suitable for pessimistic people. Just take the lowest value of each column (d_{i}) and compute the maximum of the lowest values you just took. Let´s see the matrix before.

The minimum of each decision column (d_{i}) is (*first step*):

The maximum of the minimum is (*second step*):

### The maximum and maximum criteria

This criterion has an optimistic sight of the decision. So take the biggest value and compute the maximum among the biggest values, as follows (*first step*):

*Secondly*, calculate the maximum of these values, which are:

However, these two criteria do not match the interests and preferences (probabilities of carrying out the decision) of the decision maker. They only choose the best decision according to their real values.

### The expected value criteria

For the expected value we use the vector P, which are the probabilities of carrying out the decision. Multiply by the probabilities each decision (according to each state of nature) and take out the biggest value (maximum). The highest value represents the best decision, and the value obtained through the computation is the expected earnings from the decision.

In the example, where p(e_{i}) is the probabilities vector, and a_{ij }each demand influenced by correspondent state of nature, and “m” the matrix size:

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