# Tool for robust decision making by minimax regret

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## Description

If the future is described by a set of scenarios for the future state of the world, e.g. by means of a set of climate scenarios, it is possible to choose a set of measures and to establish by means of cost benefit analysis how each set of measures will perform under the set of scenarios that are considered relevant for the analysis. The performance can be expressed in terms of the net present value as usual in cost benefit analysis.

In that case it is possible to select the set of measures that is minimizing the maximum regret that you will obtain if the scenarios are different from the optimal situation for that set of measures and if the best set of measure had been selected for the scenario that would occur.

This is a specific decision rule that was introduced in Niehans (1948) and also described in Savage (1951).

In the excelsheet for robust decision making an example is given voor this type of Minimax regret analysis for 3 sets of measures A, B and C and three scenarios, i.e. Scenario 1, Scenario 2 and Scenario 3. As an example the Net present values (NPV) are given in the tab Conventional MR analysis for all combinations of measures and scenarios.

It is then possible to calculate the maximum regrets that you may obtain if the scenarios are different from the optimal scenario for the given set of measures. These regret are shown in the tab Regret Table. Based on the maximum regrets the set of measures can be selected that minimizes the maximum regret for all scenarios that are considered in the analysis.

In the example the set of measures B is selected because this generates the lowest maximum regret: the maximum regret is restricted to 5 in this example. It occurs if scenario 1 prevails and set B was chosen. The other sets of measures generate maximum regret of 45 (set of measures A) or 41 (set of measures B). By selecting set of measures B the decision maker has made a robust decision: the decision will do a good job under all scenarios, because the maximum regret is restricted to 5.

## Bibliography

Niehans J (1948) Zur Preisbildungen bei ungewissen Erwartungen. Swiss Journal of Economics and Statistics 84:433-456

Savage LJ (1951) The theory of statistical decision. J Amer Statistical Assoc 46(253):55-67.