Wald Criterion, or How to get the best guaranteed result

Many of us do not like to get into a situation where there is very little information on external factors, or it is completely absent, and an important choice is urgently needed. Most likely, this is why most people prefer to avoid responsibility at work and are content with a modest but at the same time relatively quiet official position. If they knew about the theory of games and how the criteria of Wald, Savage, Hurwitz could serve, the career of the most intelligent of them would surely have swiftly gone up.

Count on the worst

This is how you can characterize the first of these principles. The Wald criterion is often called the criterion of extreme pessimism or the rule of minimal evil. In conditions of limited resources and a precarious, unstable situation, it seems logical to assume a reinsurance position, which is designed for the worst case. Wald's maxim's criterion focuses on maximizing winnings under the most unfavorable circumstances. An example of its use can serve as a maximum increase in the minimum income, maximize the minimum amount of cash, etc. Such a strategy justifies itself in those cases when the person making decisions is not so much interested in great luck as he wants to hedge against sudden losses. In other words, the Wald criterion reduces the risk to a minimum and allows making the most secure decisions. Such an approach makes it possible to obtain a guaranteed minimum, although the actual result may not be so bad.

Wald's criterion: an example of use

Suppose an enterprise is going to produce new types of goods. In this case, one should choose between one of the four variants B ₁ , B ₂ , B ₃ , B ₄ , each of which assumes a certain type of output or a combination thereof. From the decision-making will ultimately depend on which enterprise will make a profit. It is not known exactly how the market situation will be in the future, however, analysts predict three main scenarios for the development of events: С ₁ , С ₂ , С ₃ . The obtained data allow making a table of possible winning options that correspond to each pair of possible solutions and probable situation.

Using Wald's criterion, one should choose the best strategy, the one that will be optimal for the company in question. In our case, the efficiency index

E = max {25; 22; 15; 20} = 25.

We got it by selecting the minimum result for each of the options and singling out among them the one that will bring the greatest revenue. This means that decision B ₁ will be the most optimal for the firm, according to this criterion. Even under the most unfavorable conditions, the result will be 25 (C ₁ ), while at the same time it is possible that it will reach 45 (C ₃ ). Let us note once again that the Wald criterion directs man to the most cautious line of behavior. In other circumstances, it is entirely possible to be guided by other considerations. For example, option В ₃ could bring a gain of 90 with a guaranteed result of 15. However, this case is beyond the scope of this article, and therefore we will not consider it yet.