Wald criterion, or How to get the best guaranteed result

2024 Author: Henry Conors | [email protected]. Last modified: 2024-02-12 02:55

Many of us do not like to find ourselves in a situation where there is very little or no information about external factors, and at the same time we need to urgently make an important choice. 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 calm official position. If they knew about game theory and how useful the criteria of Wald, Savage, Hurwitz can be, the careers of the smartest of them would surely skyrocket.

Expect the worst

This is how you can characterize the first of these principles. Wald's criterion is often called the criterion of extreme pessimism or the rule of minimum evil. In a situation of limited resources and a precarious, unstable situation, it seems quite logicalreinsurance position, which is designed for the worst case. Wald's maximin criterion focuses on maximizing payoff under the most unfavorable circumstances. An example of its use is maximizing the minimum income, maximizing the minimum amount of cash, etc. Such a strategy pays off in cases where the decision maker is not so much interested in big luck as he wants to insure himself against sudden losses. In other words, the Wald criterion minimizes risk and allows you to make the safest decisions. This approach makes it possible to get a guaranteed minimum, although the actual result may not be so bad.

Wald criterion: example of use

Suppose a certain enterprise is going to produce new types of goods. In this case, you should make a choice between one of four options B₁, B₂, B₃, B ₄, each of which implies a certain type of release or a combination of them. The decision will ultimately determine what kind of profit the company will receive. How exactly the market situation will develop in the future is unknown, however, analysts predict three main scenarios for the development of events: С₁, С₂, С _{3. The data obtained allows us to compile a table of possible winning options that correspond to each pair of possible solutions and probable situations.}

Product types	Market scenarios			Worst result
	C1	C2	C3
B1	25	37	45	25
B2	50	22	35	22
B3	41	90	15	15
B4	80	32	20	20

Using the Wald criterion, one should choose the best strategy, one that will be the most optimal for the enterprise in question. In our case, the performance indicator

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

We got it by choosing the minimum result for each of the options and isolating among them the one that will bring the greatest income. This means that the decision B₁ will be the most optimal for the firm according to this criterion. Even under the most unfavorable situation, a result of 25 (С₁) will be obtained, at the same time it is possible that it will reach 45 (С_3).

We note once again that the Wald criterion orients a person to the most cautious line of behavior. Atother circumstances, it may well be guided by other considerations. For example, option B_{3could bring a payoff 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.}