What is the maximax criterion in decision analysis?

1 Maximax criterion definition

The maximax criterion, also known as the optimistic criterion, is a decision rule that selects the alternative that has the highest possible payoff, regardless of the probabilities of the outcomes. It assumes that the decision maker is optimistic and prefers to maximize the maximum gain. The maximax criterion can be expressed as: Maximax = max {max (payoffs for each alternative)} In other words, for each alternative, you find the maximum payoff among all the possible outcomes, and then you choose the alternative that has the highest maximum payoff.

2 Maximax criterion example

To illustrate how the maximax criterion works, let's consider a simple example of a company that has to decide whether to launch a new product or not. The company estimates that the new product can have three possible outcomes: success, failure, or break-even, with different payoffs in millions of dollars. The table below shows the payoffs for each outcome and each alternative.

| Alternative | Success | Failure | Break-even |

| Launch | 10 | -5 | 0 |

| Do not launch | 0 | 0 | 0 |

Using the maximax criterion, the company would first find the maximum payoff for each alternative. For the launch alternative, the maximum payoff is 10, which occurs if the product is successful. For the do not launch alternative, the maximum payoff is 0, which occurs in any outcome. Then, the company would choose the alternative that has the highest maximum payoff, which is the launch alternative with 10. Therefore, the maximax criterion would recommend launching the new product.

3 Maximax criterion applications

The maximax criterion is often used when the decision maker is optimistic and willing to take risks, as well as in one-shot decisions where the consequences are not repeated or cumulative. This criterion can be applied to investment decisions, where the decision maker wants to maximize the potential return of a portfolio or project, innovation decisions to explore new opportunities or markets with high rewards, and negotiation decisions to achieve the best possible outcome or agreement.

4 Maximax criterion advantages

The maximax criterion has several benefits as a decision rule, such as its simplicity and ease of application, as it only requires finding the maximum payoff for each alternative and comparing them. It also reflects a positive and optimistic attitude, as it focuses on the best possible scenario and ignores the worst ones. Additionally, it encourages risk-taking and innovation by favoring alternatives with higher potential gains.

5 Maximax criterion disadvantages

The maximax criterion has some drawbacks as a decision rule, such as being unrealistic and naive by disregarding the probabilities and values of the other outcomes. It can also lead to poor decisions and losses by ignoring the risks and costs of the alternatives. Furthermore, it can be inconsistent and irrational, as it may alter the preference order of the alternatives depending on how the payoffs are presented or framed.

6 Here’s what else to consider

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