Maximin criterion

Max-min criterion for decision making, was presented in writing on year 1950 by Abraham Wald (1902-1950). This criterion represents a pessimistic approach in decision-making (assumes the least favorable situation during taking a decision).

The max-min criterion is a decision-making approach that considers the worst-case scenario when choosing between different options. It is often used in situations where there is a high degree of uncertainty or risk involved. The criterion is based on the idea that it is better to make a decision that minimizes the maximum potential loss, rather than maximizing the potential gain.

One common application of the max-min criterion is in portfolio optimization in finance, where investors aim to minimize the maximum potential loss of their portfolio while maximizing its potential return. The criterion can also be used in project management, where decision makers aim to minimize the negative impact of potential risks on the project's success. In operations research, it is applied to select the best action or strategy to minimize the maximum possible loss or regret.

In summary, max-min criterion is used to minimize the maximum potential loss, in situations where there is high degree of uncertainty or risk involved, in fields like finance, project management, and operations research.

Application

According to the max-min criterion first for each strategy of payoff matrix, we should determine the minimum value. And then choose the strategy, for which the minimum payout, is the largest.

$v={\underset {i}{max}}\{{\underset {j}{min}}\{a_{ij}\}\}$

Example

Example: we have an array of payments from the four possible decisions and three possible states:

${\underset {Strategies}{}}\diagdown {\overset {States\ of\ nature}{}}$	I	II	III
T1	200	100	120
T2	0	300	−200
T3	0	300	500
T4	−100	200	0

We are looking for a minimum winnings for each strategy, and then select the largest:

Strategies	${\underset {j}{min}}\{a_{ij}\}$
T1	100
T2	−200
T3	0
T4	−100

Summing up: According to the Max-min criterion manager should choose a strategy T1.

Advantages of Maximin criterion

The Maximin criterion is a decision-making approach that assumes the least favorable situation, which has many advantages for decision makers. These advantages include:

• It allows for a more conservative approach to decision making, which can help protect against potential losses.
• It provides a clear focus on the worst-case scenario, which can help the decision maker prepare for and mitigate any potential risks.
• It encourages the decision maker to consider the potential risks associated with a given decision, which can help them make more informed decisions.
• It can help the decision maker identify the most cost-effective solution, as it focuses on optimizing the minimal outcome.
• It can help the decision maker identify the most reliable solution as it focuses on minimizing any potential losses.

Limitations of Maximin criterion

The Maximin criterion is a popular decision-making approach, which assumes the least favorable situation when making a decision. Despite its popularity, it is important to consider the following limitations:

• Maximin does not take into account the potential gains from the optimal option. In other words, it does not take into account the possible benefits of making a decision that could bring higher rewards.
• Maximin is a static approach, which does not consider the dynamic nature of the decision-making process and the possible changes in the environment that could affect the decision.
• Maximin can be overly pessimistic in some cases, as it ignores the potential benefits of taking a risk.
• Maximin does not take into account the various factors that could affect the decision, such as the cost of implementing the decision, the time frame of the decision, and the impact of the decision on the environment.

Other approaches related to Maximin criterion

The following are other approaches related to the Max-min criterion for decision making:

• Optimism Criterion: This approach, also known as the Maximax criterion, assumes the best-case scenario when making decisions. It is the opposite of the Max-min criterion, as it seeks the maximum gain instead of the minimum loss.
• Hurwicz Criterion: The Hurwicz criterion, named after its inventor, Alfred Hurwicz, is a type of hybrid approach that combines the Max-min and Optimism criteria. It assigns a weight to each of the two criteria, and the decision is made based on the weighted values.
• Laplace Criterion: The Laplace criterion is a risk-neutral approach that assumes no preference for either maximum gain or minimum loss. It considers all potential outcomes equally, and the decision is made based on probability.
• Bayes Criterion: The Bayes criterion uses prior probabilities to weigh the possible outcomes of a decision. It considers the expected utility of each outcome and the probability of them occurring.

In summary, the Max-min criterion for decision making is one of several approaches that can be used when making decisions. Other approaches include the Optimism Criterion, Hurwicz Criterion, Laplace Criterion, and Bayes Criterion, which all represent different ways of weighing the pros and cons of different decisions.

Maximin criterion — recommended articles

Minimax criterion — Expected utility — Expected utility theory — Conditions of decision-making — Rational decision making — Quantitative risk analysis — Selection process in conditions of certainty and uncertainty — Project evaluation methods — Expected monetary value

References

• Hassan, N., Siew, L. W., & Shen, S. Y. (2012). Portfolio decision analysis with maximin criterion in the Malaysian stock market. Applied Mathematical Sciences, 6(110), 5483-5486.