Minimax regret

Definition

Minimax regret is a decision-making criterion used under uncertainty that aims to minimize the maximum potential regret associated with various choices. It involves evaluating possible outcomes for each decision and determining the worst-case scenario, allowing decision-makers to choose the option that has the least potential for regret, based on their risk preferences.

5 Must Know Facts For Your Next Test

1. Minimax regret helps decision-makers evaluate choices based on potential losses rather than just potential gains, allowing a more cautious approach.
2. This criterion is particularly useful when the probabilities of different states of nature are unknown or difficult to estimate.
3. The process involves creating a regret table, which quantifies the regret for each decision alternative based on the best possible outcomes.
4. By focusing on minimizing the worst-case regret, this approach encourages a conservative strategy that can be beneficial in highly uncertain environments.
5. Minimax regret is one of several decision-making strategies under uncertainty, alongside others like expected value and maximin strategies.

Review Questions

• How does minimax regret differ from other decision-making criteria like expected value?
  • Minimax regret focuses on minimizing potential regret by considering the worst-case scenario for each decision alternative, whereas expected value emphasizes maximizing average outcomes based on probabilities. While expected value calculates an overall expected gain or loss, minimax regret prioritizes avoiding the worst possible regret associated with a decision. This makes minimax regret particularly useful in situations where probabilities are uncertain or difficult to assess.
• Discuss how you would construct a regret table when applying the minimax regret criterion to a decision problem.
  • To construct a regret table, start by listing all possible decision alternatives and the states of nature. For each alternative, calculate the potential outcomes based on the different states of nature. Next, identify the best outcome for each state of nature and determine the regret for each alternative by subtracting the outcome of each decision from its best possible outcome. Finally, find the maximum regret for each alternative and select the option with the lowest maximum regret, as this reflects a minimax approach.
• Evaluate the effectiveness of using minimax regret in real-world decision-making scenarios where uncertainty plays a significant role.
  • Using minimax regret in real-world decision-making can be highly effective in situations characterized by uncertainty, as it provides a framework to avoid poor outcomes based on potential regrets. It allows individuals and organizations to make more informed choices by emphasizing caution over optimism. However, while this approach is beneficial in reducing emotional distress from regret, it may lead to overly conservative decisions that miss out on potentially better opportunities. Therefore, balancing minimax regret with other strategies could yield a more comprehensive decision-making process.

Related terms

Regret: A feeling of disappointment or distress about something that has happened or been done, particularly when comparing an outcome to a better possible scenario.

Decision Matrix: A table used to evaluate different decisions by comparing their possible outcomes against various criteria, often used in decision-making processes.

Expected Value:

The average outcome of a random variable, calculated by summing the products of each possible outcome and its probability, often used to evaluate risky decisions.