Decision-Making Strategies: Risk, Certainty, and Uncertainty

Posted on Mar 21, 2025 in Mathematics

Cooperatives grant members several rights, including participation in activities, access to necessary information, fulfillment of obligations, and the return of cooperative surpluses.

The Decision Matrix

A decision matrix is a table that encompasses all elements involved in decision-making. It provides a starting point for solving problems and offers a structured analysis:

  • Strategies: Controllable variables representing alternatives or options to choose from.
  • States of Nature: Uncontrollable variables representing possible situations.
  • Outcomes: Expected results of strategies based on specific states of nature.
  • Probability Predictions: The likelihood of each state of nature occurring.

Criteria for Decision-Making

Based on the knowledge of the state of nature, decisions can be made under three conditions:

  • Certainty: A single state of nature is known.
  • Risk: Several states exist, and their probabilities are known.
  • Uncertainty: The probabilities of possible states are unknown.

Decisions Under Certainty

When the state of nature is known with certainty, evaluate the economic outcomes of different strategies and choose the one that yields the most favorable result.

Decisions Under Risk

When the probabilities of states of nature are known, calculate the Expected Monetary Value (EMV) for each strategy. EMV is the sum of each outcome’s probability (P) multiplied by its corresponding value (D):

VE1 = P1 * D11 + P2 * D12 + … + PN * D1N

Select the strategy with the highest calculated EMV.

Decisions Under Uncertainty

When the likelihood of each state of nature is unknown, decision-making becomes subjective. Several criteria can be applied:

Wald’s Pessimistic Criterion

This criterion focuses on the worst-case scenario for each strategy.

  • Maximin Criterion: Choose the maximum value among the minimum outcomes.
  • Minimax Criterion: Choose the minimum value among the maximum outcomes.

Optimistic Criterion

Choose the strategy with the highest potential outcome (Maximax).

Laplace Criterion

Assign equal probability to each state of nature and choose the strategy with the maximum average value.

Hurwicz Criterion

This criterion combines pessimism and optimism. Define a coefficient of optimism (α) between 0 and 1. The coefficient of pessimism is then (1 – α). Consider both the minimum and maximum values, weighting them with their respective coefficients.

Savage Criterion

This criterion addresses the fear of regret. Create a new matrix of opportunity losses, replacing the original values with the differences between the chosen strategy and the best possible strategy for each state of nature.

This matrix reveals the potential gains that could have been achieved by choosing a different strategy.