Decision-making matrix model
Decision-making matrix model
Decision-making matrix model is a formalized representation of a choice problem in the form of a table (matrix) that reflects the relationships between possible alternatives and the external conditions that influence the outcome. This model is used for analyzing decisions under conditions of uncertainty, risk, and multiple criteria.
Matrix Structure
The model is built upon the following components:
- Alternatives (courses of action) — A₁, A₂, ..., Aₘ — the rows of the matrix.
- States of nature (scenarios) — E₁, E₂, ..., E_d — the columns of the matrix.
- Payoff — Yᵢⱼ = fⱼ(Aᵢ), the outcome for the combination of Aᵢ and Eⱼ.
Such a table is called a payoff matrix and has dimensions m × d, where each cell contains an evaluation of the outcome for the corresponding "alternative–state" pair.
Interpretation of Payoffs
The Yᵢⱼ values are interpreted as:
- income or profit,
- degree of goal achievement,
- utility or preferability of the outcome.
If the evaluations are of different natures, they can be normalized to a common scale, for example, from 0 to 1.
Purpose and Advantages of the Model
The matrix model serves as a basis for:
- applying choice criteria (Wald, Savage, Laplace, Hurwicz, etc.),
- analyzing the behavior of the Decision Maker (DM) without knowledge of probabilities,
- justifying robust solutions,
- transitioning to the construction of decision trees and scenarios.
Advantages:
- clarity and structure;
- suitability for computer processing;
- versatility.
Example of a Matrix Structure
| Alternative | State E₁ | State E₂ | ... | State E_d |
|---|---|---|---|---|
| A₁ | Y₁₁ | Y₁₂ | ... | Y₁d |
| A₂ | Y₂₁ | Y₂₂ | ... | Y₂d |
| ... | ... | ... | ... | ... |
| Aₘ | Yₘ₁ | Yₘ₂ | ... | Yₘd |
Application in Decision Making
The matrix model is applied:
- under uncertainty — with deterministic criteria;
- under risk — with given probabilities;
- in multi-criteria analysis — as a basis for aggregation;
- in decision support systems.