Fundamentals of the AHP Methodology

Knowing that the AHP is widely accepted in government, commercial, and academic settings is important; appreciating the theoretical underpinnings of the methodology illuminates why. Essentially the AHP is a set of characteristics, steps, and axioms that together yield an elegant and reasonable approach to making difficult decisions. The AHP methodology has three major process steps:

1. Structure. Complex decisions require that decision makers properly analyze and structure the benefits, costs, scenarios, and risks associated with the decision. By breaking down the decision problem into its component parts and structuring them hierarchically into homogeneous clusters, decision makers can reach agreement on the nature of the problem and minimize miscommunication and complexity.

2. Measure. Once the hierarchy of objectives or criteria is structured, decision makers prioritize the objectives using a simple paired comparison measurement system to determine their relative importance. When comparing all possible paired comparisons in each cluster in the hierarchy (a process known as redundant paired comparison), it has been shown that decision makers can produce ratio-scale priorities. Paired comparison judgments may also be used on the alternatives (the projects or programs) of the model, as well as ratio-based rating scales, step functions, and utility curves.

3. Synthesize. Once the decision makers have completed their measurements, they calculate and combine the results to determine the priorities, a process known as synthesis. This process fuses together the qualitative judgment from the various decision makers with the quantitative data and other information about the projects or alternatives. Decision makers then iterate to ensure the priorities make sense and perform sensitivity analysis to consider what-if scenarios.

Underpinning these major process steps are four straightforward axioms, or assumptions:3

• Homogeneity: When comparing objectives, criteria, or alternatives, it is essential to compare elements that are relatively homogeneous; otherwise, errors in judgment can occur.

• Reciprocals: Paired comparison judgments yield reciprocal judgments. "Thus for example, if one stone is judged to be five times heavier than another, then the other is automatically one fifth as heavy as the first because it participated in making the first judgment."4

• Hierarchic composition: Elements at higher levels in the hierarchy are independent of lower levels in the hierarchy.

• Expectations: This final axiom indicates that a decision maker's reasonable beliefs should be adequately reflected in the outcomes. In addition, all relevant objectives or criteria should be included in the analysis.

Understanding these axioms and the methodology through which they are applied helps to appreciate their applicability to portfolio management decision making.

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