Weighting method · Saaty, 1977

AHP

Analytic Hierarchy Process

Turns pairwise 'which matters more, and by how much?' judgments into defensible criteria weights.

How it works

1. Compare criteria pairwise on the Saaty 1–9 scale (matrix grid or questionnaire).
2. Derive weights as the principal eigenvector of the judgment matrix.
3. Check the Consistency Ratio; CR ≥ 0.10 blocks the weights and the inconsistency doctor points at the judgment to fix.
4. Hierarchies: compare main criteria groups first, then sub-criteria within each group global weight = main × local.
5. Groups: several participants' matrices are merged by element-wise geometric mean, with per-person consistency checks and a disagreement view.

Use it when

• Weights should come from expert judgment, elicited in a structured, auditable way.
• You have many criteria organize them in a hierarchy of small comparisons.
• Several stakeholders must agree on the weights.

Watch out for

• Beyond ~7 criteria a single flat matrix becomes hard to keep consistent use a hierarchy.
• Group geometric means can average away a real disagreement; read the disagreement view.

Parameters

Pairwise judgments on the 1–9 scale; CR must stay below 0.10.

Cite the method

Saaty, T. L. (1980). The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation. McGraw-Hill.

@book{saaty1980ahp,
  author    = {Saaty, Thomas L.},
  title     = {The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation},
  publisher = {McGraw-Hill},
  address   = {New York},
  year      = {1980}
}