Analytic hierarchy process

Use when

• You cannot state weights directly but can say which of two criteria matters more, and by roughly how much.
• Several people must agree on weights and direct numbers cause deadlock.
• You want a consistency check on your own preferences.

Do not use when

• There are many criteria — n criteria need n(n−1)/2 comparisons, so seven criteria is twenty-one judgements.
• Speed matters. This is the slowest method in the cluster.
• The precision would be false. The arithmetic is exact; the inputs are not.

Inputs required

• Criteria
• Patience for pairwise comparisons
• Options scored per criterion

Procedure

1. 01

   Build the hierarchy

   Goal at the top, criteria beneath, options at the bottom. Sub-criteria only where a criterion genuinely splits.

2. 02

   Compare criteria in pairs

   For each pair, state which matters more on a 1–9 scale: 1 equal, 3 moderately, 5 strongly, 7 very strongly, 9 extremely. Record the reciprocal automatically.

3. 03

   Derive the weights

   The normalised principal eigenvector of the comparison matrix gives the weights. In practice, normalise each column, then average the rows — that approximation is close enough at this scale.

4. 04

   Check consistency

   Compute the consistency ratio. Above about 0.1, your comparisons contradict each other — you said A > B, B > C and C > A. Revisit, do not proceed.

5. 05

   Score and combine

   Compare options pairwise within each criterion, or score them directly. Combine with the derived weights for a final ranking.