The Analytic Hierarchy Process

Choosing a vendor, a city for an office, or a product direction usually means weighing several criteria at once — cost, quality, speed, risk. Ask someone to assign a percentage weight to each and they stall, because the mind can't hold five things in balance simultaneously.

The Analytic Hierarchy Process, developed by Thomas Saaty, solves this by never asking for more than a comparison of two things at a time. From those simple judgments it reconstructs a full set of priority weights — and, crucially, tells you whether the judgments hung together.

The 1–9 Comparison Scale

For each pair of criteria, the respondent says which is more important and by how much, on Saaty's 1–9 scale.

The reciprocal fills the mirror cell: if cost is "5" versus speed, then speed is "1/5" versus cost. For n criteria there are n(n−1)/2 comparisons — a handful of simple judgments rather than one impossible ranking.

From Comparisons to Weights

The pairwise judgments fill a comparison matrix, like the one above. AHP then extracts the priority weights as the matrix's principal eigenvector — computed by the power method — which balances all the comparisons into a single normalized set of weights that sum to 100%.

These weights can then score each option — multiply how well each option does on each criterion by that criterion's weight, and the highest total wins.

The Consistency Check

Here is what sets AHP apart from a simple survey: it can detect contradictory judgments. If you say cost beats quality, quality beats speed, but then speed beats cost, your answers are inconsistent. AHP quantifies this with the Consistency Ratio (CR).

Running an AHP Study

1. 1Structure the decision: a goal at the top, criteria beneath it, options at the bottom.
2. 2Collect pairwise comparisons on the 1–9 scale for every pair of criteria.
3. 3Compute the priority weights from the comparison matrix via the eigenvector.
4. 4Check the consistency ratio, and exclude or re-survey respondents whose CR is too high.
5. 5Score the options against the weighted criteria and read the ranking.

AHP in the SKARI Survey Lab

SKARI's Survey Lab runs the full AHP method: it collects the pairwise comparisons, derives weights by the eigenvector power method, and computes consistency automatically.

• Pairwise comparison collection on the 1–9 scale
• Priority weights via the eigenvector (power method)
• Consistency ratio per respondent with the standard 0.1 / 0.2 thresholds
• A CR filter to exclude inconsistent respondents before aggregating

Frequently Asked Questions

How many criteria can AHP handle?

Keep it to about 5–7 per level. More than that and the comparison count explodes and consistency drops. Use a hierarchy of sub-criteria for larger problems.

What if my CR is too high?

Revisit the contradictory comparisons, or exclude that respondent. SKARI's CR filter makes the second option a single toggle.

AHP or conjoint?

AHP weights explicit criteria for a decision; conjoint infers preferences from choices between products. Use AHP when the criteria are known and named.

Key Takeaways

AHP turns an overwhelming multi-criteria decision into a series of easy comparisons, assembles them into transparent weights, and — uniquely — verifies that the underlying judgments were consistent.