Do your priorities hang together?

Ranking a pile of options at once is hard; judging them two at a time is easy. Saaty's AHPThe Analytic Hierarchy Process: derive weights from pairwise comparisons, and measure how coherent those comparisons are. turns those pairwise calls into priority weights — and, more usefully, measures whether they're even coherent. Say Search beats Billing beats Mobile beats Search and there's no ranking that fits; the consistency ratioA measure of how far your comparisons stray from a self-consistent set, scaled against what purely random judgments would score. Below about 0.10 is the rule of thumb for a trustworthy ranking. catches it.

SearchBilling
Search is 3× as important as Billing
SearchMobile
Mobile is 2× as important as Search
SearchDocs
Search is 5× as important as Docs
BillingMobile
Billing is 3× as important as Mobile
BillingDocs
Billing is 4× as important as Docs
MobileDocs
Mobile is 4× as important as Docs
Inconsistent
1Search
35%
2Billing
30%
3Mobile
27%
4Docs
7%
0.28consistency ratioConsistency ratio = consistency index ÷ random index. 0 is perfectly coherent; under 0.10 is trustworthy; well above means the comparisons contradict each other.

Your calls contain a loop: Search ▸ Billing ▸ Mobile Search. Each beats the next, yet the last beats the first — so no ranking can honour every comparison. The weights below are the least-bad fit, but the consistency ratio (0.28) is the signal to revisit a judgment.

Saaty's Analytic Hierarchy Process — priority weights from pairwise comparisons, with the consistency ratio