| name | ahp-weighting |
| description | SOP: Use the AHP (Analytic Hierarchy Process) to determine scoring-dimension weights, outputting a weight vector |
| version | 1.0.0 |
| category | hypothesis-formation |
| type | sop |
| campaign | gap-prioritization |
| input | List of dimensions (string array) + optional pairwise comparison preference matrix |
| output | AHPWeights — weight vector, consistency ratio (CR), and judgment matrix |
| dependencies | {"skills":["subagent-spawning"]} |
AHP Weighting
Use the AHP (Analytic Hierarchy Process) to determine scoring-dimension weights, outputting a weight vector.
HARD-GATE
- The number of input dimensions must be in the range [2, 9] (AHP applicability range)
- The elements of the output weight vector must sum to 1.0 (±0.001 tolerance allowed)
- The consistency ratio CR must be computed and reported; if CR > 0.1 a warning must be flagged
Pipeline
- Precondition check: verify the dimension list is non-empty and its count is in the range [2, 9]
- Dimension list confirmation: output the dimension list for the caller to confirm; if a comparison matrix is already provided, skip to step 4
- Pairwise comparison matrix construction: for each pair of dimensions (i, j) assign a Saaty scale value (1-9); the matrix must satisfy a[j][i] = 1/a[i][j]
- Eigenvector computation: normalize each column then take row means to obtain the priority vector (weights)
- Consistency ratio check: compute the largest eigenvalue λ_max → consistency index CI = (λ_max - n)/(n-1) → CR = CI/RI (look up the Saaty RI table); CR < 0.1 is acceptable
- Output: return the AHPWeights object; if CR > 0.1 attach revision suggestions
Output Format
{
"dimensions": ["importance", "feasibility", "novelty", "impact"],
"comparison_matrix": [[1, 3, 2, 2], [0.33, 1
