ahp-weighting

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

1. Precondition check: verify the dimension list is non-empty and its count is in the range [2, 9]
2. Dimension list confirmation: output the dimension list for the caller to confirm; if a comparison matrix is already provided, skip to step 4
3. 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]
4. Eigenvector computation: normalize each column then take row means to obtain the priority vector (weights)
5. 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
6. 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