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

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, 0.5, 0.5], [0.5, 2, 1, 1], [0.5, 2, 1, 1]],
  "weights": { "importance": 0.40, "feasibility": 0.15, "novelty": 0.23, "impact": 0.22 },
  "lambda_max": 4.02,
  "ci": 0.007,
  "ri": 0.90,
  "cr": 0.008,
  "cr_acceptable": true,
  "warnings": [],
  "revision_suggestions": []
}