coherence-diagnosis

Research

Strategy for auditing preference consistency using Consistency Ratio, cycle enumeration, and mElo to detect and resolve intransitivities.

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Coherence Diagnosis

Purpose

Audit an existing comparison matrix for logical consistency. Detect cycles, quantify transitivity violations, localize problematic judgments, and recommend corrections. Essential as a quality gate before finalizing any ranking.

When to use

Existing comparison data needs validation
Suspicion of inconsistent judgments
Pre-finalization quality gate
AHP consistency ratio check required
Debugging unexpected ranking results

Budget

Resource	Allocation
Cycle detection	Full matrix scan
Consistency metric	CR < 0.1 (AHP) or transitivity > 90%
Repair comparisons	≤ 20% of original comparisons
Iterations	1-3 audit-repair cycles

State Ledger

comparison_matrix: {}   # pair → winner
candidates: []
consistency_metrics: {cr: null, transitivity: null, cycles_count: 0}
cycles: []              # [[a>b, b>c, c>a], ...]
problematic_pairs: []   # pairs involved in most cycles
repair_log: []          # [{pair, old_judgment, new_judgment, reason}]
iteration: 0

Available Tactics

consistency-audit-loop — detect, localize, repair, recompute

Available SOPs

cycle-detection
inconsistency-localization
comparison-executor (for re-comparison)
rating-update (for recomputation)
convergence-check
ranking-synthesis

Execution Guidance

Run cycle-detection on full comparison matrix
Compute consistency metrics (CR, transitivity score)
If consistent (CR < 0.1): proceed to ranking-synthesis
If inconsistent: run inconsistency-localization
Re-compare problematic pairs via comparison-executor
Recompute ratings and re-check consistency
Repeat until consistent or repair budget exhausted
Document all repairs in audit trail

Output Format

diagnosis:
  consistency_ratio: 0.04
  transitivity_score: 0.97
  cycles_found: 1
  cycles_resolved: 1
  repairs_made: 2
audit_trail:
  - {pair: ["b", "d"], original: "b", revised: "d", reason: "..."}
final_ranking_valid: true
method: consistency-ratio

Available Tactics

Optional, no fixed order; the final leaf is always a sop.

Tactic	When to use
consistency-audit-loop	Detect preference cycles, localize inconsistent judgments, request corrections, and recompute ratings until consistency threshold is met.

Available SOPs

Optional, no fixed order; the final leaf is always a sop.

SOP	When to use
convergence-check	Evaluate whether the ranking has stabilized by analyzing rating history and computing stability metrics.
ranking-synthesis	Produce the final ranking artifact from converged ratings and consistency report.
rating-update	Incorporate a new judgment into the rating model and return updated ratings for all candidates.