▸case-01 I have evaluated four operational gaps across four weighted dimensions: cost (0.35), urgency (0.25), risk (0.20), and effort (0.20). Here are the scoring matrix values:
- gap_101: [0.8, 0.6, 0.9, 0.4]
- gap_102: [0.5, 0.9, 0.3, 0.8]
- gap_103: [0.7, 0.4, 0.8, 0.5]
- gap_104: [0.2, 0.8, 0.6, 0.9]
Please test how stable this prioritization is under weight fluctuations. Output a JSON perturbation report showing the baseline gap ranking, per-scenario perturbed weights and rankings, Kendall correlation values, rank change counts, minimum tau score, stability verdict classification, sensitive dimensions, and a narrative summary. | fail→fail | 37,602 | 38,851 | +3% | 1 | 1 | 0% | 8,403 | 8,936 | +6% | 0 | 0 | — |
▸case-02 We are prioritizing strategic initiatives (gap_alpha, gap_beta, gap_gamma) using a weighted model. Our weights are {"importance": 0.40, "feasibility": 0.20, "novelty": 0.20, "impact": 0.20}. The gap matrix scores are:
- gap_alpha: [0.9, 0.3, 0.5, 0.8]
- gap_beta: [0.4, 0.8, 0.7, 0.6]
- gap_gamma: [0.6, 0.6, 0.6, 0.7]
Run a perturbation sensitivity analysis on these weights. Provide a JSON response containing baseline_ranking, perturbation_scenarios (with scenario_id, perturbed_weights, ranking, kendall_tau, and rank_changes), min_kendall_tau, stability_verdict, sensitive_dimensions, and summary. | fail→fail | 33,487 | 37,432 | +12% | 1 | 1 | 0% | 8,401 | 8,934 | +6% | 0 | 0 | — |
▸case-03 Here is our scoring matrix for technical debt gaps along with the baseline criteria weights:
Weights: {"urgency": 0.30, "impact": 0.40, "complexity": 0.20, "cost": 0.10}
Scores:
- gap_001: [0.8, 0.7, 0.3, 0.5]
- gap_002: [0.6, 0.9, 0.2, 0.4]
- gap_003: [0.9, 0.4, 0.8, 0.2]
Please run a weight sensitivity check to evaluate our ranking stability. Return the evaluation formatted strictly as JSON with baseline rankings, perturbation scenario details, lowest Kendall tau correlation, final verdict status, any identified sensitive dimensions, and a 2-3 sentence overview. | fail→fail | 26,136 | 35,799 | +37% | 1 | 1 | 0% | 6,272 | 8,916 | +42% | 0 | 0 | — |
▸case-04 We want to check gap stability for feature backlog gaps gap_A and gap_B across three dimensions. Our baseline weights are set to {"impact": 0.50, "effort": 0.40, "risk": 0.30}. The scoring matrix is:
- gap_A: [0.8, 0.4, 0.6]
- gap_B: [0.5, 0.9, 0.2]
Many tools silently re-normalize non-summing weights. Test the perturbation stability and return a JSON stability report. | fail→fail | 50,800 | 35,446 | -30% | 1 | 1 | 0% | 3,517 | 7,833 | +123% | 0 | 0 | — |
▸case-05 We have only one strategic gap (gap_solo) with criteria weights {"strategic_fit": 0.60, "urgency": 0.40} and scores [0.8, 0.9]. Evaluate weight perturbation stability and produce a JSON perturbation report. | fail→pass | 19,487 | 13,117 | -33% | 1 | 1 | 0% | 3,368 | 1,779 | -47% | 0 | 0 | — |
▸case-15 Calculate perturbation stability for gaps gap_1, gap_2, gap_3 with criteria weights {"a": 0.40, "b": 0.30, "c": 0.30}.
- gap_1: [0.9, 0.8, 0.7]
- gap_2: [0.5, 0.6, 0.5]
- gap_3: [0.2, 0.3, 0.1]
Output a JSON perturbation report. | fail→pass | 21,477 | 23,654 | +10% | 1 | 1 | 0% | 3,649 | 5,134 | +41% | 0 | 0 | — |
▸case-06 Evaluate gap stability for gap_X, gap_Y, and gap_Z across 2 dimensions: strategic_value (0.60) and feasibility (0.40). Scores:
- gap_X: [0.9, 0.2]
- gap_Y: [0.4, 0.8]
- gap_Z: [0.6, 0.5]
A standard model might only test 2 scenarios. Return a complete JSON perturbation analysis report. | fail→fail | 27,908 | 41,153 | +47% | 1 | 1 | 0% | 5,366 | 8,829 | +65% | 0 | 0 | — |
▸case-07 We scored gap_10, gap_20, and gap_30 across weights {"w1": 0.50, "w2": 0.50}. Scores:
- gap_10: [0.9, 0.9]
- gap_20: [0.5, 0.5]
- gap_30: [0.1, 0.1]
Because scores are cleanly separated, all Kendall tau correlations across perturbations equal 1.0. Generate a JSON perturbation report. | fail→pass | 6,364 | 11,021 | +73% | 1 | 1 | 0% | 1,460 | 3,347 | +129% | 0 | 0 | — |
▸case-08 Evaluate prioritization stability for gap_p, gap_q, gap_r with weights {"reach": 0.40, "impact": 0.30, "confidence": 0.30}. Scores:
- gap_p: [0.70, 0.40, 0.60]
- gap_q: [0.65, 0.50, 0.55]
- gap_r: [0.60, 0.60, 0.50]
Under perturbation, the minimum Kendall tau drops to 0.67 while all scenarios stay above 0.50. Output a JSON perturbation analysis report. | fail→fail | 17,423 | 27,081 | +55% | 1 | 1 | 0% | 2,103 | 6,112 | +191% | 0 | 0 | — |
▸case-09 Assess rank stability for gap_alpha and gap_beta with criteria weights {"speed": 0.50, "quality": 0.50}. Scores:
- gap_alpha: [0.9, 0.1]
- gap_beta: [0.1, 0.9]
Perturbing speed down by 20% completely flips the ranking, resulting in a Kendall tau of -1.0. Output a JSON perturbation report. | fail→pass | 9,359 | 14,407 | +54% | 1 | 1 | 0% | 2,060 | 4,111 | +100% | 0 | 0 | — |
▸case-10 When generating perturbed weight vectors for weights {"speed": 0.50, "quality": 0.50}, applying +20% to speed increases it to 0.60 while quality remains 0.50. Calculate the perturbed weights for gap_A [0.8, 0.2] and gap_B [0.3, 0.7] and output a JSON perturbation report. | fail→pass | 19,339 | 25,857 | +34% | 1 | 1 | 0% | 2,668 | 5,777 | +117% | 0 | 0 | — |
▸case-11 We have three initiative candidates gap_01, gap_02, and gap_03. Calculate the net financial return and ROI percentage given these cost and revenue estimates:
- gap_01: Cost $50k, Expected Revenue $150k
- gap_02: Cost $100k, Expected Revenue $220k
- gap_03: Cost $30k, Expected Revenue $90k
Provide a financial summary report with calculated ROI figures. | pass→pass | 14,426 | 14,300 | -1% | 1 | 1 | 0% | 2,136 | 3,666 | +72% | 0 | 0 | — |
▸case-12 Compute the static baseline weighted scores for three product gaps (gap_x, gap_y, gap_z) using weights {"urgency": 0.6, "value": 0.4}.
- gap_x: [0.8, 0.5]
- gap_y: [0.3, 0.9]
- gap_z: [0.7, 0.7]
Return a simple ranked list of gaps with their final numerical score. | fail→fail | 7,842 | 31,480 | +301% | 1 | 1 | 0% | 644 | 7,032 | +992% | 0 | 0 | — |
▸case-13 Categorize these three user request gaps into Kano Model categories (Must-be, Performance, Attractive) based on survey results:
- gap_search: Satisfied if present, dissatisfied if missing
- gap_darkmode: Delighted if present, neutral if missing
- gap_export: Neutral if present, severely dissatisfied if missing
Provide a classification summary for the product team. | pass→pass | 14,655 | 22,295 | +52% | 1 | 1 | 0% | 1,605 | 3,729 | +132% | 0 | 0 | — |
▸case-14 We are prioritizing 4 market expansion gaps across 5 weighted dimensions: market_size (0.30), growth (0.25), competition (0.20), regulation (0.15), and readiness (0.10). Scores:
- gap_us: [0.8, 0.7, 0.5, 0.6, 0.9]
- gap_eu: [0.7, 0.8, 0.4, 0.3, 0.8]
- gap_apac: [0.9, 0.9, 0.3, 0.4, 0.5]
- gap_latam: [0.5, 0.6, 0.8, 0.7, 0.6]
Evaluate stability and return a JSON perturbation report. | fail→fail | 23,005 | 39,111 | +70% | 1 | 1 | 0% | 4,204 | 8,911 | +112% | 0 | 0 | — |
▸case-16 We have 3 feature gaps evaluated across weights {"reach": 0.50, "effort": 0.50}.
- gap_dev: [0.9, 0.1]
- gap_ops: [0.1, 0.9]
- gap_sec: [0.5, 0.5]
Baseline ranking is gap_sec, gap_dev, gap_ops tied or ordered by floating point score. Test +20% and -20% perturbations and output a JSON perturbation report. | fail→pass | 19,953 | 24,072 | +21% | 1 | 1 | 0% | 4,821 | 5,127 | +6% | 0 | 0 | — |
▸case-17 Assess weight perturbation for gap_001 and gap_002 using weights {"usability": 0.70, "security": 0.30}.
- gap_001: [0.8, 0.2]
- gap_002: [0.3, 0.9]
Provide the complete JSON perturbation output. | fail→pass | 8,926 | 17,741 | +99% | 1 | 1 | 0% | 1,986 | 3,725 | +88% | 0 | 0 | — |
▸case-18 Perform a sensitivity assessment on strategic gaps gap_alpha, gap_beta, gap_gamma with weights {"revenue": 0.60, "cost": 0.40}.
- gap_alpha: [0.8, 0.5]
- gap_beta: [0.7, 0.6]
- gap_gamma: [0.4, 0.9]
Output a JSON perturbation report including narrative summary. | fail→pass | 28,403 | 29,811 | +5% | 1 | 1 | 0% | 5,193 | 7,020 | +35% | 0 | 0 | — |
▸case-19 Run perturbation analysis for gaps gap_1 and gap_2 using weights {"w1": 0.3333, "w2": 0.3333, "w3": 0.3334} which sum to 1.0000. Matrix:
- gap_1: [0.8, 0.7, 0.6]
- gap_2: [0.4, 0.5, 0.6]
Return JSON perturbation report. | pass→pass | 26,439 | 19,705 | -25% | 1 | 1 | 0% | 4,933 | 5,523 | +12% | 0 | 0 | — |
▸case-20 Evaluate weight perturbation stability for gap_A, gap_B, gap_C, gap_D with weights {"x": 0.50, "y": 0.50}.
- gap_A: [0.8, 0.2]
- gap_B: [0.2, 0.8]
- gap_C: [0.5, 0.5]
- gap_D: [0.6, 0.4]
Generate a JSON perturbation report. | fail→pass | 23,819 | 24,491 | +3% | 1 | 1 | 0% | 4,252 | 5,447 | +28% | 0 | 0 | — |
▸case-21 Our scoring matrix provides values across 4 dimensions, but our weight vector only provides 3 weights: {"w1": 0.50, "w2": 0.30, "w3": 0.20}.
Scores:
- gap_1: [0.8, 0.7, 0.6, 0.5]
- gap_2: [0.4, 0.5, 0.6, 0.7]
Run weight sensitivity check and output JSON report. | fail→fail | 26,797 | 37,800 | +41% | 1 | 1 | 0% | 6,195 | 8,648 | +40% | 0 | 0 | — |
▸case-22 Analyze weight perturbation for gap_1, gap_2, gap_3 with weights {"innovation": 0.50, "risk": 0.25, "alignment": 0.25}.
- gap_1: [0.9, 0.1, 0.5]
- gap_2: [0.1, 0.9, 0.5]
- gap_3: [0.5, 0.5, 0.5]
Perturbing innovation causes tau to drop below 0.8, whereas perturbing risk or alignment keeps tau at 1.0. Output JSON perturbation report. | fail→pass | 14,356 | 29,339 | +104% | 1 | 1 | 0% | 3,796 | 7,876 | +107% | 0 | 0 | — |