{
  "evaluation_id": "EVAL-20260315-060532",
  "question_id": "EVAL-20260315-060532",
  "question_text": "Hospital A has a higher survival rate than Hospital B for both heart surgery (A: 90%, B: 85%) and knee surgery (A: 95%, B: 92%). But Hospital B has a higher overall survival rate (B: 91%, A: 89%). (1) Construct exact numbers that produce this paradox. (2) Which hospital is actually better? (3) A health insurance company uses overall survival rate to recommend hospitals. What goes wrong? (4) How should the comparison be done correctly?",
  "category": "reasoning",
  "timestamp": "2026-03-15T06:05:32.303Z",
  "display_date": "Mar 15, 2026",
  "winner": {
    "name": "Qwen 3 8B",
    "provider": "openrouter",
    "score": 9.51
  },
  "avg_score": 8.539,
  "matrix_size": 68,
  "models_used": [
    {
      "id": "devstral",
      "name": "Devstral Small",
      "provider": "openrouter"
    },
    {
      "id": "gemma3_27b",
      "name": "Gemma 3 27B",
      "provider": "openrouter"
    },
    {
      "id": "llama4_scout",
      "name": "Llama 4 Scout",
      "provider": "openrouter"
    },
    {
      "id": "phi4",
      "name": "Phi-4 14B",
      "provider": "openrouter"
    },
    {
      "id": "granite_40",
      "name": "Granite 4.0 Micro",
      "provider": "openrouter"
    },
    {
      "id": "qwen3_8b",
      "name": "Qwen 3 8B",
      "provider": "openrouter"
    },
    {
      "id": "mistral_nemo",
      "name": "Mistral Nemo 12B",
      "provider": "openrouter"
    },
    {
      "id": "llama31_8b",
      "name": "Llama 3.1 8B",
      "provider": "openrouter"
    },
    {
      "id": "qwen3_32b",
      "name": "Qwen 3 32B",
      "provider": "openrouter"
    },
    {
      "id": "kimi_k25",
      "name": "Kimi K2.5",
      "provider": "openrouter"
    }
  ],
  "rankings": {
    "qwen3_8b": {
      "display_name": "Qwen 3 8B",
      "provider": "openrouter",
      "average_score": 9.51,
      "score_count": 8,
      "min_score": 8.6,
      "max_score": 10,
      "rank": 1
    },
    "gemma3_27b": {
      "display_name": "Gemma 3 27B",
      "provider": "openrouter",
      "average_score": 9.37,
      "score_count": 9,
      "min_score": 7.3,
      "max_score": 10,
      "rank": 2
    },
    "phi4": {
      "display_name": "Phi-4 14B",
      "provider": "openrouter",
      "average_score": 8.98,
      "score_count": 8,
      "min_score": 8.55,
      "max_score": 9.6,
      "rank": 3
    },
    "mistral_nemo": {
      "display_name": "Mistral Nemo 12B",
      "provider": "openrouter",
      "average_score": 8.69,
      "score_count": 9,
      "min_score": 6.2,
      "max_score": 9.8,
      "rank": 4
    },
    "granite_40": {
      "display_name": "Granite 4.0 Micro",
      "provider": "openrouter",
      "average_score": 8.36,
      "score_count": 8,
      "min_score": 6.5,
      "max_score": 9.45,
      "rank": 5
    },
    "devstral": {
      "display_name": "Devstral Small",
      "provider": "openrouter",
      "average_score": 8.28,
      "score_count": 8,
      "min_score": 6.1,
      "max_score": 9.45,
      "rank": 6
    },
    "qwen3_32b": {
      "display_name": "Qwen 3 32B",
      "provider": "openrouter",
      "average_score": 8.25,
      "score_count": 1,
      "min_score": 8.25,
      "max_score": 8.25,
      "rank": 7
    },
    "kimi_k25": {
      "display_name": "Kimi K2.5",
      "provider": "openrouter",
      "average_score": 8.25,
      "score_count": 1,
      "min_score": 8.25,
      "max_score": 8.25,
      "rank": 8
    },
    "llama31_8b": {
      "display_name": "Llama 3.1 8B",
      "provider": "openrouter",
      "average_score": 7.86,
      "score_count": 8,
      "min_score": 6.3,
      "max_score": 8.6,
      "rank": 9
    },
    "llama4_scout": {
      "display_name": "Llama 4 Scout",
      "provider": "openrouter",
      "average_score": 7.85,
      "score_count": 8,
      "min_score": 6.4,
      "max_score": 10,
      "rank": 10
    }
  },
  "judgments": [
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 9,
      "brief_justification": "The response accurately constructs an example of Simpson's paradox, correctly identifies Hospital A as better for both surgery types, explains the flaw in using overall survival rates, and suggests a proper comparison method. It is clear, thorough, and actionable, though the example rates slightly differ from the question's specified values."
    },
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 9.6,
      "brief_justification": "The response correctly constructs numbers demonstrating Simpson's Paradox, thoroughly addresses all four questions, and provides clear, actionable solutions. It explains the statistical mechanism behind the paradox and offers insightful methods for accurate comparison."
    },
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 7.15,
      "brief_justification": "The response correctly identifies Simpson's Paradox and explains the concept well, but fails to fully construct the exact numbers requested in part (1). The mathematical derivations are sound but incomplete, and the final example doesn't match the specific survival rates given in the question."
    },
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 8.8,
      "brief_justification": "The response correctly constructs numbers demonstrating Simpson's Paradox, identifies the issue with overall survival rates, and provides valid solutions. It is clear and useful but could slightly improve depth by explicitly mentioning the role of differing case volumes in the paradox."
    },
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 6.5,
      "brief_justification": "The example in part (1) is invalid because the calculated overall survival rates (92.5% for both hospitals) contradict the stated 89% and 91%. Correctness is reduced due to this error. The rest of the response accurately addresses the paradox, explains the limitations of overall rates, and suggests appropriate methods for comparison."
    },
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 9.6,
      "brief_justification": "The response accurately constructs numbers for Simpson's Paradox, explains the paradox's implications, and provides clear, actionable solutions. It thoroughly addresses all four questions with logical consistency and practical insights."
    },
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 8.6,
      "brief_justification": "The response accurately constructs a Simpson's paradox example with clear numerical reasoning, addresses all four questions, and explains the case-mix bias issue. It provides actionable recommendations but could slightly improve by explicitly naming Simpson's paradox and elaborating on statistical adjustment methods."
    },
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 7.95,
      "brief_justification": "The response correctly constructs numbers to demonstrate Simpson's paradox and explains the issue with overall survival rates. However, it incorrectly calculates the final overall survival rates (stating A has 90.4% when the question says B has higher overall rate). The explanation of the paradox and solution is clear and thorough."
    },
    {
      "judge_key": "kimi_k25",
      "judge_name": "Kimi K2.5",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 7.3,
      "brief_justification": "The response correctly identifies Simpson's Paradox and provides sound qualitative analysis for parts 2-4, but contains a critical mathematical error in Part 1: the constructed example yields Hospital A with 92.5% overall survival (not 89%) and actually shows A having a higher overall rate than B (92.5% vs 91.3%), which is the opposite of the requested paradox. To correctly demonstrate the paradox, Hospital A should perform a higher proportion of the riskier heart surgeries, not an equal split."
    },
    {
      "judge_key": "kimi_k25",
      "judge_name": "Kimi K2.5",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 6.2,
      "brief_justification": "The response fails to properly demonstrate Simpson's Paradox by introducing a third surgery category where Hospital B performs better, rather than showing how differential case volumes of heart and knee surgeries create the reversal. While the calculations are clear, the analysis misses key concepts like confounding variables and incorrectly suggests Hospital B is 'better overall' without acknowledging this is a statistical artifact of case mix."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 9.8,
      "brief_justification": "The response is factually accurate, logically valid, and thoroughly covers the topic. It is well-structured and clear, with insightful analysis beyond surface level. The practical value and actionability are high, providing a detailed explanation of the paradox and how to correctly compare hospitals."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 6.65,
      "brief_justification": "The response provides a detailed explanation of Simpson's Paradox and attempts to construct an example, but the calculations are not entirely accurate and the final answer is not clearly stated."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 9.6,
      "brief_justification": "The response accurately explains Simpson's Paradox and provides a clear, detailed example with exact numbers. It also addresses all aspects of the question, including the correct way to compare hospitals."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 9.45,
      "brief_justification": "The response accurately addresses all parts of the question with clear, well-structured communication and practical insights, though it could delve deeper into statistical nuances."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 9.8,
      "brief_justification": "The response accurately explains the paradox and provides a clear, thorough, and insightful analysis with practical recommendations."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 9.25,
      "brief_justification": "The response accurately explains the paradox and provides a clear, detailed, and actionable analysis."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 8.15,
      "brief_justification": "The response provides a detailed and mostly accurate explanation of the paradox and how to correctly compare hospitals. However, there are some minor inconsistencies in the calculations and the final answer is not clearly stated."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 6.55,
      "brief_justification": "The response correctly identifies the paradox and explains why overall survival rate can be misleading. However, the initial numbers constructed in part (1) do *not* produce the stated paradox (A: 90/95, B: 85/92, B overall > A overall). It also lacks deeper discussion of weighting or risk-adjusted comparisons."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 6.4,
      "brief_justification": "The response correctly identifies Simpson's Paradox and attempts to construct examples, but struggles to consistently produce numbers that match *all* the given percentages. The explanation is generally clear, but the numerous attempts and corrections detract from its overall quality. It correctly identifies the flaw in the insurance company's approach."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 9,
      "brief_justification": "The response accurately identifies and explains Simpson's Paradox, constructs a valid numerical example, and provides sound advice for correct comparison; the rounding introduces minor inaccuracies but doesn't detract from the overall quality."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 8.8,
      "brief_justification": "The response correctly identifies the paradox and provides a valid numerical example. It clearly explains the issue with using overall survival rate and offers a reasonable solution, though it could delve deeper into why this happens (case mix)."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 10,
      "brief_justification": "The response flawlessly identifies and explains Simpson's Paradox, providing a clear numerical example, correctly determining which hospital is better based on surgical skill, and accurately outlining the pitfalls of using overall survival rates. The suggested solution for correct comparison is also well-articulated."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 9,
      "brief_justification": "The response accurately explains the paradox and provides a valid numerical example. It clearly identifies the flaw in using overall survival rate and offers sound advice for a correct comparison."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 7.35,
      "brief_justification": "The response correctly identifies the paradox and attempts to construct numbers to demonstrate it, but contains some calculation errors and inconsistencies throughout the steps. The explanation of why the insurance company's approach is flawed is good, and the suggestion for correct comparison is reasonable."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 9.45,
      "brief_justification": "The response accurately constructs numbers to produce the paradox, correctly identifies Hospital A as better based on surgery-specific rates, explains the flaw in using overall survival rates for comparison, and provides a correct method for comparison."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 10,
      "brief_justification": "The response accurately addresses all parts of the question, providing exact numbers to produce the paradox, insights into which hospital is actually better, issues with using overall survival rates, and methods for correct comparison. The explanation is clear, thorough, and offers practical advice."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 8.55,
      "brief_justification": "The response correctly identifies Simpson's Paradox and provides a clear example. It also offers a thorough explanation of the issue and suggests appropriate methods for a fair comparison."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 9.25,
      "brief_justification": "The response accurately constructs a paradoxical scenario, correctly identifies the issue with using overall survival rates for recommendations, and provides a clear and practical approach for comparing hospital performance."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 9.8,
      "brief_justification": "The response accurately constructs a paradoxical scenario, correctly interprets the situation, identifies the flaw in using overall survival rates, and provides a clear method for correct comparison. The analysis is thorough and provides practical insights."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 8.8,
      "brief_justification": "The response accurately constructs numbers to demonstrate Simpson's paradox, correctly identifies the better hospital based on specific surgeries, and provides a clear explanation of the insurance company's mistake and how to compare hospitals correctly."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 8.25,
      "brief_justification": "The response provides a clear and correct construction of the paradox, identifies the issue with using overall survival rates for comparison, and offers a correct approach for comparing hospitals. However, some parts of the explanation could be more detailed or clearer."
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 9.45,
      "brief_justification": "The response correctly identifies the paradox by constructing exact numbers and explains the discrepancy between overall and specific surgery survival rates. It accurately concludes that Hospital A is better based on individual surgery rates and highlights the flaw in using overall survival rates for recommendations. The analysis is insightful, though it could further explore implications for different types of surgeries or patient demographics."
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 9.8,
      "brief_justification": "The response accurately explains the paradox using precise numbers and provides a comprehensive analysis of the factors involved. It clearly outlines the issue with using overall survival rates and suggests sophisticated methods like risk adjustment and surgery-specific comparisons for accurate evaluation. The explanation is clear, structured, and offers practical insights into evaluating hospital performance."
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 10,
      "brief_justification": "The response correctly identifies and explains Simpson's Paradox by constructing a scenario with exact numbers. It accurately describes how the paradox arises from the differing proportions of surgeries performed at each hospital and provides a clear explanation of why the health insurance company's recommendation based on overall survival rates might be misleading. The response also correctly suggests comparing survival rates for specific procedures rather than overall rates to avoid the parado"
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 9,
      "brief_justification": "The response accurately constructs numbers to illustrate the paradox and correctly identifies the issue with using overall survival rates. It provides a clear and actionable recommendation for comparing hospitals based on specific surgeries. However, it could delve deeper into statistical concepts like Simpson's paradox."
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 10,
      "brief_justification": "The response correctly constructs the numbers that illustrate Simpson's Paradox, clearly explains why Hospital A is better at individual surgeries, identifies the issue with using overall survival rates for recommendations, and provides a thorough explanation of how comparisons should be done correctly by considering stratified analysis and patient distribution across surgeries."
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 9,
      "brief_justification": "The response accurately constructs numbers to demonstrate the paradox and provides a clear explanation of the issue with using overall survival rates. It offers practical advice for correct comparison, though it could delve deeper into statistical methods for weighting different types of surgeries."
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 8.6,
      "brief_justification": "The response correctly identifies the paradox and explains the calculation of survival rates for specific surgeries. It accurately determines that Hospital A is better based on individual surgery rates and highlights the flaw in using overall survival rates for recommendations. The response provides a clear and actionable method for comparing hospitals by considering the types of surgeries separately, which aligns with the criteria for evaluating the correctness of the analysis."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "qwen3_32b",
      "respondent_name": "Qwen 3 32B",
      "weighted_score": 8.25,
      "brief_justification": "The response accurately addresses each part of the question, providing a clear explanation of the paradox, evaluation of hospital performance, the issue with using overall survival rate alone, and a correct comparison method. It is thorough and well-structured."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "kimi_k25",
      "respondent_name": "Kimi K2.5",
      "weighted_score": 8.25,
      "brief_justification": "The response accurately addresses each part of the question, providing a clear explanation of the paradox, which hospital is better, the issue with using overall survival rate, and how comparisons should be done correctly. It demonstrates a good understanding of the topic while omitting a direct response, which slightly reduces completeness and usefulness."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 8.8,
      "brief_justification": "The response accurately constructs the paradox, correctly identifies Hospital A as better for both surgery types, addresses the flaw in using overall survival rate, and provides a clear, well-structured solution."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 8.8,
      "brief_justification": "The response accurately explains the statistical paradox, correctly identifies the better hospital for specific procedures, explains the flaws of using overall survival rate, and provides comprehensive, technically sound recommendations for proper comparison, demonstrating strong correctness, completeness, clarity, depth, and usefulness while maintaining a concise justification."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 8.8,
      "brief_justification": "The response accurately constructs a paradoxical example, correctly identifies the better hospital, explains the insurance company's mistake, and provides a clear method for proper comparison, demonstrating strong overall performance."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 8.8,
      "brief_justification": "The response accurately explains Simpson's Paradox, provides a concrete numerical example, correctly identifies which hospital performs better for specific surgeries, explains the flaw of using overall survival rate, and offers a clear method for proper comparison."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 8.8,
      "brief_justification": "The response accurately constructs the paradox with precise numbers, clearly identifies which hospital is better, explains the flaw in using overall survival rates, and provides a correct comparison method, demonstrating strong correctness, completeness, clarity, depth, and usefulness."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 8.8,
      "brief_justification": "The response accurately constructs the paradoxical numbers, clearly identifies which hospital is better for specific surgery types, explains the insurance company's mistake, and provides a comprehensive method for correct comparison, with minor depth limitation in discussing potential implications of the paradox."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 8.25,
      "brief_justification": "The response accurately constructs the paradox, determines the better hospital, explains the insurance company's mistake, and provides a correct comparison method, though depth could be slightly higher."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 6.1,
      "brief_justification": "Part (1) incorrectly constructs numbers that do not produce the described paradox. The rest of the response is accurate and addresses all parts of the question."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 9.6,
      "brief_justification": "The response accurately explains Simpson's Paradox with a valid numerical example, addresses all four questions thoroughly, and provides actionable solutions while maintaining clear structure and depth."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 7.2,
      "brief_justification": "The response correctly identifies Simpson's Paradox and explains the issues with overall survival rates. However, the constructed example for part (1) is incomplete and the final answer (6) is unclear. The explanation for part (1) lacks precise numerical examples matching the given percentages."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 9.4,
      "brief_justification": "The response accurately constructs Simpson's Paradox example, explains the paradox, and provides practical solutions. Minor clarity issues with rounding but overall thorough and actionable."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 7.1,
      "brief_justification": "Part (1) contains incorrect numbers that fail to produce the stated paradox. Other parts correctly address the Simpson's paradox and its implications, but the foundational error reduces overall correctness."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 9.8,
      "brief_justification": "The response accurately constructs numbers demonstrating Simpson's paradox, correctly identifies the paradox's implications, and provides practical solutions. It thoroughly addresses all parts of the question with clear explanations."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 6.3,
      "brief_justification": "The constructed example contradicts the question's paradox setup, leading to incorrect conclusions about hospital comparisons."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 8.25,
      "brief_justification": "The response accurately constructs the paradox, clearly explains which hospital is better, identifies the issue with using overall survival rate, and provides a correct method for comparison. It could delve deeper into the reasons behind the paradox and the implications of the incorrect comparison method."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 9.8,
      "brief_justification": "The response accurately explains the paradox, provides a detailed example, and offers multiple corrective approaches. It's clear, thorough, and highly useful."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 8.05,
      "brief_justification": "The response accurately explains Simpson's Paradox, constructs an example that fits the given percentages, and provides a clear analysis of which hospital is better and how to compare hospitals correctly. The response is thorough, clear, and provides useful insights, but it could be slightly more concise."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 8.6,
      "brief_justification": "The response accurately explains Simpson's Paradox and provides a step-by-step breakdown of the scenario. It could benefit from more specific numbers in the constructed example for better illustration, hence the slight deduction in completeness."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 8.2,
      "brief_justification": "The response accurately constructs the paradox, clearly explains the paradox and why Hospital B is better overall, and highlights the issue with using only overall survival rates. It also provides a useful way to compare hospitals correctly by considering specific surgeries and other factors."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 8.6,
      "brief_justification": "The response accurately explains the paradox, clearly identifies the better hospital, highlights the flaw in using overall survival rates, and provides a corrective approach. The depth could be improved by discussing more potential confounding variables."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 8.05,
      "brief_justification": "The response accurately explains the paradox, clearly outlines the steps to construct the numbers, and provides a thorough analysis. It also highlights the flaw in the insurance company's approach and suggests a more accurate comparison method. However, it could delve deeper into the reasons behind the paradox and the implications of the flawed comparison method."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 8.6,
      "brief_justification": "The response accurately identifies the paradox, explains the issue with using overall survival rate, and provides a correct comparison method. However, some minor assumptions were made to construct the paradox."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 9.6,
      "brief_justification": "The response provides a thorough and insightful analysis of the paradox, explaining the underlying causes and proposing multiple methods for a more accurate comparison of hospital quality."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 8.55,
      "brief_justification": "The response correctly identifies Simpson's Paradox, provides a detailed explanation, and offers a correct solution to the paradox. However, the initial example does not exactly match the given percentages, and the final answer is not directly related to the question."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 9.05,
      "brief_justification": "The response accurately identifies Simpson's Paradox, constructs a clear example, and provides actionable advice for correct comparison, but could benefit from more detailed explanation of weighted averages."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 8.6,
      "brief_justification": "The response accurately identifies the paradox and provides a clear explanation of the issue with the health insurance company's recommendation, but could benefit from a more detailed analysis of the implications of the paradox."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 9.45,
      "brief_justification": "The response thoroughly addresses the paradox, explains the issue with using overall survival rates, and provides a clear solution for correct comparison."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 8.8,
      "brief_justification": "The response accurately identifies the paradox, explains the exact numbers, and provides a clear and insightful analysis of the correct comparison method."
    }
  ],
  "meta": {
    "source": "The Multivac (app.themultivac.com)",
    "methodology": "10x10 blind peer matrix evaluation",
    "criteria": "correctness, completeness, clarity, depth, usefulness",
    "self_judgments": "excluded from rankings",
    "license": "Open data — cite as: The Multivac (2026)"
  }
}