{ "evaluation_id": "EVAL-20260315-055905", "question_id": "EVAL-20260315-055905", "question_text": "A disease affects 1 in 10,000 people. A test is 99% sensitive (true positive rate) and 99.5% specific (true negative rate). A patient tests positive. (1) What is the probability they have the disease? (2) If they test positive twice with independent tests, what is the probability? (3) A doctor says 'You tested positive, so you almost certainly have it.' Critique this reasoning. (4) Design a testing protocol that achieves >95% positive predictive value.", "category": "reasoning", "timestamp": "2026-03-15T05:59:05.503Z", "display_date": "Mar 15, 2026", "winner": { "name": "Gemma 3 27B", "provider": "openrouter", "score": 9.59 }, "avg_score": 8.787, "matrix_size": 65, "models_used": [ { "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": "devstral", "name": "Devstral Small", "provider": "openrouter" }, { "id": "qwen3_32b", "name": "Qwen 3 32B", "provider": "openrouter" }, { "id": "kimi_k25", "name": "Kimi K2.5", "provider": "openrouter" } ], "rankings": { "gemma3_27b": { "display_name": "Gemma 3 27B", "provider": "openrouter", "average_score": 9.59, "score_count": 8, "min_score": 8.8, "max_score": 10, "rank": 1 }, "qwen3_8b": { "display_name": "Qwen 3 8B", "provider": "openrouter", "average_score": 9.53, "score_count": 8, "min_score": 8.8, "max_score": 10, "rank": 2 }, "phi4": { "display_name": "Phi-4 14B", "provider": "openrouter", "average_score": 9.05, "score_count": 8, "min_score": 8.25, "max_score": 9.8, "rank": 3 }, "devstral": { "display_name": "Devstral Small", "provider": "openrouter", "average_score": 9.02, "score_count": 7, "min_score": 7.85, "max_score": 10, "rank": 4 }, "granite_40": { "display_name": "Granite 4.0 Micro", "provider": "openrouter", "average_score": 8.94, "score_count": 8, "min_score": 7.4, "max_score": 10, "rank": 5 }, "llama4_scout": { "display_name": "Llama 4 Scout", "provider": "openrouter", "average_score": 8.73, "score_count": 8, "min_score": 8.05, "max_score": 9.25, "rank": 6 }, "mistral_nemo": { "display_name": "Mistral Nemo 12B", "provider": "openrouter", "average_score": 8.61, "score_count": 8, "min_score": 7.4, "max_score": 9.45, "rank": 7 }, "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": 8 }, "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": 9 }, "llama31_8b": { "display_name": "Llama 3.1 8B", "provider": "openrouter", "average_score": 7.91, "score_count": 8, "min_score": 6.65, "max_score": 9.6, "rank": 10 } }, "judgments": [ { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 10, "brief_justification": "The response correctly applies Bayes' Theorem to all questions, provides clear step-by-step calculations, thoroughly critiques the doctor's reasoning, and offers actionable protocol designs. It balances mathematical rigor with intuitive explanations and addresses all parts comprehensively." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 8.45, "brief_justification": "The response correctly applies Bayes' theorem to calculate the probabilities, properly critiques the doctor's reasoning, and proposes a reasonable testing protocol. The calculations are accurate and the explanations are clear, though it could have provided more detailed calculations for the final part to fully demonstrate the solution." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 9, "brief_justification": "The response correctly applies Bayes' theorem for all parts, with accurate calculations for (1) and (2). The critique in (3) is insightful, and the protocol in (4) is logically sound though the example calculation for a 99.9% specific test contains a minor arithmetic error. Overall, the explanation is clear, structured, and actionable." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 7.75, "brief_justification": "The response correctly applies Bayes' theorem in (1) and (4), but part (2) incorrectly assumes independence without updating the prior. The critique in (3) is accurate, and the protocol in (4) is actionable but lacks explicit mention of sequential testing strategies." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "qwen3_8b", "respondent_name": "Qwen 3 8B", "weighted_score": 10, "brief_justification": "The response is mathematically correct, thoroughly addresses all four parts of the question, uses clear explanations and formulas, provides insightful analysis (e.g., base rate fallacy), and offers a practical solution for achieving high PPV." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "mistral_nemo", "respondent_name": "Mistral Nemo 12B", "weighted_score": 7.55, "brief_justification": "The response correctly applies Bayes' theorem for (1) and (3), but part (2)'s calculation is flawed (it computes P(B and B) instead of updating the posterior probability after two tests). The protocol in (4) is valid but the calculation is incomplete and contains errors. Clarity and structure are strong, but depth and completeness are limited by these inaccuracies." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 7.6, "brief_justification": "The response correctly applies Bayes' theorem for the first question and critiques the doctor's reasoning well. However, the calculation for two positive tests is incomplete and somewhat hand-wavy, and the testing protocol suggestion is reasonable but lacks specific implementation details." }, { "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 comprehensive understanding of the medical testing scenario and its implications." }, { "judge_key": "devstral", "judge_name": "Devstral Small", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 8.05, "brief_justification": "The response provides a thorough and mostly accurate explanation of the problem, but the final answer is not clearly stated for all parts." }, { "judge_key": "devstral", "judge_name": "Devstral Small", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 9.8, "brief_justification": "The response accurately applies Bayes' theorem to calculate probabilities and provides a thorough critique of the doctor's reasoning. It also suggests a protocol to achieve >95% positive predictive value." }, { "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 is factually accurate, logically valid, and thoroughly covers all aspects of the question. It is well-structured and provides insightful analysis, with practical value and actionability." }, { "judge_key": "devstral", "judge_name": "Devstral Small", "respondent_key": "qwen3_8b", "respondent_name": "Qwen 3 8B", "weighted_score": 9.8, "brief_justification": "The response is mathematically accurate, thoroughly covers all aspects of the question, is well-structured and clear, provides deep insight into the statistical reasoning, and offers practical advice for designing a testing protocol." }, { "judge_key": "devstral", "judge_name": "Devstral Small", "respondent_key": "mistral_nemo", "respondent_name": "Mistral Nemo 12B", "weighted_score": 8.6, "brief_justification": "The response is mostly correct and thorough, with clear explanations and useful insights. Minor improvements could be made in clarity and depth." }, { "judge_key": "devstral", "judge_name": "Devstral Small", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 6.65, "brief_justification": "The response provides a detailed step-by-step calculation of the positive predictive value (PPV) and addresses the critique of the doctor's reasoning. However, it lacks a clear and concise final answer for the probability of having the disease after testing positive twice, and the explanation could be more structured and concise." }, { "judge_key": "gemma3_27b", "judge_name": "Gemma 3 27B", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 8.25, "brief_justification": "The response accurately applies Bayes' theorem and correctly identifies the base rate fallacy. While the explanation is clear and well-structured, the discussion of improving PPV could be more nuanced, exploring repeat testing strategies in more detail beyond just targeting high-risk groups." }, { "judge_key": "gemma3_27b", "judge_name": "Gemma 3 27B", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 9.25, "brief_justification": "The response accurately calculates the probabilities using Bayes' theorem and provides a clear critique of the doctor's reasoning. The suggested testing protocol is reasonable, though lacks specific calculations to *prove* >95% PPV. " }, { "judge_key": "gemma3_27b", "judge_name": "Gemma 3 27B", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 8.25, "brief_justification": "The response correctly applies Bayes' Theorem and provides accurate calculations for parts 1 & 2. The critique of the doctor's reasoning is sound. The protocol design is a good starting point but the calculations for the improved PPV are flawed and don't reach the 95% target, and the explanation lacks sufficient detail on how to *guarantee* >95% PPV." }, { "judge_key": "gemma3_27b", "judge_name": "Gemma 3 27B", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 9.25, "brief_justification": "The response correctly applies Bayes' Theorem and accurately calculates the probabilities. It identifies the flaw in the doctor's reasoning and offers reasonable strategies for improving the positive predictive value, though more specific protocol details could be added." }, { "judge_key": "gemma3_27b", "judge_name": "Gemma 3 27B", "respondent_key": "qwen3_8b", "respondent_name": "Qwen 3 8B", "weighted_score": 9.8, "brief_justification": "The response is entirely correct, thoroughly explains the calculations, and clearly addresses each part of the question. The explanation of the base rate fallacy is excellent, and the proposed testing protocol is well-justified and accurate. The depth is slightly less than perfect as it doesn't explore alternative protocol designs." }, { "judge_key": "gemma3_27b", "judge_name": "Gemma 3 27B", "respondent_key": "mistral_nemo", "respondent_name": "Mistral Nemo 12B", "weighted_score": 8.8, "brief_justification": "The response accurately applies Bayes' Theorem and addresses all parts of the question with clear explanations. The discussion of the base rate fallacy and the proposed testing protocol are well-reasoned, though the sensitivity/specificity trade-off could be emphasized more." }, { "judge_key": "gemma3_27b", "judge_name": "Gemma 3 27B", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 6.85, "brief_justification": "The response correctly calculates the PPV for one test and identifies the issue with the doctor's reasoning. However, the explanation for the two-test scenario is convoluted and relies on several approximations that aren't fully justified, and the protocol design is vague." }, { "judge_key": "llama4_scout", "judge_name": "Llama 4 Scout", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 9.8, "brief_justification": "The response accurately applies Bayes' theorem and provides a thorough analysis of the problem, including critiques of flawed reasoning and a clear design for an improved testing protocol." }, { "judge_key": "llama4_scout", "judge_name": "Llama 4 Scout", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 9.8, "brief_justification": "The response accurately applies Bayes' Theorem to solve the problem, provides thorough explanations, and offers clear insights into the implications of test results in a low-prevalence disease scenario. The critique of the doctor's reasoning and the design of a testing protocol to achieve >95% PPV are particularly useful." }, { "judge_key": "llama4_scout", "judge_name": "Llama 4 Scout", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 9.8, "brief_justification": "The response accurately solves the problem using Bayes' theorem, provides thorough calculations, and offers a clear critique of the doctor's statement and a method to achieve >95% positive predictive value." }, { "judge_key": "llama4_scout", "judge_name": "Llama 4 Scout", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 9.45, "brief_justification": "The response accurately applies Bayes' theorem and provides a thorough analysis of the problem. The critique of the doctor's reasoning and the design of a testing protocol to achieve >95% positive predictive value demonstrate depth and usefulness." }, { "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 answers all parts of the question, providing thorough calculations and explanations. The critique of the doctor's reasoning and the design of a testing protocol to achieve >95% PPV are particularly insightful and useful." }, { "judge_key": "llama4_scout", "judge_name": "Llama 4 Scout", "respondent_key": "mistral_nemo", "respondent_name": "Mistral Nemo 12B", "weighted_score": 9.45, "brief_justification": "The response accurately applies Bayes' theorem and provides a thorough analysis of the problem. The critique of the doctor's reasoning and the proposed testing protocol are insightful and practical." }, { "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 thorough calculation of the probability of having the disease given a positive test result and critiques the doctor's reasoning effectively. However, some steps could be clarified, and the response could benefit from a more concise summary of the testing protocol design." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 10, "brief_justification": "The response accurately applies Bayes' theorem to calculate probabilities, provides a clear critique of the doctor's reasoning, and effectively designs a testing protocol to achieve the desired positive predictive value. The explanation is thorough, logically sound, and practically useful." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 10, "brief_justification": "The response accurately applies Bayes' Theorem to calculate probabilities, thoroughly covers each part of the question, and provides clear, well-structured explanations. It includes insightful analysis of the implications of test results and offers practical strategies for improving positive predictive value." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 8.9, "brief_justification": "The response accurately applies Bayes' theorem to calculate probabilities, clearly explains the steps, and critiques the doctor's reasoning effectively. It also provides a thoughtful approach to designing a testing protocol, though more detail on the protocol's implementation could enhance completeness and usefulness." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 10, "brief_justification": "The response correctly applies Bayes' theorem to calculate the probability of having the disease given a positive test result, accurately critiques the doctor's reasoning, and provides a practical protocol to achieve a positive predictive value greater than 95%." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "qwen3_8b", "respondent_name": "Qwen 3 8B", "weighted_score": 10, "brief_justification": "The response accurately applies Bayes' Theorem to calculate the probability of having the disease given a positive test result, considering the low prevalence and high sensitivity/specificity of the test. It critiques the doctor's reasoning by highlighting the base rate fallacy and suggests a protocol involving multiple independent tests to achieve a PPV greater than 95%." }, { "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 applies Bayes' theorem and provides a clear explanation of the calculations. It thoroughly addresses each part of the question, including the critique of the doctor's reasoning and the design of a testing protocol. The explanation is clear and well-structured, though the depth could be enhanced with a more detailed discussion of the trade-offs in the testing protocol." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 9.6, "brief_justification": "The response accurately calculates the probability of having the disease after a positive test using Bayes' theorem and critiques the doctor's reasoning effectively. It also provides a clear protocol for achieving a higher positive predictive value, demonstrating practical application and depth in understanding diagnostic testing." }, { "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 provides accurate calculations for conditional probability, addresses multiple parts of the question, critiques the doctor's reasoning, and suggests a protocol to improve predictive value, though the depth could be enhanced with more discussion on Bayesian updating and protocol specifics." }, { "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 correctly applies Bayes' theorem to calculate probabilities, covers all requested scenarios, communicates clearly with appropriate formulas, provides insightful critique of the doctor's reasoning, and suggests a protocol to improve predictive value, though the depth could be slightly higher by discussing potential limitations and trade-offs." }, { "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 applies Bayes' theorem, provides clear calculations, critiques the doctor's reasoning well, and proposes a practical testing protocol to achieve the desired PPV, with only minor depth limitations in the final section." }, { "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 applies Bayes' Theorem, provides clear calculations, critiques the doctor's reasoning, and proposes effective testing protocols, demonstrating strong overall performance with minor room for improvement in depth." }, { "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 applies Bayes' theorem, calculates probabilities for single and repeated positive tests, critiques the doctor's reasoning, and proposes a protocol for high positive predictive value, 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 applies Bayes' theorem, provides clear calculations, and offers insightful critiques and suggestions for improving testing protocols, though it could delve deeper into alternative testing strategies for achieving higher predictive values." }, { "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 applies Bayes' theorem, calculates probabilities for single and multiple tests, critiques the doctor's reasoning, and proposes a protocol achieving >95% PPV, with minor minor depth limitation in the critique." }, { "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 applies Bayes' theorem, provides clear calculations, critiques the doctor's reasoning, and proposes a protocol to achieve high positive predictive value, though with lower sensitivity. It is well-structured and valuable for understanding the probabilistic aspects of disease testing." }, { "judge_key": "granite_40", "judge_name": "Granite 4.0 Micro", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 8.2, "brief_justification": "The response accurately calculates probabilities, critiques reasoning, and proposes a protocol to improve predictive value, though some steps could be more detailed for deeper insight." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 7.85, "brief_justification": "Correctness is lower due to an error in calculating the probability after two tests. The rest of the answers are accurate and well-explained." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 9.45, "brief_justification": "Accurately applies Bayes' Theorem to all parts, thoroughly explains concepts, and provides actionable testing strategies while addressing cognitive biases." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 9.25, "brief_justification": "Correctly applies Bayes' theorem for parts 1-3, provides actionable protocol suggestions, but part 4's example lacks detailed calculation to demonstrate >95% PPV." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 8.8, "brief_justification": "The response correctly applies Bayes' theorem and critiques the doctor's reasoning. It provides a structured protocol for part (4) but the example calculation doesn't fully achieve the 95% PPV target, requiring further adjustments." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 7.4, "brief_justification": "Correctly applies Bayes' theorem for (1) and critiques the doctor's reasoning (3), but incorrectly states probability remains same for (2) and provides flawed examples in (4)." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "mistral_nemo", "respondent_name": "Mistral Nemo 12B", "weighted_score": 7.4, "brief_justification": "The response correctly applies Bayes' theorem for parts (1) and (3), but part (2) incorrectly calculates the probability of two positive tests by squaring the single-test probability instead of using joint probability. Part (4)'s protocol calculation is approximate and lacks precise derivation, reducing overall correctness and usefulness." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 7.5, "brief_justification": "The response correctly calculates the initial PPV (1.98%) and critiques the doctor's reasoning. However, the second test probability calculation is incomplete and lacks precise Bayesian updating. The protocol suggestions are vague and could benefit from specific numerical thresholds." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 9.65, "brief_justification": "The response accurately calculates probabilities using Bayes' theorem, provides a thorough explanation, and offers practical solutions. It's well-structured but could be slightly more concise." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 9.05, "brief_justification": "The response accurately applies Bayes' Theorem to calculate probabilities, discusses the implications, critiques the doctor's reasoning, and provides practical solutions to achieve a high positive predictive value. It is thorough, insightful, and provides actionable steps. The only minor deduction is for not providing an exact calculation for the third part of the question, but it still offers a clear explanation of the concept." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 8.3, "brief_justification": "The response accurately calculates probabilities using Bayes' theorem and critiques the doctor's reasoning. It also suggests a testing protocol to improve positive predictive value. However, it lacks a final, concise summary of the protocol's details." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 8.85, "brief_justification": "The response accurately calculates probabilities using Bayes' theorem, covers all aspects of the question, explains concepts clearly, provides in-depth analysis, and offers practical suggestions for improving the testing protocol. The usefulness score is slightly lower because the suggested protocol might require further refinement to achieve the desired positive predictive value." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 8.65, "brief_justification": "The response accurately calculates the probabilities and explains the reasoning behind each step. It also provides a thorough critique of the doctor's reasoning and offers a practical solution to improve the testing protocol. However, it could have provided more insight into the trade-offs and limitations of the proposed solutions." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "qwen3_8b", "respondent_name": "Qwen 3 8B", "weighted_score": 9.2, "brief_justification": "The response demonstrates excellent understanding and application of Bayes' theorem, providing detailed calculations and clear explanations. It also addresses the doctor's flawed reasoning and proposes an effective testing protocol. The only minor deduction is that the language could be slightly simplified for better clarity." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 8.65, "brief_justification": "The response accurately calculates probabilities and critically evaluates the doctor's reasoning. It also provides a practical solution for improving the testing protocol. However, some steps could be simplified for clarity." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 8.8, "brief_justification": "The response accurately applies Bayes' theorem, identifies the base rate fallacy, and designs a testing protocol with >95% positive predictive value. However, some calculations could be simplified and the explanation of the base rate fallacy could be more concise." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 9.8, "brief_justification": "The response provides a thorough and accurate explanation of Bayes' Theorem and its application to medical testing, including the importance of considering base rates and designing testing protocols to achieve high positive predictive value." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 8.8, "brief_justification": "The response accurately applies Bayes' theorem to calculate the probability of having the disease given a positive test result, and provides a clear critique of the doctor's reasoning. The suggested testing protocol for >95% positive predictive value is also well-reasoned." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 9.1, "brief_justification": "The response accurately applies Bayes' theorem, critiques the doctor's reasoning, and proposes a testing protocol to achieve >95% positive predictive value, but some calculations could be simplified and the usefulness of the protocol could be further explored." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 9.6, "brief_justification": "The response accurately applies Bayes' theorem, critiques the doctor's reasoning, and provides a clear and actionable plan to improve the testing protocol." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "qwen3_8b", "respondent_name": "Qwen 3 8B", "weighted_score": 8.8, "brief_justification": "The response accurately applies Bayes' Theorem and correctly critiques the doctor's reasoning, providing a thorough and insightful analysis." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "mistral_nemo", "respondent_name": "Mistral Nemo 12B", "weighted_score": 9.25, "brief_justification": "The response accurately applies Bayes' theorem, correctly critiques the doctor's reasoning, and designs a testing protocol to achieve high positive predictive value, while also acknowledging the trade-off with sensitivity." } ], "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)" } }