{ "evaluation_id": "EVAL-20260318-162600", "question_id": "EVAL-20260318-162600", "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": "2026-03-18T16:26:00.069Z", "display_date": "Mar 18, 2026", "winner": { "name": "GPT-5.4", "provider": "openrouter", "score": 9.92 }, "avg_score": 9.546667, "matrix_size": 21, "models_used": [ { "id": "minimax_01", "name": "MiniMax-01", "provider": "openrouter" }, { "id": "judge_claude_sonnet", "name": "Claude Sonnet 4.6", "provider": "openrouter" }, { "id": "judge_gpt54", "name": "GPT-5.4", "provider": "openrouter" } ], "rankings": { "judge_gpt54": { "display_name": "GPT-5.4", "provider": "openrouter", "average_score": 9.92, "score_count": 7, "min_score": 9.65, "max_score": 10, "rank": 1 }, "judge_claude_sonnet": { "display_name": "Claude Sonnet 4.6", "provider": "openrouter", "average_score": 9.46, "score_count": 7, "min_score": 7.85, "max_score": 10, "rank": 2 }, "minimax_01": { "display_name": "MiniMax-01", "provider": "openrouter", "average_score": 9.26, "score_count": 7, "min_score": 8.25, "max_score": 10, "rank": 3 } }, "judgments": [ { "judge_key": "minimax_m27", "judge_name": "MiniMax M2.7", "respondent_key": "minimax_01", "respondent_name": "MiniMax-01", "weighted_score": 9.8, "brief_justification": "All four parts are correctly solved with accurate Bayes' theorem calculations, clear step-by-step explanations, and insightful critique of the base rate fallacy. The sequential testing protocol effectively achieves >95% PPV through three independent positive tests (≈99.9% probability)." }, { "judge_key": "minimax_m27", "judge_name": "MiniMax M2.7", "respondent_key": "judge_claude_sonnet", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 10, "brief_justification": "Comprehensive Bayesian analysis with correct calculations, natural frequency visualizations, multiple strategies for achieving >95% PPV, and thorough critique of reasoning fallacies. Exceptionally well-structured with tables, flowcharts, and verification methods." }, { "judge_key": "minimax_m27", "judge_name": "MiniMax M2.7", "respondent_key": "judge_gpt54", "respondent_name": "GPT-5.4", "weighted_score": 10, "brief_justification": "The response is mathematically precise with correct Bayesian calculations throughout, provides thorough coverage including intuitive explanations with the 100,000-person framework, organizes the complex problem clearly with headings and LaTeX, demonstrates deep understanding of base rate fallacies and test characteristics, and delivers practical recommendations for clinical protocols. The multi-part structure comprehensively addresses all aspects of the question with both quantitative rigor and " }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "minimax_01", "respondent_name": "MiniMax-01", "weighted_score": 10, "brief_justification": "The response provides mathematically correct Bayesian calculations for all four parts, clearly explains the base rate fallacy in the doctor's reasoning, and designs a sequential testing protocol that achieves >95% PPV (99.9% with three positive tests). The explanation is well-structured with clear notation and step-by-step derivations." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "judge_claude_sonnet", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 9.8, "brief_justification": "Excellent Bayesian analysis with correct calculations, intuitive natural frequency explanations, comprehensive critique of the doctor's reasoning covering multiple fallacies, and a well-designed sequential testing protocol achieving 99.87% PPV. Slight deduction for incomplete ending in Part 4." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "judge_gpt54", "respondent_name": "GPT-5.4", "weighted_score": 10, "brief_justification": "Excellent response with correct Bayesian calculations, thorough coverage of all four parts, clear mathematical exposition with intuitive 100,000-person example, insightful critique of base rate neglect, and practical testing protocol design achieving >95% PPV." }, { "judge_key": "minimax_m21", "judge_name": "MiniMax M2.1", "respondent_key": "minimax_01", "respondent_name": "MiniMax-01", "weighted_score": 10, "brief_justification": "The response correctly applies Bayes' theorem with accurate calculations (1.94% for single test, 79.6% for two tests), provides a insightful critique of the doctor's base rate neglect, and designs an effective sequential testing protocol achieving >95% PPV with three tests (99.9%). The explanation is clear, well-structured, and demonstrates thorough understanding of conditional probability and its practical implications in medical testing." }, { "judge_key": "minimax_m21", "judge_name": "MiniMax M2.1", "respondent_key": "judge_claude_sonnet", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 9.25, "brief_justification": "Accurate Bayesian calculations with excellent natural frequency visualizations. Comprehensive critique of reasoning fallacies. Part 4 is incomplete (Strategy B calculation is cut off mid-equation and Strategy C is missing)." }, { "judge_key": "minimax_m21", "judge_name": "MiniMax M2.1", "respondent_key": "judge_gpt54", "respondent_name": "GPT-5.4", "weighted_score": 10, "brief_justification": "The response is exemplary: all Bayes theorem calculations are correct, it provides excellent intuition with the 100,000 person example, thoroughly critiques the base rate fallacy, and designs a practical protocol achieving >95% PPV with three independent tests (99.87%). The structure is clear with proper mathematical notation throughout." }, { "judge_key": "minimax_m2", "judge_name": "MiniMax M2", "respondent_key": "minimax_01", "respondent_name": "MiniMax-01", "weighted_score": 9.45, "brief_justification": "All calculations are mathematically correct using Bayes' theorem. The response thoroughly covers all four parts with clear explanations, proper notation, and insightful critique of base rate neglect. The sequential testing protocol effectively achieves >95% PPV." }, { "judge_key": "minimax_m2", "judge_name": "MiniMax M2", "respondent_key": "judge_claude_sonnet", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 9.35, "brief_justification": "Excellent Bayesian analysis with correct calculations (1.94% and 79.7%), comprehensive critique of reasoning fallacies, and practical protocol design. Minor deduction for incomplete response (truncated calculation in risk stratification section)." }, { "judge_key": "minimax_m2", "judge_name": "MiniMax M2", "respondent_key": "judge_gpt54", "respondent_name": "GPT-5.4", "weighted_score": 10, "brief_justification": "The response provides mathematically correct Bayesian calculations for all parts of the question, includes excellent intuitive explanations (the 100,000 person example), thoroughly critiques the base rate fallacy, and offers a practical testing protocol. The structure is clear with proper notation and step-by-step reasoning." }, { "judge_key": "minimax_m1", "judge_name": "MiniMax M1", "respondent_key": "minimax_01", "respondent_name": "MiniMax-01", "weighted_score": 9.05, "brief_justification": "All calculations are mathematically correct, the critique properly identifies the base rate fallacy, and the sequential testing protocol achieves >95% PPV. Minor deduction for completeness as alternative approaches (e.g., using a higher-specificity test) could have been mentioned." }, { "judge_key": "minimax_m1", "judge_name": "MiniMax M1", "respondent_key": "judge_claude_sonnet", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 10, "brief_justification": "Exceptional response with mathematically correct Bayesian calculations, clear natural frequency explanations, thorough critique of five distinct reasoning failures, and a practical multi-strategy protocol achieving 99.87% PPV with three sequential tests." }, { "judge_key": "minimax_m1", "judge_name": "MiniMax M1", "respondent_key": "judge_gpt54", "respondent_name": "GPT-5.4", "weighted_score": 10, "brief_justification": "Comprehensive and mathematically accurate response that correctly applies Bayes' theorem, provides clear intuition, properly critiques the base rate fallacy, and designs a practical protocol achieving >95% PPV through requiring three independent positive tests." }, { "judge_key": "minimax_01", "judge_name": "MiniMax-01", "respondent_key": "judge_claude_sonnet", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 10, "brief_justification": "The response demonstrates exceptional accuracy, thoroughness, clarity, and depth in addressing all parts of the question, including the mathematical reasoning, critique of the doctor's reasoning, and practical protocol design. It is highly useful for understanding the problem and implementing solutions." }, { "judge_key": "minimax_01", "judge_name": "MiniMax-01", "respondent_key": "judge_gpt54", "respondent_name": "GPT-5.4", "weighted_score": 9.65, "brief_justification": "The response is factually accurate, thoroughly explains all aspects of the problem, and provides clear reasoning with high depth of analysis. The explanation is mostly clear, though the mathematical formatting could be slightly more polished for readability." }, { "judge_key": "judge_claude_sonnet", "judge_name": "Claude Sonnet 4.6", "respondent_key": "minimax_01", "respondent_name": "MiniMax-01", "weighted_score": 8.25, "brief_justification": "The mathematical calculations are accurate and well-presented, correctly applying Bayes' theorem for all three probability scenarios. The critique of the doctor's reasoning is valid but could be deeper (e.g., discussing base rate neglect as a cognitive bias, or mentioning that the doctor should update priors based on clinical presentation). The testing protocol section correctly shows three tests achieve >95% PPV, but doesn't explore alternative approaches like pre-test probability adjustment, c" }, { "judge_key": "judge_claude_sonnet", "judge_name": "Claude Sonnet 4.6", "respondent_key": "judge_gpt54", "respondent_name": "GPT-5.4", "weighted_score": 9.8, "brief_justification": "The response is mathematically rigorous and correct throughout all four parts, with clear Bayesian calculations, excellent intuitive explanations (the 100,000 people example), a well-articulated critique of the base-rate fallacy, and a practical protocol design. The depth is excellent, though it could have briefly mentioned alternative approaches like using a more specific confirmatory test rather than just repeating the same test." }, { "judge_key": "judge_gpt54", "judge_name": "GPT-5.4", "respondent_key": "minimax_01", "respondent_name": "MiniMax-01", "weighted_score": 8.25, "brief_justification": "The response correctly applies Bayes’ theorem and gets the key numerical results essentially right: about 1.94% after one positive, about 79.6% after two independent positives, and >95% after three. Its main weakness is that the testing protocol discussion is somewhat simplistic and assumes independence/identical tests without noting practical concerns like confirmatory tests with different error structures or targeted screening." }, { "judge_key": "judge_gpt54", "judge_name": "GPT-5.4", "respondent_key": "judge_claude_sonnet", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 7.85, "brief_justification": "The response correctly computes the single-test PPV (~1.94%) and two independent positives (~79.7%), and gives a strong critique of base-rate neglect. However, it contains a notable error in stating specificity as P(+|No Disease)=0.995 before correcting to 0.005, and Part 4 is incomplete/truncated, though the three-positive-test idea would indeed exceed 95% PPV under independence." } ], "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)" } }