{ "evaluation_id": "EVAL-20260402-165004", "question_id": "REASON-016", "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": "2026-04-02T16:50:04.172Z", "display_date": "Apr 02, 2026", "winner": { "name": "Claude Sonnet 4.6", "provider": "openrouter", "score": 9.44 }, "avg_score": 5.955, "matrix_size": 70, "models_used": [ { "id": "deepseek_v4", "name": "DeepSeek V4", "provider": "openrouter" }, { "id": "claude_opus_46", "name": "Claude Opus 4.6", "provider": "openrouter" }, { "id": "gpt_5_4", "name": "GPT-5.4", "provider": "openrouter" }, { "id": "grok_420", "name": "Grok 4.20", "provider": "openrouter" }, { "id": "claude_sonnet_46", "name": "Claude Sonnet 4.6", "provider": "openrouter" }, { "id": "mimo_v2_flash", "name": "MiMo-V2-Flash", "provider": "Xiaomi" }, { "id": "gemini_25_flash", "name": "Gemini 2.5 Flash", "provider": "openrouter" }, { "id": "gemini_31_pro", "name": "Gemini 3.1 Pro", "provider": "openrouter" } ], "rankings": { "claude_sonnet_46": { "display_name": "Claude Sonnet 4.6", "provider": "openrouter", "average_score": 9.44, "score_count": 8, "min_score": 8.45, "max_score": 10, "rank": 1 }, "gpt_5_4": { "display_name": "GPT-5.4", "provider": "openrouter", "average_score": 9.16, "score_count": 9, "min_score": 8.55, "max_score": 10, "rank": 2 }, "claude_opus_46": { "display_name": "Claude Opus 4.6", "provider": "openrouter", "average_score": 8.34, "score_count": 9, "min_score": 5.9, "max_score": 10, "rank": 3 }, "gemini_25_flash": { "display_name": "Gemini 2.5 Flash", "provider": "openrouter", "average_score": 4.83, "score_count": 9, "min_score": 2.85, "max_score": 7.3, "rank": 4 }, "deepseek_v4": { "display_name": "DeepSeek V4", "provider": "openrouter", "average_score": 4.82, "score_count": 9, "min_score": 2.65, "max_score": 7.4, "rank": 5 }, "mimo_v2_flash": { "display_name": "MiMo-V2-Flash", "provider": "Xiaomi", "average_score": 4.74, "score_count": 9, "min_score": 2.45, "max_score": 7.2, "rank": 6 }, "gemini_31_pro": { "display_name": "Gemini 3.1 Pro", "provider": "openrouter", "average_score": 3.99, "score_count": 8, "min_score": 2.05, "max_score": 5.85, "rank": 7 }, "grok_420": { "display_name": "Grok 4.20", "provider": "openrouter", "average_score": 2.32, "score_count": 9, "min_score": 0.2, "max_score": 5, "rank": 8 } }, "judgments": [ { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 5.15, "brief_justification": "" }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 5.9, "brief_justification": "" }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 10, "brief_justification": "The model brilliantly identifies a mathematical impossibility in the prompt's constraints, provides a valid corrected alternative, and excellently answers all parts of the question with exceptional clarity and depth." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 0.2, "brief_justification": "The model failed to recognize that the requested overall percentages are mathematically impossible (a weighted average of 90% and 95% cannot be 89%). It got stuck in a loop of failed calculations, ignored the other three questions, and cut off mid-sentence." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 9, "brief_justification": "" }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 2.45, "brief_justification": "" }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 5.1, "brief_justification": "The model correctly identified that the provided numbers for Hospital A are mathematically impossible. However, the response cuts off abruptly in the middle of part 1 and completely fails to answer parts 2, 3, and 4." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 5.85, "brief_justification": "The response identifies Simpson’s Paradox but fails to construct exact numbers or fully answer the questions. Clarity is decent, but completeness and usefulness are lacking." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 9.8, "brief_justification": "The response accurately constructs the paradox, correctly identifies the better hospital, explains the insurance company's error, and provides a thorough method for correct comparison. It is insightful and actionable." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9.2, "brief_justification": "Accurate, thorough, and insightful with clear practical implications." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 5, "brief_justification": "Struggles to provide exact matching numbers, lacks clarity in presentation, and fails to fully resolve the paradox." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 9.65, "brief_justification": "Highly accurate, thorough, and insightful with clear practical implications." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 7.2, "brief_justification": "Detailed and correct but overly complex and unclear at times." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 6.95, "brief_justification": "Correctly identifies Simpson's Paradox but struggles with constructing exact numbers due to an inconsistency in the problem statement. Provides insightful analysis and clear communication." }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 2.1, "brief_justification": "The response is cut off almost immediately after beginning. It correctly identifies Simpson's Paradox and starts to note a mathematical constraint, but it fails to answer any of the four parts of the question. No numbers are constructed, no analysis of which hospital is better, no discussion of insurance company implications, and no correct comparison methodology is provided. The response is essentially incomplete/truncated." }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 2.65, "brief_justification": "The response fails to construct valid exact numbers for part (1), gets stuck in algebraic errors and never resolves them. It correctly identifies Simpson's Paradox but then discovers the given overall rates (89% and 91%) are impossible when both category rates exceed 89%, yet doesn't clearly state this or offer corrected numbers. Parts (2), (3), and (4) are either incomplete or missing entirely — the response cuts off mid-sentence. The algebraic work is messy and confusing, and the answer provid" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9.2, "brief_justification": "The response demonstrates exceptional understanding of Simpson's paradox. It correctly identifies that the original question's numbers are internally inconsistent (A's overall rate cannot be 89% if subgroup rates are 90% and 95%), which shows deep mathematical rigor. It then constructs a valid corrected example with exact numbers that produce the paradox. All four parts are thoroughly addressed: the numerical construction, the determination that Hospital A is better within each category, the exp" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 1.05, "brief_justification": "The response is a chaotic mess of failed attempts to construct numbers for Simpson's Paradox. The model never successfully produces a valid example where Hospital A beats Hospital B in both categories but B wins overall - it repeatedly fails and acknowledges failure without ever arriving at a correct answer. Parts (2), (3), and (4) of the question are never answered at all. The response demonstrates a fundamental inability to solve the arithmetic problem and presents an extremely confusing, unst" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 9.8, "brief_justification": "The response is exemplary across all dimensions. The constructed numbers are verified and correct, producing the paradox as required. The explanation of which hospital is better is precise and well-justified using conditional probability notation. The insurance company analysis goes beyond surface-level to identify perverse incentives and adverse selection consequences. The standardization method is correctly applied with concrete calculations. The only minor note is that the depth could go slig" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 3.25, "brief_justification": "The response correctly identifies Simpson's Paradox and understands the conceptual mechanism (Hospital A doing more risky surgeries), but fails badly at the core task of constructing exact numbers that match the stated paradox (A: 89%, B: 91%). The multiple failed attempts shown in the response are messy and confusing, and the final numbers don't match the prompt's targets. The response is also clearly cut off mid-sentence in parts (3) and entirely missing part (4). Parts (2) and the beginning o" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 2.85, "brief_justification": "The response correctly identifies Simpson's Paradox and understands the mechanism (different proportions of surgery types). However, it critically fails to notice that the given numbers are mathematically impossible - an overall rate of 89% cannot result from mixing 90% and 95% rates. While the response eventually discovers this impossibility, it never completes the construction with corrected numbers, and parts (2), (3), and (4) are never answered. The response is incomplete, cut off mid-calcul" }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 2.05, "brief_justification": "The response correctly identifies Simpson’s Paradox and notices a potential inconsistency, but it is incomplete and does not answer the requested parts. It provides no constructed numbers, no conclusion about comparison, and no practical guidance on the insurance-company error or the correct method." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 4.35, "brief_justification": "The response correctly identifies Simpson's paradox and notices a key inconsistency: A's overall rate cannot be 89% if only heart (90%) and knee (95%) surgeries are included. However, it fails to give a valid exact construction, leaves parts (3) and (4) incomplete, and does not cleanly resolve the implications of the inconsistency. Writing is reasonably clear but the answer is ultimately not very actionable." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 6.3, "brief_justification": "Well-structured and covers all parts, but the constructed numbers do not actually produce the stated overall rates: A's example gives 94.5%, not about 89%, so the paradox is not correctly instantiated. The later explanation also contains confusion about the case mix mechanism. Still, the discussion of stratification and standardized comparisons is generally clear and useful." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 1.6, "brief_justification": "The response repeatedly fails to construct valid numbers, contains contradictions and unfinished calculations, and never properly answers parts (2)-(4). It identifies Simpson's paradox in spirit but is largely incorrect and not useful." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 4, "brief_justification": "The response identifies Simpson’s paradox and the confounding role of surgery type, but it repeatedly fails to construct valid exact numbers matching the prompt, includes impossible fractional survivors and inconsistent tables, and is cut off before fully answering parts (3) and (4)." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 4.05, "brief_justification": "The response correctly notices that the stated numbers are internally inconsistent because Hospital A’s overall rate cannot be below both of its subgroup rates. However, it fails to complete the construction, does not answer parts (2)-(4), and ends abruptly. Clarity is decent up to the cutoff, but the answer is incomplete and not very useful overall." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 5.85, "brief_justification": "The response correctly identifies Simpson's Paradox but is incomplete as it stops mid-sentence without providing the required numbers, analysis of which hospital is better, or recommendations. It correctly notes the weighted average issue but fails to fully address all four parts of the query." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 5, "brief_justification": "The response correctly identifies Simpson's paradox and explains the weighting issue, but fails to provide exact integer numbers satisfying the given rates (shows math error leading to impossibility) and leaves overall rates mismatched. It gives partial answers to (2)-(4) but is incomplete and contains calculation contradictions." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 8.6, "brief_justification": "The response accurately constructs numbers illustrating Simpson's paradox, correctly identifies Hospital A as better, explains the insurance flaw due to confounding, and provides proper stratified/standardized comparison methods with clear tables and causal insights." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 8.8, "brief_justification": "Response accurately identifies inconsistency in given numbers, provides valid corrected example of Simpson's paradox, correctly explains causes and proper comparison methods with clear structure and practical advice." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 8.85, "brief_justification": "The response accurately constructs numbers illustrating Simpson's paradox (with minor rounding in totals), correctly identifies Hospital A as superior per subgroup, explains the confounding issue rigorously with formulas, and provides actionable standardization methods. Slight deduction for not exactly matching the query's given percentages while still demonstrating the paradox effectively." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 4.4, "brief_justification": "The response attempts to explain Simpson's paradox but fails to provide exact integer numbers matching the given rates (90%, 85%, 95%, 92%, 89%, 91%). Multiple inconsistent tables and calculations are presented with errors (e.g., wrong percentages, non-integer survivors). Parts 2-4 are partially addressed but incomplete due to the flawed data." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 5.2, "brief_justification": "Identifies Simpson's paradox and the weighting issue correctly but fails to construct valid exact numbers due to impossible given rates (overall cannot be below the minimum subgroup rate). Provides partial explanation and adjustment but does not fully answer all parts (2-4) or give correct numbers." }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 3.8, "brief_justification": "The response correctly identifies Simpson's Paradox and begins to address a mathematical constraint, but it is severely incomplete - it cuts off mid-sentence and fails to answer any of the four questions asked. No numbers are constructed, no recommendation about which hospital is better, no analysis of the insurance company problem, and no correct comparison methodology is provided." }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 4.05, "brief_justification": "The response correctly identifies Simpson's Paradox and attempts to construct numbers, but critically fails to produce valid exact numbers satisfying the given constraints. The mathematical analysis even shows the given numbers are inconsistent (getting negative values) without resolving this properly. The response cuts off mid-sentence and never completes questions 3 and 4. The attempt is earnest but the execution is poor - the core task of constructing exact numbers is not achieved, and the re" }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 9.55, "brief_justification": "Excellent response that constructs exact numbers correctly, clearly explains the paradox mechanism, gives sound reasoning about which hospital is better, identifies specific harms from the insurance company's approach, and provides actionable correct methodology including standardization. Minor self-correction mid-explanation is slightly awkward but the final conclusions are all correct. Covers all four parts thoroughly with practical depth." }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 8.55, "brief_justification": "The response correctly identifies the mathematical inconsistency in the original problem (A's overall rate cannot be below 90% if subgroup rates are 90% and 95%), which shows strong analytical rigor. It then constructs a valid numerical example demonstrating Simpson's paradox, clearly explains which hospital is better and why, identifies the confounding issue with the insurer's approach, and provides multiple correct methods for proper comparison including standardization and risk-adjustment. Th" }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 2.25, "brief_justification": "The response is a chaotic, disorganized stream of failed attempts to construct the numbers, never successfully completing part (1) or addressing parts (2), (3), and (4) at all. The model repeatedly tries and abandons approaches, showing it cannot solve the basic algebra. The response is extremely unclear, cuts off mid-sentence, and provides essentially no practical value. A correct solution requires Hospital A to do mostly hard (heart) surgeries and Hospital B to do mostly easy (knee) surgeries," }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 5.4, "brief_justification": "The response correctly identifies Simpson's Paradox and provides good conceptual explanations for parts 2-4. However, part 1 is severely flawed: the model repeatedly fails to construct exact numbers matching the stated targets (A: 89%, B: 91% overall), going through multiple failed attempts with contradictory results, and never produces a clean, correct numerical example. The response also appears truncated, cutting off mid-sentence in part 3. The conceptual understanding is solid but the execut" }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 4.8, "brief_justification": "The response correctly identifies this as Simpson's Paradox and attempts a systematic approach, but critically fails to notice that the given numbers in the problem are mathematically impossible (Hospital A's overall rate of 89% cannot exist when its individual rates are 90% and 95%). While the response eventually identifies this contradiction, it gets lost in lengthy calculations and the response is cut off mid-sentence without completing parts (2), (3), or (4). The response never delivers a co" }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 6.2, "brief_justification": "The response correctly identifies Simpson's Paradox but fails to construct exact integer numbers that satisfy the given percentages (it incorrectly claims it's impossible or struggles to find them). It correctly identifies Hospital A as likely better but the explanation is cut off. The analysis of the insurance company's error and correct comparison method is missing." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 9.35, "brief_justification": "Excellent response. Correctly identifies Simpson's Paradox, constructs valid numbers, and provides clear, actionable advice. Minor deduction in correctness for a momentarily confusing sentence about B's case mix, but the overall explanation is accurate and highly insightful." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9, "brief_justification": "Excellent response. It correctly identifies the mathematical impossibility in the prompt's numbers, provides a valid corrected example, and thoroughly explains the paradox, its cause, and proper methods for comparison. The analysis is deep and highly useful." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 3.4, "brief_justification": "Response is highly confusing, fails to construct correct numbers for the paradox, and provides no clear answers to the questions." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 10, "brief_justification": "Comprehensive and accurate explanation of Simpson's Paradox with exact numbers, correct identification of the better hospital, clear analysis of insurance company error, and actionable correct comparison methods." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 3.8, "brief_justification": "The response fails to construct the exact numbers as requested due to a mathematical error, incorrectly claiming the given rates are impossible. It correctly identifies Simpson's Paradox and explains the concept, but the failure to solve the core numerical task significantly impacts correctness and usefulness." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 3.05, "brief_justification": "The response identifies Simpson's paradox but fails to provide the required numbers and does not answer questions 2-4, making it incomplete and of limited practical value." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 3.65, "brief_justification": "The answer contains factual errors about feasibility, fails to provide concrete numbers, and stops short of answering several sub‑questions, limiting its usefulness." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 6, "brief_justification": "The response is well-structured and covers all requested points with good depth, but the numerical example is incorrect, undermining factual accuracy and practical usefulness." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 8.65, "brief_justification": "Accurately identifies the paradox, corrects the impossible numbers, provides a valid example, explains why the insurer's method fails, and suggests proper comparative methods with clear, well-structured explanations." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 1.25, "brief_justification": "Response is disorganized, fails to present a consistent set of numbers, and does not answer questions 2-4, making it largely incorrect, incomplete, unclear, shallow, and not useful." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 8.45, "brief_justification": "Accurate numbers and reasoning, covers all parts, clear presentation, good analytical depth, and practical guidance for proper comparison." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 4, "brief_justification": "The answer attempts to address the paradox but provides inconsistent and unclear numerical examples that don't match the required rates, omits a clear solution for part (4), and is poorly organized, limiting its practical value." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 3.4, "brief_justification": "The answer fails to provide complete numeric examples, leaves calculations unfinished, and does not address questions 2-4. It contains logical errors about feasibility of the given rates, reducing factual accuracy, though the explanation of Simpson's paradox is somewhat clear." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 5, "brief_justification": "The response correctly identifies Simpson's Paradox and points out a mathematical impossibility in the prompt, which is a good start. However, it doesn't actually answer any of the four questions posed, making it incomplete. It stops short of providing the requested numbers or addressing the core issues of which hospital is better, the insurance company's error, or the correct comparison method." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 4.9, "brief_justification": "The model struggles significantly with the first part of the question, failing to construct valid numbers for Simpson's Paradox. This impacts subsequent answers." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 10, "brief_justification": "The response is exceptionally well-structured, accurate, and provides a deep understanding of Simpson's Paradox. The numerical example is perfectly constructed, and the explanations for each part of the question are thorough and insightful, offering practical advice for correct comparison." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 10, "brief_justification": "The response correctly identifies the paradox, provides a valid numerical example after correcting the initial inconsistency, and thoroughly explains the implications and correct comparison methods. It demonstrates a deep understanding of Simpson's Paradox and its practical application in healthcare evaluation." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 1.25, "brief_justification": "The model failed to construct the numbers for the paradox despite multiple attempts. It got stuck in a loop of trying and failing, demonstrating a lack of understanding of the core mathematical concept required to solve the problem. The response is a long series of failed attempts rather than a coherent answer." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 10, "brief_justification": "The response is exceptionally well-structured, accurate, and comprehensive. It not only provides the correct answers but also delves into the underlying principles of Simpson's Paradox, offering practical implications and correct methodologies. The use of tables, mathematical notation, and clear explanations makes it a perfect answer." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 6.25, "brief_justification": "The model struggled significantly with constructing the exact numbers for the paradox, requiring multiple attempts and still not precisely matching the prompt's given overall rates. While the explanation of Simpson's Paradox and its implications was generally correct, the core task of number construction was not fully met. The explanation for why Hospital A is better and what goes wrong with the insurance company's method is accurate, but the overall presentation is a bit messy due to the iterat" }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 4.2, "brief_justification": "Response correctly identifies Simpson's Paradox but is incomplete - it cuts off mid-sentence without providing the exact numbers, answering which hospital is better, explaining the insurance company's error, or showing correct comparison method." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 7.4, "brief_justification": "Correctly explains Simpson's Paradox and identifies case mix as the cause, but fails to construct exact numbers matching the given percentages. Clear structure and explanation, though the solution is incomplete." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 9.6, "brief_justification": "Excellent response that correctly constructs the paradox with exact numbers, properly identifies Hospital A as the better choice, explains the insurance company's flawed methodology, and provides the correct stratified comparison approach. Well-structured with clear tables and thorough explanations including causal inference concepts." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9, "brief_justification": "Excellent response that correctly identifies Simpson's paradox, provides valid exact numbers (correcting the internally inconsistent original ones), explains why A is better within each surgery type, identifies the case mix confounding problem, and provides multiple correct comparison methods." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 4.9, "brief_justification": "Demonstrates understanding of Simpson's Paradox concept but fails to construct valid exact numbers matching the stated paradox. Response is repetitive and confusing, never successfully solving the core mathematical problem. Parts 2-4 are inadequately addressed." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 9.8, "brief_justification": "Mathematically correct numbers that produce the paradox, clear identification of Hospital A as better, excellent explanation of the confounding (case mix) problem, and proper standardization method with concrete calculation. Well-structured with tables and equations. Only minor room for improvement is slightly more explicit discussion of causal inference concepts." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 5.7, "brief_justification": "Explains Simpson's Paradox correctly but fails to construct exact numbers matching the prompt (89% vs 91%). Response is incomplete - part 3 is cut off and part 4 (correct comparison method) is entirely missing." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 7.3, "brief_justification": "Correctly identifies Simpson's Paradox and discovers the mathematical impossibility in the given numbers, providing a corrected example instead. The explanation of the paradox mechanism and correct comparison method is solid, but the numerical construction is incomplete and doesn't use the exact figures from the question." } ], "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)" } }