{ "evaluation_id": "EVAL-20260207-133151", "question_id": "REASON-003", "question_text": "Estimate how many piano tuners there are in Chicago. Show your reasoning step by step, including:\n1. All assumptions you make\n2. How you derived each number\n3. Sensitivity analysis (what if your assumptions are wrong?)\n4. Final estimate with confidence interval", "category": "reasoning", "timestamp": "2026-01-28T00:00:00.000Z", "display_date": "Jan 28, 2026", "winner": { "name": "Claude Opus 4.5", "provider": "Anthropic", "score": 9.52 }, "avg_score": 8.943, "matrix_size": 90, "models_used": [ { "id": "gemini_2_5_flash", "name": "Gemini 2.5 Flash", "provider": "Google" }, { "id": "olmo_think", "name": "OLMo Think", "provider": "Allen AI" }, { "id": "gemini_3_pro", "name": "Gemini 3 Pro Preview", "provider": "Google" }, { "id": "gemini_3_flash", "name": "Gemini 3 Flash Preview", "provider": "Google" }, { "id": "claude_opus", "name": "Claude Opus 4.5", "provider": "Anthropic" }, { "id": "claude_sonnet", "name": "Claude Sonnet 4.5", "provider": "Anthropic" }, { "id": "deepseek_v3", "name": "DeepSeek V3.2", "provider": "DeepSeek" }, { "id": "gpt_oss_120b", "name": "GPT-OSS-120B", "provider": "OpenAI" }, { "id": "grok_direct", "name": "Grok 3 (Direct)", "provider": "xAI" }, { "id": "mimo_v2_flash", "name": "MiMo-V2-Flash", "provider": "Xiaomi" } ], "rankings": { "claude_opus": { "display_name": "Claude Opus 4.5", "provider": "Anthropic", "average_score": 9.52, "score_count": 8, "min_score": 9.05, "max_score": 10, "rank": 1 }, "gpt_oss_120b": { "display_name": "GPT-OSS-120B", "provider": "OpenAI", "average_score": 9.5, "score_count": 7, "min_score": 9.15, "max_score": 10, "rank": 2 }, "claude_sonnet": { "display_name": "Claude Sonnet 4.5", "provider": "Anthropic", "average_score": 9.34, "score_count": 7, "min_score": 9.05, "max_score": 9.55, "rank": 3 }, "grok_direct": { "display_name": "Grok 3 (Direct)", "provider": "xAI", "average_score": 9.29, "score_count": 7, "min_score": 8.85, "max_score": 9.8, "rank": 4 }, "gemini_3_flash": { "display_name": "Gemini 3 Flash Preview", "provider": "Google", "average_score": 9.28, "score_count": 8, "min_score": 8.85, "max_score": 10, "rank": 5 }, "mimo_v2_flash": { "display_name": "MiMo-V2-Flash", "provider": "Xiaomi", "average_score": 9.24, "score_count": 9, "min_score": 8.65, "max_score": 9.8, "rank": 6 }, "deepseek_v3": { "display_name": "DeepSeek V3.2", "provider": "DeepSeek", "average_score": 9.22, "score_count": 7, "min_score": 8.4, "max_score": 9.8, "rank": 7 }, "gemini_2_5_flash": { "display_name": "Gemini 2.5 Flash", "provider": "Google", "average_score": 8.92, "score_count": 7, "min_score": 8.25, "max_score": 9.6, "rank": 8 }, "olmo_think": { "display_name": "OLMo Think", "provider": "Allen AI", "average_score": 7.87, "score_count": 3, "min_score": 7.45, "max_score": 8.2, "rank": 9 }, "gemini_3_pro": { "display_name": "Gemini 3 Pro Preview", "provider": "Google", "average_score": 7.25, "score_count": 3, "min_score": 5.55, "max_score": 8.75, "rank": 10 } }, "judgments": [ { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.25, "brief_justification": "The response presents accurate Fermi calculations and clear reasoning, but it omits an explicit confidence interval as requested, reducing completeness." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 0, "brief_justification": "No response was provided to evaluate, so all criteria receive the lowest score." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 0, "brief_justification": "No response was provided to evaluate. The response field is completely empty, making it impossible to assess any of the requested criteria." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9.35, "brief_justification": "The response provides a logically sound Fermi estimate with clear, reasonable assumptions and step-by-step math. It demonstrates strong depth by including a sensitivity analysis and contextualizing the result against real-world data (PTG/Yelp), validating the methodology." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.55, "brief_justification": "Excellent Fermi estimation with sound methodology, clear assumptions, comprehensive sensitivity analysis, and reality check validation. Minor point: could have explored correlation between variables in uncertainty analysis, but otherwise exemplary systematic reasoning." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 0, "brief_justification": "The response is empty and contains no content, failing to address any part of the prompt." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.55, "brief_justification": "The response demonstrates excellent Fermi estimation skills with logical assumptions, clear step-by-step reasoning, and thorough sensitivity analysis. The methodology is sound, numbers are reasonable, and the final estimate with confidence interval is well-justified. Minor deduction for correctness only because some numbers (like exact Chicago population or institutional pianos) are estimates without explicit sourcing, but this is inherent to the exercise." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.55, "brief_justification": "The response demonstrates excellent Fermi problem-solving methodology with clear, logical assumptions and robust sensitivity analysis. The estimate is reasonable, though the 10% household piano ownership might be slightly high for modern urban Chicago (5-8% would be more typical), but this is a reasonable assumption for a Fermi estimate." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.55, "brief_justification": "The response demonstrates excellent Fermi estimation skills with a logically sound framework, thorough breakdown of assumptions, and appropriate sensitivity analysis. The methodology is sound, calculations are clear, and the final estimate is well-justified with realistic confidence intervals." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 8.75, "brief_justification": "The response provides a clear, step-by-step Fermi estimate with explicit assumptions and a sensitivity analysis. The logic is sound and well-structured, though the final confidence interval is somewhat narrow given the high uncertainty in the input parameters." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 9.55, "brief_justification": "The response is a textbook example of a Fermi problem, demonstrating strong logical reasoning and clear structure. All requested components (assumptions, derivations, sensitivity analysis, final estimate) are thoroughly addressed. The calculation is correct and the sensitivity analysis is particularly insightful, correctly identifying the most impactful variables." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.55, "brief_justification": "The response is a textbook example of a Fermi estimate, providing a logically sound chain of reasoning with cited assumptions. It thoroughly addresses all requested components, including a detailed sensitivity analysis and confidence interval. The structure is exceptionally clear, and the final estimate is both reasonable and actionable." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 7.95, "brief_justification": "The response follows a standard Fermi estimation structure with clear steps and a sensitivity analysis. However, it contains a minor logical flaw by double-counting the number of pianos (assuming 10% of households and 10% of businesses have pianos, then adding a separate number for institutions, which likely overlap)." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9.55, "brief_justification": "The response is a textbook example of a Fermi problem solution, following a logical structure with clear assumptions and derivations. The calculations are correct, and the sensitivity analysis is thorough. The only minor deduction is for not accounting for institutional pianos, but this is explicitly noted." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 9.8, "brief_justification": "The response provides a textbook-perfect execution of a Fermi problem. It clearly outlines assumptions, provides logical derivations for each variable, includes a robust sensitivity analysis, and correctly identifies that institutional demand (schools/churches) would likely increase the base household estimate." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.55, "brief_justification": "The response provides a classic Fermi problem solution with excellent structure. It addresses all requested components, including a robust sensitivity analysis and a distinction between full-time equivalents and actual individuals, which adds significant depth and realism to the estimate." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.8, "brief_justification": "The response perfectly follows the Fermi problem methodology, providing clear assumptions, step-by-step calculations, a thorough sensitivity analysis, and a well-reasoned confidence interval. It correctly identifies the key variables that influence the final estimate and provides a realistic range." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 10, "brief_justification": "The response is a textbook-perfect example of a Fermi estimation. It breaks down the problem into logical components, provides clear justifications for every assumption, includes a robust sensitivity analysis, and provides a final estimate with confidence intervals as requested." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 9.6, "brief_justification": "The response provides a classic Fermi estimation with logical steps and clear mathematical derivations. It correctly identifies the most sensitive variables and provides a structured sensitivity analysis, though the final confidence interval was slightly less formal than a statistical range (e.g., 30-60 tuners)." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.15, "brief_justification": "The response follows the Fermi estimation methodology perfectly, providing clear steps, assumptions, and a sensitivity analysis. However, the final estimate of 10 tuners is likely an underestimate for a city of 2.7 million people (real-world data usually suggests 50-100 for a city that size), primarily because the assumption of 6 tunings per day is extremely high for a single professional including travel time." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 0, "brief_justification": "The response is empty and contains no content, failing to address any part of the prompt." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9.8, "brief_justification": "The response provides a textbook-perfect execution of a Fermi problem. It clearly outlines all assumptions, provides logical step-by-step derivations, includes a robust sensitivity analysis that identifies which variables impact the result most, and concludes with a reasonable confidence interval." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 9.55, "brief_justification": "Exemplary Fermi estimation with sound methodology, clear mathematical derivations, and comprehensive sensitivity analysis. All assumptions are explicitly stated and justified, with proper consideration of edge cases and institutional demand that many would overlook." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9.4, "brief_justification": "Excellent Fermi estimation with sound methodology, clear mathematical derivations, and comprehensive sensitivity analysis. The response demonstrates strong logical reasoning, addresses all required components, and provides practical context with real-world validation." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.55, "brief_justification": "Excellent Fermi estimation with sound logic, clear assumptions, and proper mathematical reasoning. The sensitivity analysis thoroughly explores how varying assumptions affect the outcome, and the confidence interval is well-justified. Minor point: could have validated against real-world data if available." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 9.4, "brief_justification": "Excellent Fermi estimation with sound methodology, clear step-by-step reasoning, and comprehensive sensitivity analysis. Minor point: the final confidence interval is missing (response appears truncated), but the approach and execution are exemplary for this type of problem." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.55, "brief_justification": "Exceptionally thorough Fermi estimation with well-justified assumptions, clear mathematical derivations, comprehensive sensitivity analysis across multiple variables, and appropriate confidence intervals. The sanity check against real-world data validates the methodology, though minor assumptions (like tuning time) could be questioned." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 0, "brief_justification": "No response was provided to evaluate. The response field is completely empty, making it impossible to assess any of the requested criteria including assumptions, derivations, sensitivity analysis, or final estimates." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9.4, "brief_justification": "Excellent Fermi estimation with sound methodology, clear assumptions, and thorough sensitivity analysis. All calculations are accurate and the reasoning is logically valid. The response fully addresses all four requirements with exceptional clarity and provides practical insights into the estimation process." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 9.4, "brief_justification": "The response is logically sound and methodically structured, covering all requested components with clear assumptions, derivations, sensitivity analysis, and a final estimate with confidence interval. It demonstrates strong reasoning and practical application, though some assumptions could be slightly refined for even greater accuracy." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9.4, "brief_justification": "The response is logically sound, thoroughly covers all requested components, and is exceptionally clear and well-structured, with insightful sensitivity analysis and a realistic confidence interval." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.25, "brief_justification": "The response demonstrates strong logical reasoning with well-documented assumptions and calculations, provides comprehensive sensitivity analysis, and delivers a clear, structured estimate with confidence intervals, though the usefulness is slightly limited as it's a hypothetical estimation exercise." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.4, "brief_justification": "The response demonstrates strong logical reasoning with well-justified assumptions, thoroughly covers all requested components including sensitivity analysis and confidence intervals, and provides a realistic estimate validated against external data." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 5.55, "brief_justification": "The response correctly applies a Fermi estimation framework and provides a plausible final estimate, but it fails to address the requested sensitivity analysis and confidence interval, making it incomplete and lacking in depth." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.4, "brief_justification": "The response demonstrates strong Fermi estimation methodology with logical assumptions and clear calculations, though some assumptions like piano ownership percentage lack specific Chicago context. It thoroughly addresses all requested components including sensitivity analysis and provides a well-structured, actionable estimation approach." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.6, "brief_justification": "The response demonstrates a highly accurate and logical Fermi estimation process, thoroughly covering all requested components including assumptions, derivations, sensitivity analysis, and a final estimate with confidence intervals. It is exceptionally clear, well-structured, and insightful, with practical value confirmed by a real-world sanity check." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 8.2, "brief_justification": "The response provides a logically sound, step-by-step estimation with clear assumptions and a sensitivity analysis, but the confidence interval is somewhat arbitrary and the depth of alternative scenario exploration is limited." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9.4, "brief_justification": "The response is highly accurate in its Fermi estimation approach, thoroughly covers all requested components with clear step-by-step reasoning, and provides practical sensitivity analysis and a confidence interval, though it could slightly deepen the discussion on institutional pianos." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 8.95, "brief_justification": "Excellent Fermi estimation with clear logical chain, well-documented assumptions, and thorough sensitivity analysis. The methodology is sound, calculations are correct, and the response appropriately acknowledges institutional demand as an overlooked factor. Minor deduction for correctness as some assumptions (like 4% piano ownership) could be better justified, but the final estimate of 40-45 is reasonable and well-defended." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9.4, "brief_justification": "Excellent Fermi estimation with clearly stated assumptions, logical step-by-step derivation, and thoughtful sensitivity analysis. The response addresses all requested components, provides a reasonable confidence interval, and even validates against real-world data sources. Minor deduction for correctness as some assumptions (like 2% ownership) could be debated, but the methodology is sound." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.4, "brief_justification": "Excellent Fermi estimation with well-reasoned assumptions, clear step-by-step derivation, and thorough sensitivity analysis covering low/medium/high scenarios. The response includes reality checks against external data points and properly distinguishes between FTE and actual headcount. Minor deduction for some assumptions that could use more justification (e.g., church piano ownership rate)." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.4, "brief_justification": "Excellent Fermi estimation with clear logical steps, reasonable assumptions (population, household size, piano ownership), and thorough sensitivity analysis. The final estimate of ~280 tuners aligns well with real-world data (~100-300 typically cited). Minor deduction for not considering part-time tuners or geographic metro area distinctions, but overall exemplary problem-solving demonstration." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 0, "brief_justification": "The response is completely empty with no content provided. No attempt was made to answer the Fermi estimation question about piano tuners in Chicago." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.4, "brief_justification": "The response demonstrates excellent Fermi estimation methodology with clear assumptions, step-by-step calculations, and meaningful sensitivity analysis. The math is sound and the reasoning is transparent. Minor deductions for not explicitly providing a confidence interval as requested and for some complexity in the full-time/part-time calculation that could be simplified. The estimate of ~43 tuners is reasonable and well-justified." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.4, "brief_justification": "Excellent Fermi estimation with well-sourced assumptions, clear step-by-step derivation, and thorough sensitivity analysis. The response includes all requested elements, uses appropriate mathematical notation, and validates against real-world data. Minor deduction for not accounting for institutional pianos (universities, recording studios) as a separate category, though the overhead factor partially addresses this." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 0, "brief_justification": "The response is completely empty with no content provided. There is no attempt to answer the Fermi estimation question about piano tuners in Chicago." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9, "brief_justification": "Excellent Fermi estimation with well-justified assumptions, clear step-by-step derivation, and thorough sensitivity analysis. The response correctly identifies key variables and their impact on the estimate. Minor deductions for not more thoroughly considering commercial/institutional pianos and for the confidence interval methodology being somewhat informal rather than statistically rigorous." }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 9.8, "brief_justification": "The response is a textbook execution of a Fermi problem with accurate math, clear logic, and a robust sensitivity analysis. It intelligently adjusts the final estimate to account for institutional demand (churches, schools) which was a critical insight beyond the basic household calculation." }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 10, "brief_justification": "The response is a textbook execution of a Fermi problem. It provides clear, reasonable assumptions, accurate calculations, a thoughtful sensitivity analysis, and validates the estimate against real-world data." }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 10, "brief_justification": "The response provides a flawless execution of a Fermi estimation. It breaks down assumptions logically (specifically the tiered tuning frequency), performs accurate arithmetic, includes a robust sensitivity analysis, and distinguishes between the city proper and metro area." }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 9.4, "brief_justification": "The response provides a comprehensive and well-structured Fermi estimation, clearly outlining assumptions, derivations, and a robust sensitivity analysis. The final estimate and confidence interval are well-justified." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9, "brief_justification": "The response provides a comprehensive and well-reasoned solution to the Fermi problem, clearly outlining assumptions, derivations, and sensitivity analysis." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.4, "brief_justification": "The response provides a very thorough and well-structured estimation, clearly outlining assumptions, calculations, and a robust sensitivity analysis. The reasoning is sound and addresses potential variations effectively." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9, "brief_justification": "The response provides a comprehensive and well-structured Fermi problem solution, clearly outlining assumptions, calculations, and a robust sensitivity analysis. The final estimate and confidence interval are well-supported." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.4, "brief_justification": "The response provides a very thorough and well-structured Fermi estimation, clearly outlining assumptions, derivations, and a strong sensitivity analysis. The final confidence intervals and reality check add significant value." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 7.45, "brief_justification": "The response provides a reasonable Fermi estimate for piano tuners in Chicago, clearly outlining assumptions and calculations. However, it lacks a formal sensitivity analysis and a confidence interval." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 10, "brief_justification": "The response provides a comprehensive and well-structured Fermi estimate, covering all requested elements with clear reasoning and a thorough sensitivity analysis." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 7.45, "brief_justification": "The response provides a reasonable Fermi estimate for piano tuners in Chicago, clearly outlining assumptions and calculations. However, it lacks a formal sensitivity analysis and a confidence interval." }, { "judge_key": "gemini_2_5_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9, "brief_justification": "The response provides a thorough and well-structured Fermi estimation, clearly outlining assumptions, derivations, and a robust sensitivity analysis. The final estimate and confidence interval are well-supported." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 8.65, "brief_justification": "The answer presents a logically consistent Fermi estimate with clear assumptions, correct arithmetic, and a sensible sensitivity analysis, though it could quantify institutional piano demand more explicitly." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 8.85, "brief_justification": "The response correctly follows the requested structure, performs accurate calculations, and provides reasonable assumptions with sensitivity analysis, though some assumptions could be debated." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.2, "brief_justification": "The answer follows the requested structure, makes reasonable assumptions, shows clear derivations, includes sensitivity scenarios and a confidence interval, and provides a plausible Fermi estimate of Chicago piano tuners." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 8.4, "brief_justification": "The answer follows the requested structure, clearly states assumptions, derives numbers step‑by‑step, and provides a sensitivity analysis and confidence interval; the methodology is sound though some assumptions (e.g., piano ownership rate) may be optimistic, affecting absolute accuracy." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.2, "brief_justification": "The answer thoroughly follows the prompt, presenting clear assumptions, step-by-step derivations, sensitivity analysis, and confidence intervals, with plausible numbers and a realistic final estimate." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 8.85, "brief_justification": "The response accurately performs a Fermi calculation with correct arithmetic, covers all requested components, is well‑organized, and adds thoughtful sensitivity analysis and caveats, though it could explore more nuanced factors for deeper insight." }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 8.8, "brief_justification": "The response uses a rigorous Fermi problem approach with clear assumptions, sensitivity analysis, and structured reasoning. However, the final estimate's confidence interval is somewhat subjective due to unquantified institutional demand factors." }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "olmo_think", "judge_name": "OLMo Think", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 8.85, "brief_justification": "The response is highly logical, with well-documented assumptions and derivations, though minor factual checks (e.g., exact population) could enhance correctness. It thoroughly addresses all aspects of the question with clear structure, insightful sensitivity analysis, and practical estimation." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 8.85, "brief_justification": "The response is highly accurate and logical, with clear step-by-step reasoning and well-stated assumptions. It includes a thorough sensitivity analysis, though deeper exploration of certain variables could enhance depth." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.05, "brief_justification": "The response is highly accurate and logical, with detailed step-by-step reasoning, comprehensive assumptions, and sensitivity analysis. Minor uncertainty in exact numbers prevents a perfect score in correctness and usefulness." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 8.85, "brief_justification": "The response is highly accurate in its logical approach to a Fermi problem, with detailed assumptions and calculations. It covers all requested aspects including sensitivity analysis and confidence intervals, though some assumptions (e.g., 10% piano ownership) could be better justified." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.05, "brief_justification": "The response is highly accurate with logical reasoning, covers all requested aspects including sensitivity analysis, and is clearly structured. It provides deep insight into assumptions and variability, though practical usefulness is slightly limited by the speculative nature of the estimate." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 0, "brief_justification": "The response is missing entirely, so it cannot be evaluated for any of the criteria." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "gemini_2_5_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.85, "brief_justification": "The response is highly accurate and thorough, with detailed step-by-step reasoning and sensitivity analysis. Minor adjustments could enhance depth and practical application." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.25, "brief_justification": "The response is highly accurate with well-reasoned assumptions and real-world data checks. It covers all requested aspects thoroughly, is clearly structured, offers deep analysis through sensitivity testing, and provides practical estimates, though direct applicability is limited." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "olmo_think", "respondent_name": "OLMo Think", "weighted_score": 0, "brief_justification": "The response is missing entirely, so it cannot be evaluated on any criteria." } ], "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)" } }