{ "evaluation_id": "EVAL-20260315-062610", "question_id": "EVAL-20260315-062610", "question_text": "A committee of 5 people must rank 3 candidates (A, B, C). Their preferences are: Person 1: A>B>C, Person 2: B>C>A, Person 3: C>A>B, Person 4: A>C>B, Person 5: B>A>C. (1) Show that majority rule produces a cycle. (2) Apply Borda count, instant-runoff, and Condorcet methods. Do they agree? (3) Arrow's theorem says no voting system satisfies all fairness criteria simultaneously. Which criterion would you sacrifice, and why?", "category": "reasoning", "timestamp": "2026-03-15T06:26:10.346Z", "display_date": "Mar 15, 2026", "winner": { "name": "Kimi K2.5", "provider": "openrouter", "score": 9.18 }, "avg_score": 8.323, "matrix_size": 74, "models_used": [ { "id": "kimi_k25", "name": "Kimi K2.5", "provider": "openrouter" }, { "id": "devstral", "name": "Devstral Small", "provider": "openrouter" }, { "id": "gemma3_27b", "name": "Gemma 3 27B", "provider": "openrouter" }, { "id": "llama4_scout", "name": "Llama 4 Scout", "provider": "openrouter" }, { "id": "phi4", "name": "Phi-4 14B", "provider": "openrouter" }, { "id": "qwen3_8b", "name": "Qwen 3 8B", "provider": "openrouter" }, { "id": "llama31_8b", "name": "Llama 3.1 8B", "provider": "openrouter" }, { "id": "granite_40", "name": "Granite 4.0 Micro", "provider": "openrouter" }, { "id": "mistral_nemo", "name": "Mistral Nemo 12B", "provider": "openrouter" }, { "id": "qwen3_32b", "name": "Qwen 3 32B", "provider": "openrouter" } ], "rankings": { "kimi_k25": { "display_name": "Kimi K2.5", "provider": "openrouter", "average_score": 9.18, "score_count": 9, "min_score": 8.3, "max_score": 10, "rank": 1 }, "qwen3_8b": { "display_name": "Qwen 3 8B", "provider": "openrouter", "average_score": 9.1, "score_count": 8, "min_score": 8.05, "max_score": 10, "rank": 2 }, "gemma3_27b": { "display_name": "Gemma 3 27B", "provider": "openrouter", "average_score": 9.09, "score_count": 8, "min_score": 7.9, "max_score": 9.8, "rank": 3 }, "phi4": { "display_name": "Phi-4 14B", "provider": "openrouter", "average_score": 9.05, "score_count": 8, "min_score": 7.9, "max_score": 9.8, "rank": 4 }, "mistral_nemo": { "display_name": "Mistral Nemo 12B", "provider": "openrouter", "average_score": 8.49, "score_count": 7, "min_score": 6.75, "max_score": 9.45, "rank": 5 }, "devstral": { "display_name": "Devstral Small", "provider": "openrouter", "average_score": 8.38, "score_count": 9, "min_score": 6.6, "max_score": 9.65, "rank": 6 }, "qwen3_32b": { "display_name": "Qwen 3 32B", "provider": "openrouter", "average_score": 8.05, "score_count": 2, "min_score": 7.85, "max_score": 8.25, "rank": 7 }, "granite_40": { "display_name": "Granite 4.0 Micro", "provider": "openrouter", "average_score": 8.03, "score_count": 7, "min_score": 6.05, "max_score": 9.05, "rank": 8 }, "llama4_scout": { "display_name": "Llama 4 Scout", "provider": "openrouter", "average_score": 7.44, "score_count": 8, "min_score": 6, "max_score": 8.55, "rank": 9 }, "llama31_8b": { "display_name": "Llama 3.1 8B", "provider": "openrouter", "average_score": 6.42, "score_count": 8, "min_score": 4.4, "max_score": 8, "rank": 10 } }, "judgments": [ { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "kimi_k25", "respondent_name": "Kimi K2.5", "weighted_score": 10, "brief_justification": "The response accurately analyzes all three parts of the question with precise calculations, clear explanations, and insightful reasoning. It correctly identifies A as the Condorcet winner, explains the hypothetical cycle scenario, and provides a well-reasoned argument for sacrificing IIA in Arrow's theorem. The structure is logical, and the depth of analysis addresses both technical and philosophical aspects of voting systems." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 8, "brief_justification": "The response correctly identifies the cycle in majority rule and explains Condorcet's paradox. However, the Borda count and instant-runoff calculations contain errors (e.g., Borda points are miscalculated, and the instant-runoff redistribution logic is flawed). The reasoning for sacrificing independence of irrelevant alternatives is valid but could be more detailed." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 8.8, "brief_justification": "The response correctly demonstrates the Condorcet paradox, accurately applies Borda count, IRV, and Condorcet methods, and provides a well-reasoned analysis of Arrow's theorem. Minor issues include the Borda count tie resolution being arbitrary and the IRV explanation slightly oversimplifying the redistribution process." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 6.35, "brief_justification": "The response correctly identifies Borda count and Condorcet results but contains errors in the instant-runoff calculation (B should win only if C's votes split to B, but the explanation is flawed). The majority rule analysis fails to clearly demonstrate a cycle (A beats B, B beats C, but C does not beat A). The Arrow's theorem discussion is conceptually accurate but lacks specific examples of trade-offs." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 9.8, "brief_justification": "The response accurately demonstrates majority rule cycles, correctly applies all three voting methods, and provides a well-reasoned analysis of Arrow's theorem. It is clear, thorough, and actionable for understanding voting system trade-offs." }, { "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 accurately demonstrates majority rule's cycle, correctly applies all three voting methods, and provides a well-reasoned justification for sacrificing the Condorcet criterion. It is thorough, logically structured, and offers insightful analysis of trade-offs in voting systems." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 5.4, "brief_justification": "The response correctly identifies the cycle in majority rule and the instant-runoff winner but contains errors in Borda count calculations (e.g., incorrect point totals) and misunderstands Arrow's theorem by mislabeling the Condorcet criterion as a fairness criterion within Arrow's framework. Clarity is moderate, but depth and usefulness are limited by these inaccuracies." }, { "judge_key": "kimi_k25", "judge_name": "Kimi K2.5", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 6.6, "brief_justification": "The response correctly identifies the Condorcet cycle and instant-runoff winner, but contains significant factual errors in the Borda count calculation (claiming 4 first-place votes for A out of 5 voters). Part 3 provides a defensible choice (sacrificing IIA) but with superficial justification." }, { "judge_key": "devstral", "judge_name": "Devstral Small", "respondent_key": "kimi_k25", "respondent_name": "Kimi K2.5", "weighted_score": 9.2, "brief_justification": "The response is highly accurate, thorough, and well-structured, providing deep insights and practical value." }, { "judge_key": "devstral", "judge_name": "Devstral Small", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 9.45, "brief_justification": "The response accurately and thoroughly addresses all parts of the question, demonstrating a deep understanding of voting systems and Arrow's theorem. It is well-structured and provides practical insights into the trade-offs involved in voting methods." }, { "judge_key": "devstral", "judge_name": "Devstral Small", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 7.45, "brief_justification": "The response is mostly correct and thorough, but the clarity is hindered by some confusion in the cycle explanation. The depth could be improved with more insight into the implications of the cycle and the trade-offs in voting systems." }, { "judge_key": "devstral", "judge_name": "Devstral Small", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 9.45, "brief_justification": "The response accurately and thoroughly addresses all parts of the question, demonstrating a deep understanding of voting theory and Arrow's theorem. The analysis is clear and well-structured, with practical insights into the trade-offs of different voting systems." }, { "judge_key": "devstral", "judge_name": "Devstral Small", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 8.05, "brief_justification": "The response is mostly correct and thorough, with clear explanations. It provides a good analysis of the voting methods and Arrow's theorem, but could benefit from more depth in discussing the implications of sacrificing 'Independence of Irrelevant Alternatives'." }, { "judge_key": "devstral", "judge_name": "Devstral Small", "respondent_key": "qwen3_8b", "respondent_name": "Qwen 3 8B", "weighted_score": 9.45, "brief_justification": "The response is factually accurate, logically valid, and thoroughly covers the topic. It is well-structured and clear, with insightful analysis and practical value." }, { "judge_key": "devstral", "judge_name": "Devstral Small", "respondent_key": "mistral_nemo", "respondent_name": "Mistral Nemo 12B", "weighted_score": 8.05, "brief_justification": "The response is mostly correct and thorough, with clear explanations. It provides a good analysis of the voting methods and Arrow's theorem, but could benefit from a deeper exploration of the trade-offs between fairness criteria." }, { "judge_key": "devstral", "judge_name": "Devstral Small", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 6.45, "brief_justification": "The response provides a thorough analysis of the voting methods but contains some inaccuracies and lacks clear structure." }, { "judge_key": "gemma3_27b", "judge_name": "Gemma 3 27B", "respondent_key": "kimi_k25", "respondent_name": "Kimi K2.5", "weighted_score": 9, "brief_justification": "The response accurately demonstrates the cycle in majority rule (with a necessary correction to the initial preferences), correctly applies the voting methods, and provides a well-reasoned justification for sacrificing IIA based on Arrow's theorem. The explanation is clear and thorough." }, { "judge_key": "gemma3_27b", "judge_name": "Gemma 3 27B", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 9.25, "brief_justification": "The response accurately demonstrates the cycle in majority rule, correctly applies the Borda count, instant-runoff, and Condorcet methods, and provides a reasonable justification for sacrificing the independence of irrelevant alternatives criterion." }, { "judge_key": "gemma3_27b", "judge_name": "Gemma 3 27B", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 8, "brief_justification": "The response correctly identifies the cycle in majority rule and accurately applies the Borda count, IRV, and Condorcet methods. The explanation of Arrow's theorem and the justification for sacrificing IIA are reasonable, though the initial cycle identification was slightly flawed and needed correction within the response." }, { "judge_key": "gemma3_27b", "judge_name": "Gemma 3 27B", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 9.45, "brief_justification": "The response accurately demonstrates the cycle in majority rule, correctly applies Borda count, IRV, and the Condorcet method, and provides a reasonable justification for sacrificing IIA in Arrow's theorem. The depth is slightly lower as it doesn't explore the implications of sacrificing other criteria." }, { "judge_key": "gemma3_27b", "judge_name": "Gemma 3 27B", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 8.25, "brief_justification": "The response accurately demonstrates the cycle in majority rule and correctly applies the Borda count, instant-runoff, and Condorcet methods, though the Instant-Runoff explanation is a bit brief. The discussion of Arrow's theorem and the justification for sacrificing IIA are reasonable." }, { "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 accurately demonstrates the cycle in majority rule, correctly applies all three voting methods, and provides a well-reasoned justification for sacrificing the Condorcet criterion based on Arrow's theorem. The explanation is clear, thorough, and insightful." }, { "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 demonstrates a voting cycle with majority rule and correctly applies the Borda count, IRV, and Condorcet methods. The explanation of Arrow's theorem and the justification for sacrificing the Condorcet criterion are well-reasoned, though the Condorcet violation explanation is slightly off." }, { "judge_key": "gemma3_27b", "judge_name": "Gemma 3 27B", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 7.2, "brief_justification": "The response correctly identifies the cycle in majority rule and applies the voting methods. However, the Borda count calculation is flawed (should be weighted by the number of voters, not multiplied by 3, 2, and 1). The justification for sacrificing the Condorcet criterion is reasonable, but lacks deeper exploration of the trade-offs." }, { "judge_key": "llama4_scout", "judge_name": "Llama 4 Scout", "respondent_key": "kimi_k25", "respondent_name": "Kimi K2.5", "weighted_score": 10, "brief_justification": "The response accurately addresses all parts of the question, providing thorough explanations and justifications for the conclusions drawn about majority rule, Borda count, instant-runoff, Condorcet methods, and Arrow's theorem." }, { "judge_key": "llama4_scout", "judge_name": "Llama 4 Scout", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 9.45, "brief_justification": "The response accurately addresses all parts of the question, providing clear explanations and thorough analysis. The only minor deduction is for clarity, as some sentences could be rephrased for better flow." }, { "judge_key": "llama4_scout", "judge_name": "Llama 4 Scout", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 9.65, "brief_justification": "The response accurately addresses all parts of the question, providing clear explanations and thorough analysis of different voting methods and Arrow's theorem. The reasoning is logical and well-structured." }, { "judge_key": "llama4_scout", "judge_name": "Llama 4 Scout", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 8.6, "brief_justification": "The response accurately analyzes the voting methods and applies Arrow's theorem correctly. It provides clear explanations and useful insights into the limitations of voting systems." }, { "judge_key": "llama4_scout", "judge_name": "Llama 4 Scout", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 8, "brief_justification": "The response accurately demonstrates the cycle in majority rule and applies various voting methods. However, there are minor errors and lack of detail in the instant-runoff explanation." }, { "judge_key": "llama4_scout", "judge_name": "Llama 4 Scout", "respondent_key": "qwen3_8b", "respondent_name": "Qwen 3 8B", "weighted_score": 8.45, "brief_justification": "The response accurately addresses all parts of the question, providing detailed explanations and correct applications of various voting methods, though some minor improvements in clarity and depth could be made." }, { "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 addresses all parts of the question, demonstrating a thorough understanding of voting systems and Arrow's theorem. The explanations are clear and provide useful insights into the methods discussed." }, { "judge_key": "llama4_scout", "judge_name": "Llama 4 Scout", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 8, "brief_justification": "The response accurately describes the application of various voting methods and addresses the question of which criterion to sacrifice. However, some steps could be more clearly explained, and the conclusion could be more concise." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "qwen3_32b", "respondent_name": "Qwen 3 32B", "weighted_score": 7.85, "brief_justification": "The response correctly identifies the cyclical nature of majority rule and applies Borda count, instant-runoff, and Condorcet methods, explaining their outcomes. It accurately discusses Arrow's theorem and the trade-offs involved in choosing a voting system. However, it does not provide a specific recommendation on which criterion to sacrifice, which would enhance completeness and depth." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "kimi_k25", "respondent_name": "Kimi K2.5", "weighted_score": 9.45, "brief_justification": "The response correctly demonstrates the Condorcet paradox with a cycle using majority rule and provides a clear analysis of Borda count, Instant-runoff, and Condorcet methods. It accurately applies Arrow's theorem, explaining the rationale for sacrificing IIA due to its practical implications and common violations in real-world voting systems. The response is thorough and insightful, offering a practical perspective on the criteria." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 9.65, "brief_justification": "The response accurately explains the cycle in majority rule, correctly applies Borda count, instant-runoff, and Condorcet methods, and thoughtfully discusses Arrow's theorem with a justified criterion sacrifice." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 9.4, "brief_justification": "The response accurately demonstrates the cycle in majority rule, correctly applies Borda count, IRV, and Condorcet methods, and thoughtfully discusses Arrow's theorem. It is clear, thorough, and insightful, with practical reasoning for sacrificing IIA." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 8.55, "brief_justification": "The response correctly identifies the cycle produced by majority rule and applies Borda count, instant-runoff, and Condorcet methods accurately. It discusses Arrow's theorem and suggests sacrificing the independence of irrelevant alternatives criterion, which is a valid consideration given the theorem's implications. The response is clear and thorough, providing practical insight into the voting methods and their outcomes." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 8.9, "brief_justification": "The response correctly demonstrates the cycle in majority rule and accurately applies the Borda count, instant-runoff, and Condorcet methods, showing how they agree or differ in outcomes. It also provides a reasoned explanation for choosing to sacrifice the Independence of Irrelevant Alternatives criterion, aligning with Arrow's theorem. The explanation is thorough but could explore more practical implications of sacrificing this criterion." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "qwen3_8b", "respondent_name": "Qwen 3 8B", "weighted_score": 9.45, "brief_justification": "The response correctly identifies the cycle in majority rule and applies Borda count, instant-runoff, and Condorcet methods. It explains why these methods do not agree due to the cycle and discusses the implications of Arrow's theorem, suggesting the sacrifice of the Condorcet criterion to ensure determinate outcomes. The explanation is thorough, clear, and provides practical insight into voting systems." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "mistral_nemo", "respondent_name": "Mistral Nemo 12B", "weighted_score": 8.9, "brief_justification": "The response accurately demonstrates the cycle produced by majority rule and correctly applies the Borda count, instant-runoff, and Condorcet methods, showing agreement among them. It also effectively discusses Arrow's theorem and the trade-offs involved in satisfying different criteria, providing a practical analysis of the voting systems." }, { "judge_key": "phi4", "judge_name": "Phi-4 14B", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 4.45, "brief_justification": "The response partially addresses the question but contains errors in calculations and logic, particularly in the Borda count and the analysis of pairwise contests. The explanation lacks depth and clarity in some areas, and the conclusion about sacrificing the Condorcet criterion is not well-supported." }, { "judge_key": "granite_40", "judge_name": "Granite 4.0 Micro", "respondent_key": "qwen3_32b", "respondent_name": "Qwen 3 32B", "weighted_score": 8.25, "brief_justification": "The response accurately analyzes the voting methods, identifies the cycle, and discusses Arrow's impossibility theorem, though it could provide more depth in the justification for sacrificing a criterion." }, { "judge_key": "granite_40", "judge_name": "Granite 4.0 Micro", "respondent_key": "kimi_k25", "respondent_name": "Kimi K2.5", "weighted_score": 8.8, "brief_justification": "The response accurately analyzes the voting paradox, applies multiple methods correctly, and thoughtfully addresses Arrow's theorem with a reasoned justification for sacrificing IIA, demonstrating strong overall understanding and communication." }, { "judge_key": "granite_40", "judge_name": "Granite 4.0 Micro", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 8.65, "brief_justification": "The response accurately demonstrates the cycle produced by majority rule, applies the voting methods correctly, and provides a reasonable justification for sacrificing independence of irrelevant alternatives in light of Arrow's theorem." }, { "judge_key": "granite_40", "judge_name": "Granite 4.0 Micro", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 8.65, "brief_justification": "The response accurately analyzes the voting scenario, demonstrating cycles with majority rule, applying various methods, and discussing Arrow's theorem and IIA. It provides a clear, well-structured explanation while sacrificing IIA for practical reasons." }, { "judge_key": "granite_40", "judge_name": "Granite 4.0 Micro", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 8, "brief_justification": "The response accurately addresses each part of the question, demonstrating a good understanding of voting methods and Arrow's impossibility theorem, with minor oversights in the cycle explanation and a slightly less thorough discussion of the independence of irrelevant alternatives." }, { "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 analyzes the voting methods, demonstrates the cycle in majority rule, applies Borda count, instant-runoff, and Condorcet methods, and correctly identifies Arrow's theorem criteria to sacrifice, with minor depth due to brevity." }, { "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 demonstrates cycle formation, applies multiple voting methods with clear results, and correctly identifies Arrow's theorem implications while making a reasonable trade-off choice." }, { "judge_key": "granite_40", "judge_name": "Granite 4.0 Micro", "respondent_key": "mistral_nemo", "respondent_name": "Mistral Nemo 12B", "weighted_score": 8.65, "brief_justification": "The response accurately demonstrates the cycle created by majority rule, applies multiple voting methods correctly, and thoughtfully addresses Arrow's impossibility theorem by discussing trade-offs between fairness criteria." }, { "judge_key": "granite_40", "judge_name": "Granite 4.0 Micro", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 8, "brief_justification": "The response accurately analyzes voting methods, identifies cycles, applies multiple criteria, and makes a reasonable trade-off, though some depth could be added to the justification of sacrificing Condorcet." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "kimi_k25", "respondent_name": "Kimi K2.5", "weighted_score": 8.8, "brief_justification": "The response accurately addresses all parts of the question with clear explanations and correct analysis of voting methods. It demonstrates strong understanding of Arrow's theorem and trade-offs, though depth could be enhanced with more nuanced discussion of fairness criteria." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 7, "brief_justification": "The Borda count calculation contains an error, affecting correctness. The response is clear and covers all parts but lacks depth in analysis." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 9.8, "brief_justification": "The response accurately addresses all parts of the question with clear, structured explanations. It thoroughly analyzes voting methods and Arrow's theorem, providing insightful reasoning for sacrificing IIA." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 6, "brief_justification": "The response correctly applies Borda count and IRV but misrepresents the Condorcet method (A is the Condorcet winner). The majority rule cycle explanation is unclear and incomplete." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 9.6, "brief_justification": "The response accurately demonstrates majority cycles, correctly applies all voting methods, and provides a clear rationale for sacrificing IIA in Arrow's theorem. It is well-structured and practical but could delve deeper into the philosophical trade-offs of Arrow's theorem." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 6.05, "brief_justification": "Part (1) correctly identifies the cycle, but parts (2) contain factual errors in Borda count, instant-runoff, and Condorcet method calculations. Part (3) provides a reasonable justification for sacrificing a fairness criterion." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "mistral_nemo", "respondent_name": "Mistral Nemo 12B", "weighted_score": 6.75, "brief_justification": "The Borda count calculation contains a critical error (incorrect point totals), affecting correctness. The majority rule cycle explanation is accurate, but the flawed Borda count undermines overall correctness. Other sections are clear and thorough." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 4.4, "brief_justification": "The response contains errors in majority rule analysis and Borda count calculations. It fails to properly demonstrate the cycle or conduct complete pairwise comparisons for Condorcet. The Arrow's theorem discussion lacks specific criterion identification." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "kimi_k25", "respondent_name": "Kimi K2.5", "weighted_score": 8.3, "brief_justification": "The response accurately explains the voting methods, demonstrates a cycle, and applies the methods to the problem. It also discusses Arrow's theorem and provides a well-reasoned argument for sacrificing IIA. However, it could be more concise and structured for better clarity." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 8.25, "brief_justification": "The response accurately demonstrates a cycle in majority rule, applies voting methods correctly, but could delve deeper into the implications of Arrow's theorem. It provides useful insights and is well-structured." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 7.9, "brief_justification": "The response accurately explains the voting methods and demonstrates the cycle in majority rule. It covers all methods asked but lacks some depth in explaining why certain criteria are sacrificed. The analysis is clear and well-structured, but some practical implications or real-world examples could enhance its usefulness." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 7.2, "brief_justification": "The response correctly explains the voting methods and applies them to the given scenario. However, the explanation of the cycle in majority rule is unclear and incomplete. The analysis of Arrow's theorem could be deeper, and the justification for sacrificing a criterion is brief." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 7.9, "brief_justification": "The response accurately describes the voting situation, applies various voting methods, and discusses Arrow's theorem. It could have provided more details on the trade-offs of sacrificing IIA. The analysis is clear and well-structured, but some steps in the voting methods could be explained more concisely." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 7.9, "brief_justification": "The response accurately explains the majority rule cycle and applies different voting methods. It also provides a reasonable explanation for Arrow's theorem. However, it could benefit from more examples or real-world applications to improve practical value." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "qwen3_8b", "respondent_name": "Qwen 3 8B", "weighted_score": 8.05, "brief_justification": "The response accurately demonstrates a cycle in majority rule, applies voting methods correctly, and discusses Arrow's theorem. It could provide more examples or details for 'depth' and 'usefulness'." }, { "judge_key": "mistral_nemo", "judge_name": "Mistral Nemo 12B", "respondent_key": "llama31_8b", "respondent_name": "Llama 3.1 8B", "weighted_score": 7.45, "brief_justification": "The response accurately describes the voting methods and their outcomes, but it could have provided more insight into why the Condorcet criterion is sacrificed." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "kimi_k25", "respondent_name": "Kimi K2.5", "weighted_score": 9.05, "brief_justification": "The response accurately and thoroughly explains the voting methods and their outcomes, providing a clear and insightful analysis of the problem. It also offers a well-reasoned argument for sacrificing IIA in favor of other fairness criteria." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "devstral", "respondent_name": "Devstral Small", "weighted_score": 8.6, "brief_justification": "The response accurately and thoroughly explains the concepts of majority rule, Borda count, instant-runoff, and Condorcet methods, and provides a clear justification for sacrificing the independence of irrelevant alternatives criterion." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "gemma3_27b", "respondent_name": "Gemma 3 27B", "weighted_score": 9.05, "brief_justification": "The response thoroughly analyzes the voting methods and provides a clear explanation of Arrow's theorem and its implications, but some minor points could be elaborated upon for maximum depth." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "llama4_scout", "respondent_name": "Llama 4 Scout", "weighted_score": 8, "brief_justification": "The response accurately explains the voting methods and their outcomes, but could benefit from clearer explanations of the cycles and Arrow's theorem implications." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "phi4", "respondent_name": "Phi-4 14B", "weighted_score": 8.8, "brief_justification": "The response accurately and thoroughly explains the voting methods and their results, and provides a clear justification for sacrificing the Independence of Irrelevant Alternatives criterion." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "granite_40", "respondent_name": "Granite 4.0 Micro", "weighted_score": 9.05, "brief_justification": "The response accurately and thoroughly explains the concepts of majority rule, Borda count, instant-runoff, and Condorcet methods, and provides a clear analysis of Arrow's Impossibility Theorem." }, { "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 and thoroughly explains the concepts of majority rule, Borda count, instant-runoff, and Condorcet methods, and provides a clear justification for sacrificing the Condorcet criterion." }, { "judge_key": "llama31_8b", "judge_name": "Llama 3.1 8B", "respondent_key": "mistral_nemo", "respondent_name": "Mistral Nemo 12B", "weighted_score": 8.8, "brief_justification": "The response accurately explains the majority rule cycle, applies Borda count, instant-runoff, and Condorcet methods, and discusses Arrow's theorem. It also provides a clear justification for sacrificing the Condorcet criterion." } ], "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)" } }