{ "evaluation_id": "EVAL-20260317-025517", "question_id": "EVAL-20260317-025517", "question_text": "You must choose between three investments. Investment A returns 10% with 90% probability, -50% with 10% probability. Investment B returns 5% with certainty. Investment C returns 100% with 20% probability, 0% with 80% probability. (1) Rank them by expected value. (2) Rank them by the Kelly criterion. (3) You have $10,000 your entire savings. Does this change your answer? Why? (4) Now you have $10,000,000. Does it change again? Derive the general principle.", "category": "reasoning", "timestamp": "2026-03-17T02:55:17.050Z", "display_date": "Mar 17, 2026", "winner": { "name": "Qwen 3.5 27B", "provider": "openrouter", "score": 9.96 }, "avg_score": 8.858, "matrix_size": 22, "models_used": [ { "id": "qwen3_32b", "name": "Qwen 3 32B", "provider": "openrouter" }, { "id": "qwen3_coder_next", "name": "Qwen 3 Coder Next", "provider": "openrouter" }, { "id": "qwen35_27b", "name": "Qwen 3.5 27B", "provider": "openrouter" }, { "id": "qwen35_397b_a17b", "name": "Qwen 3.5 397B-A17B", "provider": "openrouter" }, { "id": "qwen3_8b", "name": "Qwen 3 8B", "provider": "openrouter" } ], "rankings": { "qwen35_27b": { "display_name": "Qwen 3.5 27B", "provider": "openrouter", "average_score": 9.96, "score_count": 5, "min_score": 9.8, "max_score": 10, "rank": 1 }, "qwen35_397b_a17b": { "display_name": "Qwen 3.5 397B-A17B", "provider": "openrouter", "average_score": 9.95, "score_count": 4, "min_score": 9.8, "max_score": 10, "rank": 2 }, "qwen3_32b": { "display_name": "Qwen 3 32B", "provider": "openrouter", "average_score": 9.56, "score_count": 4, "min_score": 8.45, "max_score": 10, "rank": 3 }, "qwen3_8b": { "display_name": "Qwen 3 8B", "provider": "openrouter", "average_score": 8.33, "score_count": 3, "min_score": 7, "max_score": 9.8, "rank": 4 }, "qwen3_coder_next": { "display_name": "Qwen 3 Coder Next", "provider": "openrouter", "average_score": 6.49, "score_count": 6, "min_score": 5.1, "max_score": 9.25, "rank": 5 } }, "judgments": [ { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "qwen3_32b", "respondent_name": "Qwen 3 32B", "weighted_score": 10, "brief_justification": "The response accurately calculates expected values and Kelly criterion, thoroughly addresses all questions, and clearly explains the general principle that capital size does not affect rankings. It provides insightful analysis and practical context." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "qwen3_coder_next", "respondent_name": "Qwen 3 Coder Next", "weighted_score": 9.25, "brief_justification": "The response accurately calculates expected values and Kelly criterion, thoroughly explains the reasoning, and addresses all parts of the question. The only minor issue is an incomplete cutoff in part (3)." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "qwen35_27b", "respondent_name": "Qwen 3.5 27B", "weighted_score": 10, "brief_justification": "The response accurately calculates expected values and Kelly criterion, thoroughly addresses all questions, and provides insightful analysis on how wealth affects risk tolerance with clear practical implications." }, { "judge_key": "qwen3_8b", "judge_name": "Qwen 3 8B", "respondent_key": "qwen35_397b_a17b", "respondent_name": "Qwen 3.5 397B-A17B", "weighted_score": 10, "brief_justification": "The response accurately calculates expected values and Kelly criterion, addresses all four questions thoroughly, explains the diminishing marginal utility principle, and provides actionable insights for different wealth scenarios with clear structure and logical flow." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "qwen3_8b", "respondent_name": "Qwen 3 8B", "weighted_score": 7, "brief_justification": "The response correctly ranks investments by expected value but contains significant errors in the Kelly criterion calculations (e.g., incorrect optimal fractions for A and C). The reasoning for parts (3) and (4) is valid, but the flawed Kelly analysis reduces overall accuracy. Clarity and structure are strong, though depth and usefulness are limited by the errors." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "qwen3_coder_next", "respondent_name": "Qwen 3 Coder Next", "weighted_score": 7.9, "brief_justification": "The response correctly calculates expected values and Kelly rankings, with detailed mathematical derivations. However, the analysis for parts (3) and (4) is cut off mid-sentence, leaving the general principle and wealth-impact discussion incomplete. The explanation is clear where present but lacks full elaboration on risk tolerance and wealth scale implications." }, { "judge_key": "qwen3_32b", "judge_name": "Qwen 3 32B", "respondent_key": "qwen35_27b", "respondent_name": "Qwen 3.5 27B", "weighted_score": 10, "brief_justification": "The response is mathematically precise, thoroughly addresses all four questions, and provides deep insights into risk preferences, utility theory, and the Kelly criterion. It clearly explains how wealth affects investment choices and derives a general principle with practical applications." }, { "judge_key": "qwen3_coder_next", "judge_name": "Qwen 3 Coder Next", "respondent_key": "qwen3_8b", "respondent_name": "Qwen 3 8B", "weighted_score": 8.2, "brief_justification": "The expected value calculations are correct, but the Kelly criterion analysis contains errors: for Investment A, the optimal fraction and expected log return are miscalculated (correct f_A ≈ 0.25, log return ≈ 0.022); for Investment C, the optimal fraction is actually f_C = 0.2 (not 1.0), and the expected log return with full investment would be negative due to ruin risk. The response correctly emphasizes scale invariance of Kelly but misapplies it by ignoring that full investment in risky asset" }, { "judge_key": "qwen3_coder_next", "judge_name": "Qwen 3 Coder Next", "respondent_key": "qwen3_32b", "respondent_name": "Qwen 3 32B", "weighted_score": 10, "brief_justification": "The response correctly computes expected values and Kelly criterion values, explains why capital size doesn’t affect rankings (only investment fractions), and articulates the general principle clearly and rigorously—addressing all parts of the question with precise mathematics and economic intuition." }, { "judge_key": "qwen3_coder_next", "judge_name": "Qwen 3 Coder Next", "respondent_key": "qwen35_27b", "respondent_name": "Qwen 3.5 27B", "weighted_score": 10, "brief_justification": "The response correctly computes expected values, applies the Kelly criterion with proper optimization and growth rate calculations, and thoughtfully integrates behavioral and economic considerations (survival risk, DARA, time horizon) to explain how wealth level changes optimal choices—offering a principled, generalizable insight." }, { "judge_key": "qwen3_coder_next", "judge_name": "Qwen 3 Coder Next", "respondent_key": "qwen35_397b_a17b", "respondent_name": "Qwen 3.5 397B-A17B", "weighted_score": 10, "brief_justification": "The response correctly computes expected values and Kelly criterion (log growth), accurately explains how wealth scale affects optimal choice via utility theory and survival constraints, and derives the general principle of diminishing marginal utility of wealth—demonstrating exceptional rigor, clarity, and practical insight." }, { "judge_key": "qwen35_35b_a3b", "judge_name": "Qwen 3.5 35B-A3B", "respondent_key": "qwen3_coder_next", "respondent_name": "Qwen 3 Coder Next", "weighted_score": 5.5, "brief_justification": "The mathematical derivations for EV and Kelly are accurate and well-structured, but the response cuts off mid-sentence in part (3) and fails to address part (4) entirely, severely impacting completeness and usefulness." }, { "judge_key": "qwen35_35b_a3b", "judge_name": "Qwen 3.5 35B-A3B", "respondent_key": "qwen35_27b", "respondent_name": "Qwen 3.5 27B", "weighted_score": 9.8, "brief_justification": "The model provides mathematically precise calculations for EV and Kelly Criterion, correctly identifying optimal fractions and growth rates. It offers a nuanced, economically sound analysis of how wealth levels impact risk tolerance, effectively bridging theoretical finance with practical application." }, { "judge_key": "qwen35_27b", "judge_name": "Qwen 3.5 27B", "respondent_key": "qwen3_coder_next", "respondent_name": "Qwen 3 Coder Next", "weighted_score": 5.35, "brief_justification": "The mathematical derivations for expected value and Kelly criterion are accurate and well-explained, but the response is abruptly truncated, failing to address the wealth scenarios and general principle requested in the final parts of the question." }, { "judge_key": "qwen35_27b", "judge_name": "Qwen 3.5 27B", "respondent_key": "qwen35_397b_a17b", "respondent_name": "Qwen 3.5 397B-A17B", "weighted_score": 9.8, "brief_justification": "The response demonstrates high accuracy in financial calculations and correctly applies utility theory to explain how wealth constraints alter investment choices. It is well-structured and actionable, though a deeper mathematical derivation of optimal Kelly fractions for Investment A would have slightly increased the technical depth." }, { "judge_key": "qwen35_122b_a10b", "judge_name": "Qwen 3.5 122B-A10B", "respondent_key": "qwen3_8b", "respondent_name": "Qwen 3 8B", "weighted_score": 9.8, "brief_justification": "The response accurately calculates expected values and Kelly growth rates, correctly ranks the investments, and provides a theoretically sound explanation for the scale invariance of the Kelly criterion regarding capital size." }, { "judge_key": "qwen35_122b_a10b", "judge_name": "Qwen 3.5 122B-A10B", "respondent_key": "qwen3_32b", "respondent_name": "Qwen 3 32B", "weighted_score": 9.8, "brief_justification": "The response provides mathematically precise calculations for EV and Kelly criterion, correctly deriving rankings and explaining scale invariance. It thoroughly addresses all parts of the prompt with clear structure, though it could briefly note the single-shot vs. repeated bet assumption of Kelly for added nuance." }, { "judge_key": "qwen35_122b_a10b", "judge_name": "Qwen 3.5 122B-A10B", "respondent_key": "qwen3_coder_next", "respondent_name": "Qwen 3 Coder Next", "weighted_score": 5.1, "brief_justification": "The mathematical calculations for EV and Kelly are accurate and well-structured, but the response abruptly truncates mid-sentence in section (3) and completely omits section (4)." }, { "judge_key": "qwen35_122b_a10b", "judge_name": "Qwen 3.5 122B-A10B", "respondent_key": "qwen35_397b_a17b", "respondent_name": "Qwen 3.5 397B-A17B", "weighted_score": 10, "brief_justification": "The response provides mathematically accurate calculations for EV and Kelly metrics, correctly identifies the ranking as C > B > A, and offers a nuanced, theoretically sound application of utility theory to the wealth constraint scenarios." }, { "judge_key": "qwen35_397b_a17b", "judge_name": "Qwen 3.5 397B-A17B", "respondent_key": "qwen3_32b", "respondent_name": "Qwen 3 32B", "weighted_score": 8.45, "brief_justification": "The model provides mathematically accurate calculations for Expected Value and Kelly Criterion, correctly deriving optimal fractions and rankings. It correctly identifies the scale invariance of these metrics, though it could have explored the implications of utility theory and risk of ruin more deeply regarding the 'entire savings' constraint." }, { "judge_key": "qwen35_397b_a17b", "judge_name": "Qwen 3.5 397B-A17B", "respondent_key": "qwen3_coder_next", "respondent_name": "Qwen 3 Coder Next", "weighted_score": 5.85, "brief_justification": "The mathematical derivations for EV and Kelly are accurate and clearly presented, but the response cuts off mid-sentence in section 3 and completely omits section 4. This severe incompleteness undermines the utility of the analysis despite the high quality of the initial calculations." }, { "judge_key": "qwen35_397b_a17b", "judge_name": "Qwen 3.5 397B-A17B", "respondent_key": "qwen35_27b", "respondent_name": "Qwen 3.5 27B", "weighted_score": 10, "brief_justification": "The response provides mathematically accurate calculations for both Expected Value and Kelly Criterion with clear derivations. It also offers sound economic reasoning regarding risk aversion, liquidity constraints, and Decreasing Absolute Risk Aversion (DARA) across different wealth levels." } ], "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)" } }