{
  "method": "voter-clustered bootstrap of Bradley-Terry MLE",
  "n_iterations": 1000,
  "seed": 42,
  "prior_sigma": 300.0,
  "n_voters": 315,
  "n_votes": 1262,
  "median_bootstrap_ci_width_elo": 114.2,
  "median_mcmc_ci_width_elo": 227.5,
  "rho_vs_llm_judge_likert": {
    "n_models": 20,
    "point_estimate": 0.4998,
    "p_value": 0.0248,
    "bootstrap_mean": 0.4546,
    "bootstrap_ci_low_95": 0.2467,
    "bootstrap_ci_high_95": 0.6451,
    "fraction_bootstraps_above_zero": 1.0
  },
  "per_model": [
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      "model": "claude_opus_4_6",
      "elo_mle": 1565.6,
      "boot_ci_low_95": 1505.2,
      "boot_ci_high_95": 1622.1,
      "boot_ci_width_95": 116.9,
      "elo_mcmc_mean": 1565.7,
      "mcmc_ci_low_95": 1429.9,
      "mcmc_ci_high_95": 1671.4,
      "mcmc_ci_width_95": 241.5
    },
    {
      "model": "claude_opus_4_7",
      "elo_mle": 1554.3,
      "boot_ci_low_95": 1488.9,
      "boot_ci_high_95": 1622.2,
      "boot_ci_width_95": 133.2,
      "elo_mcmc_mean": 1553.7,
      "mcmc_ci_low_95": 1419.3,
      "mcmc_ci_high_95": 1679.6,
      "mcmc_ci_width_95": 260.3
    },
    {
      "model": "claude_sonnet_4_5",
      "elo_mle": 1507.3,
      "boot_ci_low_95": 1456.9,
      "boot_ci_high_95": 1556.5,
      "boot_ci_width_95": 99.7,
      "elo_mcmc_mean": 1505.6,
      "mcmc_ci_low_95": 1391.6,
      "mcmc_ci_high_95": 1614.1,
      "mcmc_ci_width_95": 222.5
    },
    {
      "model": "deepseek_v3_2",
      "elo_mle": 1460.4,
      "boot_ci_low_95": 1406.4,
      "boot_ci_high_95": 1514.3,
      "boot_ci_width_95": 107.9,
      "elo_mcmc_mean": 1458.5,
      "mcmc_ci_low_95": 1340.6,
      "mcmc_ci_high_95": 1565.1,
      "mcmc_ci_width_95": 224.5
    },
    {
      "model": "deepseek_v4_flash",
      "elo_mle": 1492.1,
      "boot_ci_low_95": 1448.2,
      "boot_ci_high_95": 1545.1,
      "boot_ci_width_95": 96.9,
      "elo_mcmc_mean": 1490.7,
      "mcmc_ci_low_95": 1367.4,
      "mcmc_ci_high_95": 1604.9,
      "mcmc_ci_width_95": 237.5
    },
    {
      "model": "deepseek_v4_pro",
      "elo_mle": 1578.7,
      "boot_ci_low_95": 1523.3,
      "boot_ci_high_95": 1650.1,
      "boot_ci_width_95": 126.8,
      "elo_mcmc_mean": 1581.7,
      "mcmc_ci_low_95": 1461.9,
      "mcmc_ci_high_95": 1700.2,
      "mcmc_ci_width_95": 238.3
    },
    {
      "model": "gemini_2_5_flash",
      "elo_mle": 1412.2,
      "boot_ci_low_95": 1351.2,
      "boot_ci_high_95": 1465.8,
      "boot_ci_width_95": 114.6,
      "elo_mcmc_mean": 1410.8,
      "mcmc_ci_low_95": 1296.2,
      "mcmc_ci_high_95": 1522.2,
      "mcmc_ci_width_95": 226.0
    },
    {
      "model": "gemini_3_1_flash_lite",
      "elo_mle": 1559.5,
      "boot_ci_low_95": 1496.4,
      "boot_ci_high_95": 1626.1,
      "boot_ci_width_95": 129.8,
      "elo_mcmc_mean": 1557.1,
      "mcmc_ci_low_95": 1417.3,
      "mcmc_ci_high_95": 1682.5,
      "mcmc_ci_width_95": 265.2
    },
    {
      "model": "gemini_3_1_pro",
      "elo_mle": 1529.1,
      "boot_ci_low_95": 1470.3,
      "boot_ci_high_95": 1586.3,
      "boot_ci_width_95": 116.0,
      "elo_mcmc_mean": 1527.0,
      "mcmc_ci_low_95": 1415.4,
      "mcmc_ci_high_95": 1641.6,
      "mcmc_ci_width_95": 226.2
    },
    {
      "model": "gemma_4_26b",
      "elo_mle": 1506.4,
      "boot_ci_low_95": 1454.7,
      "boot_ci_high_95": 1564.2,
      "boot_ci_width_95": 109.5,
      "elo_mcmc_mean": 1504.5,
      "mcmc_ci_low_95": 1392.2,
      "mcmc_ci_high_95": 1594.9,
      "mcmc_ci_width_95": 202.7
    },
    {
      "model": "glm_4_7",
      "elo_mle": 1508.3,
      "boot_ci_low_95": 1451.7,
      "boot_ci_high_95": 1567.4,
      "boot_ci_width_95": 115.7,
      "elo_mcmc_mean": 1506.6,
      "mcmc_ci_low_95": 1399.8,
      "mcmc_ci_high_95": 1610.0,
      "mcmc_ci_width_95": 210.2
    },
    {
      "model": "glm_5_1",
      "elo_mle": 1445.2,
      "boot_ci_low_95": 1382.9,
      "boot_ci_high_95": 1506.4,
      "boot_ci_width_95": 123.5,
      "elo_mcmc_mean": 1440.6,
      "mcmc_ci_low_95": 1318.1,
      "mcmc_ci_high_95": 1562.1,
      "mcmc_ci_width_95": 244.0
    },
    {
      "model": "gpt_4_1",
      "elo_mle": 1555.3,
      "boot_ci_low_95": 1503.9,
      "boot_ci_high_95": 1614.8,
      "boot_ci_width_95": 110.9,
      "elo_mcmc_mean": 1556.5,
      "mcmc_ci_low_95": 1441.0,
      "mcmc_ci_high_95": 1670.7,
      "mcmc_ci_width_95": 229.7
    },
    {
      "model": "grok_4_1",
      "elo_mle": 1421.3,
      "boot_ci_low_95": 1361.3,
      "boot_ci_high_95": 1475.2,
      "boot_ci_width_95": 113.8,
      "elo_mcmc_mean": 1419.8,
      "mcmc_ci_low_95": 1293.4,
      "mcmc_ci_high_95": 1522.2,
      "mcmc_ci_width_95": 228.8
    },
    {
      "model": "kimi_k2_5",
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      "boot_ci_low_95": 1455.4,
      "boot_ci_high_95": 1565.2,
      "boot_ci_width_95": 109.8,
      "elo_mcmc_mean": 1510.8,
      "mcmc_ci_low_95": 1388.1,
      "mcmc_ci_high_95": 1622.3,
      "mcmc_ci_width_95": 234.2
    },
    {
      "model": "kimi_k2_6",
      "elo_mle": 1516.8,
      "boot_ci_low_95": 1461.2,
      "boot_ci_high_95": 1581.8,
      "boot_ci_width_95": 120.6,
      "elo_mcmc_mean": 1517.7,
      "mcmc_ci_low_95": 1408.2,
      "mcmc_ci_high_95": 1626.3,
      "mcmc_ci_width_95": 218.1
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    {
      "model": "llama_4_maverick",
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      "boot_ci_low_95": 1401.4,
      "boot_ci_high_95": 1504.0,
      "boot_ci_width_95": 102.6,
      "elo_mcmc_mean": 1452.2,
      "mcmc_ci_low_95": 1333.4,
      "mcmc_ci_high_95": 1555.9,
      "mcmc_ci_width_95": 222.5
    },
    {
      "model": "minimax_m2_7",
      "elo_mle": 1482.8,
      "boot_ci_low_95": 1431.4,
      "boot_ci_high_95": 1530.5,
      "boot_ci_width_95": 99.1,
      "elo_mcmc_mean": 1481.0,
      "mcmc_ci_low_95": 1363.1,
      "mcmc_ci_high_95": 1580.9,
      "mcmc_ci_width_95": 217.8
    },
    {
      "model": "mistral_small_creative",
      "elo_mle": 1528.8,
      "boot_ci_low_95": 1471.1,
      "boot_ci_high_95": 1587.0,
      "boot_ci_width_95": 115.9,
      "elo_mcmc_mean": 1527.9,
      "mcmc_ci_low_95": 1416.2,
      "mcmc_ci_high_95": 1632.1,
      "mcmc_ci_width_95": 215.9
    },
    {
      "model": "qwen3_5_flash",
      "elo_mle": 1410.9,
      "boot_ci_low_95": 1357.6,
      "boot_ci_high_95": 1463.5,
      "boot_ci_width_95": 106.0,
      "elo_mcmc_mean": 1405.5,
      "mcmc_ci_low_95": 1278.4,
      "mcmc_ci_high_95": 1511.2,
      "mcmc_ci_width_95": 232.8
    }
  ]
}