{
 "schema": "five-seat-fairness-basket-v1",
 "reference": "all_llm",
 "arms": [
  "all_llm",
  "one_rational",
  "rational_advised_llm",
  "interpreter_advised_llm",
  "one_oracle",
  "all_oracle",
  "all_rational"
 ],
 "per_party_surplus_among_deals": {
  "all_llm": {
   "n_episodes": 120,
   "n_deals": 115,
   "deal_rate": 0.9583333333333334,
   "pooling": "party-observations (5 per closed deal), clustered on instance",
   "per_party_z": {
    "mean": 0.652856953489687,
    "ci_low": 0.6201430300777417,
    "ci_high": 0.6900437826532168,
    "q1": 0.4333333333,
    "median": 0.6666666667,
    "q3": 1.0,
    "n_party_obs": 575
   },
   "episode_score": {
    "mean": 0.9105530434782609,
    "q1": 0.8383,
    "median": 0.9455,
    "q3": 1.0
   }
  },
  "one_rational": {
   "n_episodes": 120,
   "n_deals": 92,
   "deal_rate": 0.7666666666666667,
   "pooling": "party-observations (5 per closed deal), clustered on instance",
   "per_party_z": {
    "mean": 0.6386387048911086,
    "ci_low": 0.6053134954875482,
    "ci_high": 0.6745053190797836,
    "q1": 0.430555555525,
    "median": 0.6565335753,
    "q3": 1.0,
    "n_party_obs": 460
   },
   "episode_score": {
    "mean": 0.8953380434782608,
    "q1": 0.8252,
    "median": 0.9314,
    "q3": 1.0
   }
  },
  "rational_advised_llm": {
   "n_episodes": 120,
   "n_deals": 108,
   "deal_rate": 0.9,
   "pooling": "party-observations (5 per closed deal), clustered on instance",
   "per_party_z": {
    "mean": 0.6456315339927222,
    "ci_low": 0.6153988795733067,
    "ci_high": 0.6780492046556041,
    "q1": 0.4137931034,
    "median": 0.6666666667,
    "q3": 1.0,
    "n_party_obs": 540
   },
   "episode_score": {
    "mean": 0.901649074074074,
    "q1": 0.8216,
    "median": 0.9254,
    "q3": 1.0
   }
  },
  "interpreter_advised_llm": {
   "n_episodes": 120,
   "n_deals": 115,
   "deal_rate": 0.9583333333333334,
   "pooling": "party-observations (5 per closed deal), clustered on instance",
   "per_party_z": {
    "mean": 0.6561403796638609,
    "ci_low": 0.6243408250276867,
    "ci_high": 0.6904888855352304,
    "q1": 0.4428571429,
    "median": 0.6666666667,
    "q3": 1.0,
    "n_party_obs": 575
   },
   "episode_score": {
    "mean": 0.919126956521739,
    "q1": 0.8443,
    "median": 0.9608,
    "q3": 1.0
   }
  },
  "one_oracle": {
   "n_episodes": 120,
   "n_deals": 110,
   "deal_rate": 0.9166666666666666,
   "pooling": "party-observations (5 per closed deal), clustered on instance",
   "per_party_z": {
    "mean": 0.6487857962817273,
    "ci_low": 0.6107054495371693,
    "ci_high": 0.6895755574098186,
    "q1": 0.341177734775,
    "median": 0.6868872549,
    "q3": 1.0,
    "n_party_obs": 550
   },
   "episode_score": {
    "mean": 0.9042145454545453,
    "q1": 0.829375,
    "median": 0.9614499999999999,
    "q3": 1.0
   }
  },
  "all_oracle": {
   "n_episodes": 120,
   "n_deals": 120,
   "deal_rate": 1.0,
   "pooling": "party-observations (5 per closed deal), clustered on instance",
   "per_party_z": {
    "mean": 0.6447808151705168,
    "ci_low": 0.6116336184036487,
    "ci_high": 0.6812809657953525,
    "q1": 0.3103448276,
    "median": 0.6835443038,
    "q3": 1.0,
    "n_party_obs": 600
   },
   "episode_score": {
    "mean": 0.9068575,
    "q1": 0.842525,
    "median": 0.9816,
    "q3": 1.0
   }
  },
  "all_rational": {
   "n_episodes": 120,
   "n_deals": 28,
   "deal_rate": 0.23333333333333334,
   "pooling": "party-observations (5 per closed deal), clustered on instance",
   "per_party_z": {
    "mean": 0.5541257617509286,
    "ci_low": 0.5126514720991605,
    "ci_high": 0.6102331784787526,
    "q1": 0.32918806162500003,
    "median": 0.56740442655,
    "q3": 0.7625,
    "n_party_obs": 140
   },
   "episode_score": {
    "mean": 0.8093928571428572,
    "q1": 0.6987000000000001,
    "median": 0.83005,
    "q3": 0.9216
   }
  }
 },
 "n_bootstrap": 10000,
 "seed": 20260809,
 "n_episodes": {
  "all_llm": 120,
  "one_rational": 120,
  "rational_advised_llm": 120,
  "interpreter_advised_llm": 120,
  "one_oracle": 120,
  "all_oracle": 120,
  "all_rational": 120
 },
 "n_deals": {
  "all_llm": 115,
  "one_rational": 92,
  "rational_advised_llm": 108,
  "interpreter_advised_llm": 115,
  "one_oracle": 110,
  "all_oracle": 120,
  "all_rational": 28
 },
 "levels": {
  "all_llm": {
   "deal_rate": {
    "estimate": 0.9583333333333334,
    "ci_low": 0.925,
    "ci_high": 0.9833333333333333,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_accept": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 115,
    "n_instances": 24
   },
   "worst_off": {
    "estimate": 0.25662751078488905,
    "ci_low": 0.20660835047918574,
    "ci_high": 0.30600756625601455,
    "n": 115,
    "n_instances": 24
   },
   "worst_off_share": {
    "estimate": 0.07733378037747124,
    "ci_low": 0.06372168254261014,
    "ci_high": 0.08964987629498626,
    "n": 115,
    "n_instances": 24
   },
   "dist_to_nbs": {
    "estimate": 0.46360609046022655,
    "ci_low": 0.3565226072213674,
    "ci_high": 0.5826609489932553,
    "n": 115,
    "n_instances": 24
   },
   "dist_to_ks": {
    "estimate": 0.39841757139287376,
    "ci_low": 0.3159915975593445,
    "ci_high": 0.4740919744695105,
    "n": 115,
    "n_instances": 24
   },
   "normalized_gini": {
    "estimate": 0.22312596428528939,
    "ci_low": 0.19971159081455367,
    "ci_high": 0.24672232651727338,
    "n": 115,
    "n_instances": 24
   },
   "normalized_nash_welfare_conditional": {
    "estimate": 0.5347356494115132,
    "ci_low": 0.45934698095845394,
    "ci_high": 0.6015353499949824,
    "n": 115,
    "n_instances": 24
   },
   "max_share": {
    "estimate": 0.29899227726399724,
    "ci_low": 0.28754462333382413,
    "ci_high": 0.30927339521265834,
    "n": 115,
    "n_instances": 24
   },
   "below_threshold_episode": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "normalized_primary": {
    "estimate": 0.8726133333333334,
    "ci_low": 0.8327347083333333,
    "ci_high": 0.9104252291666667,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare": {
    "estimate": 0.5124549973527001,
    "ci_low": 0.4301153246627236,
    "ci_high": 0.586181608900662,
    "n": 120,
    "n_instances": 24
   },
   "justified_walk": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 5,
    "n_instances": 5
   },
   "missed_deal": {
    "estimate": 1.0,
    "ci_low": 1.0,
    "ci_high": 1.0,
    "n": 5,
    "n_instances": 5
   },
   "ir_margin_of_no_deal": {
    "estimate": 0.2305128205128205,
    "ci_low": 0.05384615384615384,
    "ci_high": 0.40717948717948715,
    "n": 5,
    "n_instances": 5
   }
  },
  "one_rational": {
   "deal_rate": {
    "estimate": 0.7666666666666667,
    "ci_low": 0.6833333333333333,
    "ci_high": 0.8416666666666667,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_accept": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 92,
    "n_instances": 24
   },
   "worst_off": {
    "estimate": 0.23923924245411646,
    "ci_low": 0.19683072717163422,
    "ci_high": 0.28224996743845204,
    "n": 92,
    "n_instances": 24
   },
   "worst_off_share": {
    "estimate": 0.0725120810975585,
    "ci_low": 0.06097860651045568,
    "ci_high": 0.08370679860351421,
    "n": 92,
    "n_instances": 24
   },
   "dist_to_nbs": {
    "estimate": 0.44434457646545117,
    "ci_low": 0.34251356481754514,
    "ci_high": 0.5676758504505426,
    "n": 92,
    "n_instances": 24
   },
   "dist_to_ks": {
    "estimate": 0.41411311378312343,
    "ci_low": 0.3323445296545228,
    "ci_high": 0.49140176345459324,
    "n": 92,
    "n_instances": 24
   },
   "normalized_gini": {
    "estimate": 0.23136952807084968,
    "ci_low": 0.2087369470730114,
    "ci_high": 0.2545594254167545,
    "n": 92,
    "n_instances": 24
   },
   "normalized_nash_welfare_conditional": {
    "estimate": 0.5063123982328782,
    "ci_low": 0.43981796588074573,
    "ci_high": 0.5641182063092108,
    "n": 92,
    "n_instances": 24
   },
   "max_share": {
    "estimate": 0.30102142748483496,
    "ci_low": 0.28908559020113483,
    "ci_high": 0.3133682464419921,
    "n": 92,
    "n_instances": 24
   },
   "below_threshold_episode": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "normalized_primary": {
    "estimate": 0.6864258333333334,
    "ci_low": 0.6125244166666667,
    "ci_high": 0.7606728333333334,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare": {
    "estimate": 0.38817283864520663,
    "ci_low": 0.3200574611095578,
    "ci_high": 0.45228780607010843,
    "n": 120,
    "n_instances": 24
   },
   "justified_walk": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 28,
    "n_instances": 17
   },
   "missed_deal": {
    "estimate": 1.0,
    "ci_low": 1.0,
    "ci_high": 1.0,
    "n": 28,
    "n_instances": 17
   },
   "ir_margin_of_no_deal": {
    "estimate": 0.3432439165619196,
    "ci_low": 0.22079647397565216,
    "ci_high": 0.46032524493968746,
    "n": 28,
    "n_instances": 17
   }
  },
  "rational_advised_llm": {
   "deal_rate": {
    "estimate": 0.9,
    "ci_low": 0.8083333333333333,
    "ci_high": 0.975,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_accept": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 108,
    "n_instances": 24
   },
   "worst_off": {
    "estimate": 0.2500726745763431,
    "ci_low": 0.20588192810419068,
    "ci_high": 0.29478521898544624,
    "n": 108,
    "n_instances": 24
   },
   "worst_off_share": {
    "estimate": 0.07598800278802065,
    "ci_low": 0.06420405442084354,
    "ci_high": 0.08721121659758677,
    "n": 108,
    "n_instances": 24
   },
   "dist_to_nbs": {
    "estimate": 0.4781650421527495,
    "ci_low": 0.38384083862143753,
    "ci_high": 0.581430530006112,
    "n": 108,
    "n_instances": 24
   },
   "dist_to_ks": {
    "estimate": 0.45763156935745003,
    "ci_low": 0.37400906809654,
    "ci_high": 0.5343891029912663,
    "n": 108,
    "n_instances": 24
   },
   "normalized_gini": {
    "estimate": 0.23159563260933352,
    "ci_low": 0.20996228671838432,
    "ci_high": 0.2532847937452672,
    "n": 108,
    "n_instances": 24
   },
   "normalized_nash_welfare_conditional": {
    "estimate": 0.525631904439619,
    "ci_low": 0.4657191892852127,
    "ci_high": 0.579545192042175,
    "n": 108,
    "n_instances": 24
   },
   "max_share": {
    "estimate": 0.3023671533397975,
    "ci_low": 0.29102942776003526,
    "ci_high": 0.3130323876584692,
    "n": 108,
    "n_instances": 24
   },
   "below_threshold_episode": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "normalized_primary": {
    "estimate": 0.8114841666666666,
    "ci_low": 0.7259901458333332,
    "ci_high": 0.8836802291666667,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare": {
    "estimate": 0.4730687139956571,
    "ci_low": 0.39187728989485976,
    "ci_high": 0.5445305354572809,
    "n": 120,
    "n_instances": 24
   },
   "justified_walk": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 12,
    "n_instances": 6
   },
   "missed_deal": {
    "estimate": 1.0,
    "ci_low": 1.0,
    "ci_high": 1.0,
    "n": 12,
    "n_instances": 6
   },
   "ir_margin_of_no_deal": {
    "estimate": 0.2559326723031295,
    "ci_low": 0.054878048780487805,
    "ci_high": 0.4563129859973735,
    "n": 12,
    "n_instances": 6
   }
  },
  "interpreter_advised_llm": {
   "deal_rate": {
    "estimate": 0.9583333333333334,
    "ci_low": 0.9166666666666666,
    "ci_high": 0.9916666666666667,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_accept": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 115,
    "n_instances": 24
   },
   "worst_off": {
    "estimate": 0.26877510570102636,
    "ci_low": 0.2246920685802303,
    "ci_high": 0.30989615487474587,
    "n": 115,
    "n_instances": 24
   },
   "worst_off_share": {
    "estimate": 0.08183640825255681,
    "ci_low": 0.06906536649344422,
    "ci_high": 0.09304294329484511,
    "n": 115,
    "n_instances": 24
   },
   "dist_to_nbs": {
    "estimate": 0.4116431753333182,
    "ci_low": 0.3108729437989708,
    "ci_high": 0.5347941667716734,
    "n": 115,
    "n_instances": 24
   },
   "dist_to_ks": {
    "estimate": 0.36606048552080234,
    "ci_low": 0.2943508222182356,
    "ci_high": 0.4300883670743269,
    "n": 115,
    "n_instances": 24
   },
   "normalized_gini": {
    "estimate": 0.2144021422360019,
    "ci_low": 0.19599785314513896,
    "ci_high": 0.2327798444558433,
    "n": 115,
    "n_instances": 24
   },
   "normalized_nash_welfare_conditional": {
    "estimate": 0.5425545088981604,
    "ci_low": 0.47726289299154334,
    "ci_high": 0.5975320288481668,
    "n": 115,
    "n_instances": 24
   },
   "max_share": {
    "estimate": 0.2960790571733364,
    "ci_low": 0.2851950555597496,
    "ci_high": 0.306583161157282,
    "n": 115,
    "n_instances": 24
   },
   "below_threshold_episode": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "normalized_primary": {
    "estimate": 0.8808299999999999,
    "ci_low": 0.8358273125,
    "ci_high": 0.9212710416666666,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare": {
    "estimate": 0.5199480710274036,
    "ci_low": 0.44140233605366574,
    "ci_high": 0.5865307672431204,
    "n": 120,
    "n_instances": 24
   },
   "justified_walk": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 5,
    "n_instances": 4
   },
   "missed_deal": {
    "estimate": 1.0,
    "ci_low": 1.0,
    "ci_high": 1.0,
    "n": 5,
    "n_instances": 4
   },
   "ir_margin_of_no_deal": {
    "estimate": 0.16575,
    "ci_low": 0.0,
    "ci_high": 0.414375,
    "n": 5,
    "n_instances": 4
   }
  },
  "one_oracle": {
   "deal_rate": {
    "estimate": 0.9166666666666666,
    "ci_low": 0.85,
    "ci_high": 0.9666666666666667,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_accept": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 110,
    "n_instances": 24
   },
   "worst_off": {
    "estimate": 0.20052420434418816,
    "ci_low": 0.15220588218325654,
    "ci_high": 0.2520162262625005,
    "n": 110,
    "n_instances": 24
   },
   "worst_off_share": {
    "estimate": 0.058582652990355755,
    "ci_low": 0.04724879521114121,
    "ci_high": 0.0697843321051137,
    "n": 110,
    "n_instances": 24
   },
   "dist_to_nbs": {
    "estimate": 0.5502155166421395,
    "ci_low": 0.4355103425799059,
    "ci_high": 0.6743700297081331,
    "n": 110,
    "n_instances": 24
   },
   "dist_to_ks": {
    "estimate": 0.5241960242972619,
    "ci_low": 0.42556402400791543,
    "ci_high": 0.6137548879342425,
    "n": 110,
    "n_instances": 24
   },
   "normalized_gini": {
    "estimate": 0.26570818208794883,
    "ci_low": 0.23680217406711732,
    "ci_high": 0.29289045515917334,
    "n": 110,
    "n_instances": 24
   },
   "normalized_nash_welfare_conditional": {
    "estimate": 0.47216530427836567,
    "ci_low": 0.39488018587278173,
    "ci_high": 0.5463052174320897,
    "n": 110,
    "n_instances": 24
   },
   "max_share": {
    "estimate": 0.3143537476799115,
    "ci_low": 0.2972221977659884,
    "ci_high": 0.3314974965305435,
    "n": 110,
    "n_instances": 24
   },
   "below_threshold_episode": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "normalized_primary": {
    "estimate": 0.8288633333333332,
    "ci_low": 0.7672437083333333,
    "ci_high": 0.8842517708333332,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare": {
    "estimate": 0.4328181955885018,
    "ci_low": 0.3494684613042903,
    "ci_high": 0.5145233653643979,
    "n": 120,
    "n_instances": 24
   },
   "justified_walk": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 10,
    "n_instances": 8
   },
   "missed_deal": {
    "estimate": 1.0,
    "ci_low": 1.0,
    "ci_high": 1.0,
    "n": 10,
    "n_instances": 8
   },
   "ir_margin_of_no_deal": {
    "estimate": 0.2390978586087305,
    "ci_low": 0.09909886322950232,
    "ci_high": 0.4198478030050496,
    "n": 10,
    "n_instances": 8
   }
  },
  "all_oracle": {
   "deal_rate": {
    "estimate": 1.0,
    "ci_low": 1.0,
    "ci_high": 1.0,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_accept": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "worst_off": {
    "estimate": 0.1664140067203309,
    "ci_low": 0.1183633018112518,
    "ci_high": 0.21966347278571574,
    "n": 120,
    "n_instances": 24
   },
   "worst_off_share": {
    "estimate": 0.0484048449564163,
    "ci_low": 0.03651114441182694,
    "ci_high": 0.06066532594641663,
    "n": 120,
    "n_instances": 24
   },
   "dist_to_nbs": {
    "estimate": 0.6306371226240565,
    "ci_low": 0.5202313278987801,
    "ci_high": 0.7559524553199843,
    "n": 120,
    "n_instances": 24
   },
   "dist_to_ks": {
    "estimate": 0.549472048212886,
    "ci_low": 0.44877145966030035,
    "ci_high": 0.6487582137658562,
    "n": 120,
    "n_instances": 24
   },
   "normalized_gini": {
    "estimate": 0.2854855910779398,
    "ci_low": 0.2557754883631389,
    "ci_high": 0.31435320789081594,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare_conditional": {
    "estimate": 0.405530944848298,
    "ci_low": 0.31578914493347343,
    "ci_high": 0.4914876556657148,
    "n": 120,
    "n_instances": 24
   },
   "max_share": {
    "estimate": 0.31912538492110715,
    "ci_low": 0.3027884961625283,
    "ci_high": 0.33555231350944,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_episode": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "normalized_primary": {
    "estimate": 0.9068575,
    "ci_low": 0.8802970625,
    "ci_high": 0.9325118541666666,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare": {
    "estimate": 0.405530944848298,
    "ci_low": 0.31578914493347343,
    "ci_high": 0.4914876556657148,
    "n": 120,
    "n_instances": 24
   },
   "justified_walk": {
    "estimate": null,
    "ci_low": null,
    "ci_high": null,
    "n": 0,
    "n_instances": 0
   },
   "missed_deal": {
    "estimate": null,
    "ci_low": null,
    "ci_high": null,
    "n": 0,
    "n_instances": 0
   },
   "ir_margin_of_no_deal": {
    "estimate": null,
    "ci_low": null,
    "ci_high": null,
    "n": 0,
    "n_instances": 0
   }
  },
  "all_rational": {
   "deal_rate": {
    "estimate": 0.23333333333333334,
    "ci_low": 0.13333333333333333,
    "ci_high": 0.3416666666666667,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_accept": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 28,
    "n_instances": 14
   },
   "worst_off": {
    "estimate": 0.14694344596801961,
    "ci_low": 0.10277973891405223,
    "ci_high": 0.19436100475353346,
    "n": 28,
    "n_instances": 14
   },
   "worst_off_share": {
    "estimate": 0.05224324367491081,
    "ci_low": 0.03743994830704269,
    "ci_high": 0.06737766341088748,
    "n": 28,
    "n_instances": 14
   },
   "dist_to_nbs": {
    "estimate": 0.5995994212802717,
    "ci_low": 0.4997858176694715,
    "ci_high": 0.6796781512666987,
    "n": 28,
    "n_instances": 14
   },
   "dist_to_ks": {
    "estimate": 0.5897606666492755,
    "ci_low": 0.520696106253425,
    "ci_high": 0.6487571656266502,
    "n": 28,
    "n_instances": 14
   },
   "normalized_gini": {
    "estimate": 0.2606935627315637,
    "ci_low": 0.23841425650619627,
    "ci_high": 0.28292756312641415,
    "n": 28,
    "n_instances": 14
   },
   "normalized_nash_welfare_conditional": {
    "estimate": 0.40783781598662144,
    "ci_low": 0.31631314866100474,
    "ci_high": 0.4849954848827147,
    "n": 28,
    "n_instances": 14
   },
   "max_share": {
    "estimate": 0.31364014160553955,
    "ci_low": 0.29899385144477997,
    "ci_high": 0.3265161495559122,
    "n": 28,
    "n_instances": 14
   },
   "below_threshold_episode": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "normalized_primary": {
    "estimate": 0.18885833333333338,
    "ci_low": 0.1109945625,
    "ci_high": 0.2776496041666667,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare": {
    "estimate": 0.09516215706354499,
    "ci_low": 0.05037852437035143,
    "ci_high": 0.14536570809198895,
    "n": 120,
    "n_instances": 24
   },
   "justified_walk": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 92,
    "n_instances": 23
   },
   "missed_deal": {
    "estimate": 1.0,
    "ci_low": 1.0,
    "ci_high": 1.0,
    "n": 92,
    "n_instances": 23
   },
   "ir_margin_of_no_deal": {
    "estimate": 0.3631886152489443,
    "ci_low": 0.285458998992857,
    "ci_high": 0.43594435365406176,
    "n": 92,
    "n_instances": 23
   }
  }
 },
 "paired_minus_reference": {
  "one_rational": {
   "deal_rate": {
    "estimate": -0.19166666666666668,
    "ci_low": -0.275,
    "ci_high": -0.10833333333333334,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_accept": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 90,
    "n_instances": 24
   },
   "worst_off": {
    "estimate": -0.010511324890106739,
    "ci_low": -0.04255100952906662,
    "ci_high": 0.01971453343067167,
    "n": 90,
    "n_instances": 24
   },
   "worst_off_share": {
    "estimate": -0.004126056934631155,
    "ci_low": -0.01489076831454836,
    "ci_high": 0.00558583432885778,
    "n": 90,
    "n_instances": 24
   },
   "dist_to_nbs": {
    "estimate": -0.04831218602726004,
    "ci_low": -0.13794809667651867,
    "ci_high": 0.04316372862164221,
    "n": 90,
    "n_instances": 24
   },
   "dist_to_ks": {
    "estimate": -0.012480152104404563,
    "ci_low": -0.09722806978288345,
    "ci_high": 0.0704278657761775,
    "n": 90,
    "n_instances": 24
   },
   "normalized_gini": {
    "estimate": 0.004812690536127199,
    "ci_low": -0.015932041148208082,
    "ci_high": 0.025852960756011917,
    "n": 90,
    "n_instances": 24
   },
   "normalized_nash_welfare_conditional": {
    "estimate": -0.023579400570546343,
    "ci_low": -0.06563801328322207,
    "ci_high": 0.013136600902372546,
    "n": 90,
    "n_instances": 24
   },
   "max_share": {
    "estimate": 0.0004958005576147857,
    "ci_low": -0.008701878109738695,
    "ci_high": 0.010019547970605178,
    "n": 90,
    "n_instances": 24
   },
   "below_threshold_episode": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "normalized_primary": {
    "estimate": -0.1861875,
    "ci_low": -0.26643779166666665,
    "ci_high": -0.10526654166666666,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare": {
    "estimate": -0.12428215870749343,
    "ci_low": -0.1881174687529279,
    "ci_high": -0.06526620244080925,
    "n": 120,
    "n_instances": 24
   }
  },
  "rational_advised_llm": {
   "deal_rate": {
    "estimate": -0.058333333333333334,
    "ci_low": -0.15,
    "ci_high": 0.016666666666666666,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_accept": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 105,
    "n_instances": 24
   },
   "worst_off": {
    "estimate": -0.00464881545199529,
    "ci_low": -0.026634591214021192,
    "ci_high": 0.01717447643383272,
    "n": 105,
    "n_instances": 24
   },
   "worst_off_share": {
    "estimate": -0.0016530070612752986,
    "ci_low": -0.00892745106814175,
    "ci_high": 0.005106863959339499,
    "n": 105,
    "n_instances": 24
   },
   "dist_to_nbs": {
    "estimate": 0.01941517414073938,
    "ci_low": -0.02865282114094069,
    "ci_high": 0.0713080376254483,
    "n": 105,
    "n_instances": 24
   },
   "dist_to_ks": {
    "estimate": 0.04359032273774962,
    "ci_low": -0.0026189139167548006,
    "ci_high": 0.09295984703308392,
    "n": 105,
    "n_instances": 24
   },
   "normalized_gini": {
    "estimate": 0.009342265150020847,
    "ci_low": -0.004358675091368589,
    "ci_high": 0.025949767022194647,
    "n": 105,
    "n_instances": 24
   },
   "normalized_nash_welfare_conditional": {
    "estimate": -0.015993210483082845,
    "ci_low": -0.037431826882713536,
    "ci_high": 0.0036075498055912108,
    "n": 105,
    "n_instances": 24
   },
   "max_share": {
    "estimate": 0.002669012637296196,
    "ci_low": -0.0037937167297463544,
    "ci_high": 0.010214984461826006,
    "n": 105,
    "n_instances": 24
   },
   "below_threshold_episode": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "normalized_primary": {
    "estimate": -0.061129166666666665,
    "ci_low": -0.15151179166666667,
    "ci_high": 0.008756312499999959,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare": {
    "estimate": -0.0393862833570429,
    "ci_low": -0.10611192521742131,
    "ci_high": 0.006728622525517536,
    "n": 120,
    "n_instances": 24
   }
  },
  "interpreter_advised_llm": {
   "deal_rate": {
    "estimate": 0.0,
    "ci_low": -0.041666666666666664,
    "ci_high": 0.041666666666666664,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_accept": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 112,
    "n_instances": 24
   },
   "worst_off": {
    "estimate": 0.01145654830300744,
    "ci_low": -0.010629106182177635,
    "ci_high": 0.03377695957784354,
    "n": 112,
    "n_instances": 24
   },
   "worst_off_share": {
    "estimate": 0.004250526761351897,
    "ci_low": -0.0014619983092622733,
    "ci_high": 0.010356071265391944,
    "n": 112,
    "n_instances": 24
   },
   "dist_to_nbs": {
    "estimate": -0.054294185752131977,
    "ci_low": -0.10956784742948435,
    "ci_high": 0.002235473073141924,
    "n": 112,
    "n_instances": 24
   },
   "dist_to_ks": {
    "estimate": -0.04025546359113811,
    "ci_low": -0.09553715401486602,
    "ci_high": 0.014842500553089307,
    "n": 112,
    "n_instances": 24
   },
   "normalized_gini": {
    "estimate": -0.008972828207228474,
    "ci_low": -0.019680807893027587,
    "ci_high": 0.00098349046435619,
    "n": 112,
    "n_instances": 24
   },
   "normalized_nash_welfare_conditional": {
    "estimate": 0.003968466360351362,
    "ci_low": -0.023131591205312392,
    "ci_high": 0.032620345158022604,
    "n": 112,
    "n_instances": 24
   },
   "max_share": {
    "estimate": -0.003043165801135127,
    "ci_low": -0.008643120823579197,
    "ci_high": 0.0022101511191889053,
    "n": 112,
    "n_instances": 24
   },
   "below_threshold_episode": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "normalized_primary": {
    "estimate": 0.008216666666666662,
    "ci_low": -0.03374610416666667,
    "ci_high": 0.05001624999999998,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare": {
    "estimate": 0.00749307367470356,
    "ci_low": -0.030863249039173733,
    "ci_high": 0.045147945492322906,
    "n": 120,
    "n_instances": 24
   }
  },
  "one_oracle": {
   "deal_rate": {
    "estimate": -0.041666666666666664,
    "ci_low": -0.1,
    "ci_high": 0.016666666666666666,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_accept": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 106,
    "n_instances": 24
   },
   "worst_off": {
    "estimate": -0.060353359738015915,
    "ci_low": -0.09190831217851632,
    "ci_high": -0.032578306440117596,
    "n": 106,
    "n_instances": 24
   },
   "worst_off_share": {
    "estimate": -0.019779060194180596,
    "ci_low": -0.030084545903446114,
    "ci_high": -0.010778549683334148,
    "n": 106,
    "n_instances": 24
   },
   "dist_to_nbs": {
    "estimate": 0.07863394787826475,
    "ci_low": 0.01669954706738832,
    "ci_high": 0.1480875448636908,
    "n": 106,
    "n_instances": 24
   },
   "dist_to_ks": {
    "estimate": 0.11593008594127932,
    "ci_low": 0.058852865312676125,
    "ci_high": 0.18001911948634597,
    "n": 106,
    "n_instances": 24
   },
   "normalized_gini": {
    "estimate": 0.04315785119943256,
    "ci_low": 0.024882836462547214,
    "ci_high": 0.0649122647011516,
    "n": 106,
    "n_instances": 24
   },
   "normalized_nash_welfare_conditional": {
    "estimate": -0.06904703502676467,
    "ci_low": -0.1093050041756435,
    "ci_high": -0.03557335786698785,
    "n": 106,
    "n_instances": 24
   },
   "max_share": {
    "estimate": 0.01533983365562051,
    "ci_low": 0.005321301460913957,
    "ci_high": 0.02748847288975931,
    "n": 106,
    "n_instances": 24
   },
   "below_threshold_episode": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "normalized_primary": {
    "estimate": -0.04375,
    "ci_low": -0.10367291666666667,
    "ci_high": 0.011113687499999988,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare": {
    "estimate": -0.0796368017641982,
    "ci_low": -0.12526255729605248,
    "ci_high": -0.03517473375957656,
    "n": 120,
    "n_instances": 24
   }
  },
  "all_oracle": {
   "deal_rate": {
    "estimate": 0.041666666666666664,
    "ci_low": 0.016666666666666666,
    "ci_high": 0.075,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_accept": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 115,
    "n_instances": 24
   },
   "worst_off": {
    "estimate": -0.08624554900577996,
    "ci_low": -0.1301636097600051,
    "ci_high": -0.043191500345152935,
    "n": 115,
    "n_instances": 24
   },
   "worst_off_share": {
    "estimate": -0.027861756178209657,
    "ci_low": -0.04176987344709631,
    "ci_high": -0.014555207275477601,
    "n": 115,
    "n_instances": 24
   },
   "dist_to_nbs": {
    "estimate": 0.15760131955439596,
    "ci_low": 0.07086603722462605,
    "ci_high": 0.24699228344281388,
    "n": 115,
    "n_instances": 24
   },
   "dist_to_ks": {
    "estimate": 0.15904260849844643,
    "ci_low": 0.06921494352147542,
    "ci_high": 0.2508546724888472,
    "n": 115,
    "n_instances": 24
   },
   "normalized_gini": {
    "estimate": 0.06112756545726602,
    "ci_low": 0.03390620327542516,
    "ci_high": 0.09087218067170595,
    "n": 115,
    "n_instances": 24
   },
   "normalized_nash_welfare_conditional": {
    "estimate": -0.12385867449133948,
    "ci_low": -0.19027316875223715,
    "ci_high": -0.06310749067699663,
    "n": 115,
    "n_instances": 24
   },
   "max_share": {
    "estimate": 0.020426943872637302,
    "ci_low": 0.007245650571591523,
    "ci_high": 0.03540837667874271,
    "n": 115,
    "n_instances": 24
   },
   "below_threshold_episode": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "normalized_primary": {
    "estimate": 0.034244166666666666,
    "ci_low": 0.0005016458333333306,
    "ci_high": 0.07396099999999999,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare": {
    "estimate": -0.10692405250440208,
    "ci_low": -0.17085581229852825,
    "ci_high": -0.04829424362115885,
    "n": 120,
    "n_instances": 24
   }
  },
  "all_rational": {
   "deal_rate": {
    "estimate": -0.725,
    "ci_low": -0.8333333333333334,
    "ci_high": -0.6083333333333333,
    "n": 120,
    "n_instances": 24
   },
   "below_threshold_accept": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 28,
    "n_instances": 14
   },
   "worst_off": {
    "estimate": -0.09601933058200689,
    "ci_low": -0.16342573048294362,
    "ci_high": -0.02434925865025404,
    "n": 28,
    "n_instances": 14
   },
   "worst_off_share": {
    "estimate": -0.028237270199012482,
    "ci_low": -0.050840661409651454,
    "ci_high": -0.005457447313703002,
    "n": 28,
    "n_instances": 14
   },
   "dist_to_nbs": {
    "estimate": 0.07613537727454613,
    "ci_low": -0.07889226696044642,
    "ci_high": 0.25444127895741897,
    "n": 28,
    "n_instances": 14
   },
   "dist_to_ks": {
    "estimate": 0.11884514841560789,
    "ci_low": -0.0242248928566769,
    "ci_high": 0.29540419783091426,
    "n": 28,
    "n_instances": 14
   },
   "normalized_gini": {
    "estimate": 0.03064648220408337,
    "ci_low": -0.00347122701135036,
    "ci_high": 0.06831991844975267,
    "n": 28,
    "n_instances": 14
   },
   "normalized_nash_welfare_conditional": {
    "estimate": -0.10288294566010638,
    "ci_low": -0.19600908216423008,
    "ci_high": -0.026211589200274752,
    "n": 28,
    "n_instances": 14
   },
   "max_share": {
    "estimate": 0.006212406645721159,
    "ci_low": -0.012709316362332234,
    "ci_high": 0.022257993484733837,
    "n": 28,
    "n_instances": 14
   },
   "below_threshold_episode": {
    "estimate": 0.0,
    "ci_low": 0.0,
    "ci_high": 0.0,
    "n": 120,
    "n_instances": 24
   },
   "normalized_primary": {
    "estimate": -0.6837549999999999,
    "ci_low": -0.7854839166666666,
    "ci_high": -0.5802898958333333,
    "n": 120,
    "n_instances": 24
   },
   "normalized_nash_welfare": {
    "estimate": -0.4172928402891551,
    "ci_low": -0.5090030332324634,
    "ci_high": -0.328382894266642,
    "n": 120,
    "n_instances": 24
   }
  }
 },
 "all_instances_feasible": true,
 "instance_geometry": [
  {
   "instance_id": "scorable_negotiation-L4-faf2ca7d47",
   "difficulty_scalar": 0.694187,
   "difficulty_tags": "hard;no-clear-win-win;pivotal-seat;small-frontier",
   "n_deals": 256,
   "n_ir_deals": 5,
   "feasible_all_ir": true,
   "ir_margin": 0.0
  },
  {
   "instance_id": "scorable_negotiation-L4-712ba36a4f",
   "difficulty_scalar": 0.706191,
   "difficulty_tags": "hard;no-clear-win-win;pivotal-seat",
   "n_deals": 256,
   "n_ir_deals": 4,
   "feasible_all_ir": true,
   "ir_margin": 0.0
  },
  {
   "instance_id": "scorable_negotiation-L3-9a673abad3",
   "difficulty_scalar": 0.699699,
   "difficulty_tags": "hard;high-conflict;pivotal-seat",
   "n_deals": 256,
   "n_ir_deals": 9,
   "feasible_all_ir": true,
   "ir_margin": 0.08620689655172414
  },
  {
   "instance_id": "scorable_negotiation-L3-9a1b1c0960",
   "difficulty_scalar": 0.689368,
   "difficulty_tags": "hard;pivotal-seat",
   "n_deals": 256,
   "n_ir_deals": 8,
   "feasible_all_ir": true,
   "ir_margin": 0.18421052631578946
  },
  {
   "instance_id": "scorable_negotiation-L2-103cef6017",
   "difficulty_scalar": 0.638165,
   "difficulty_tags": "medium;small-frontier",
   "n_deals": 256,
   "n_ir_deals": 15,
   "feasible_all_ir": true,
   "ir_margin": 0.2692307692307692
  },
  {
   "instance_id": "scorable_negotiation-L2-1fc37540c8",
   "difficulty_scalar": 0.676476,
   "difficulty_tags": "high-conflict;large-frontier;medium;no-clear-win-win",
   "n_deals": 256,
   "n_ir_deals": 17,
   "feasible_all_ir": true,
   "ir_margin": 0.3103448275862069
  },
  {
   "instance_id": "scorable_negotiation-L0-32200851b2",
   "difficulty_scalar": 0.562257,
   "difficulty_tags": "easy;high-conflict",
   "n_deals": 256,
   "n_ir_deals": 47,
   "feasible_all_ir": true,
   "ir_margin": 0.32926829268292684
  },
  {
   "instance_id": "scorable_negotiation-L1-996daa4124",
   "difficulty_scalar": 0.61343,
   "difficulty_tags": "easy;large-frontier",
   "n_deals": 256,
   "n_ir_deals": 22,
   "feasible_all_ir": true,
   "ir_margin": 0.3333333333333333
  },
  {
   "instance_id": "scorable_negotiation-L4-d49e5fe070",
   "difficulty_scalar": 0.672467,
   "difficulty_tags": "medium;small-frontier",
   "n_deals": 256,
   "n_ir_deals": 5,
   "feasible_all_ir": true,
   "ir_margin": 0.36
  },
  {
   "instance_id": "scorable_negotiation-L0-611ee402f7",
   "difficulty_scalar": 0.55854,
   "difficulty_tags": "easy",
   "n_deals": 256,
   "n_ir_deals": 43,
   "feasible_all_ir": true,
   "ir_margin": 0.417910447761194
  },
  {
   "instance_id": "scorable_negotiation-L2-df1e479b72",
   "difficulty_scalar": 0.63001,
   "difficulty_tags": "medium;small-frontier",
   "n_deals": 256,
   "n_ir_deals": 21,
   "feasible_all_ir": true,
   "ir_margin": 0.43103448275862066
  },
  {
   "instance_id": "scorable_negotiation-L3-a8641f6c33",
   "difficulty_scalar": 0.651538,
   "difficulty_tags": "medium;small-frontier",
   "n_deals": 256,
   "n_ir_deals": 8,
   "feasible_all_ir": true,
   "ir_margin": 0.43333333333333335
  },
  {
   "instance_id": "scorable_negotiation-L1-19dae4b672",
   "difficulty_scalar": 0.62258,
   "difficulty_tags": "high-conflict;medium",
   "n_deals": 256,
   "n_ir_deals": 27,
   "feasible_all_ir": true,
   "ir_margin": 0.4387755102040816
  },
  {
   "instance_id": "scorable_negotiation-L0-65113008ad",
   "difficulty_scalar": 0.624796,
   "difficulty_tags": "medium",
   "n_deals": 256,
   "n_ir_deals": 29,
   "feasible_all_ir": true,
   "ir_margin": 0.43902439024390244
  },
  {
   "instance_id": "scorable_negotiation-L0-34733a57e6",
   "difficulty_scalar": 0.561029,
   "difficulty_tags": "easy;large-frontier",
   "n_deals": 256,
   "n_ir_deals": 45,
   "feasible_all_ir": true,
   "ir_margin": 0.4523809523809524
  },
  {
   "instance_id": "scorable_negotiation-L2-adac68f4ac",
   "difficulty_scalar": 0.642993,
   "difficulty_tags": "large-frontier;medium",
   "n_deals": 256,
   "n_ir_deals": 17,
   "feasible_all_ir": true,
   "ir_margin": 0.4666666666666667
  },
  {
   "instance_id": "scorable_negotiation-L2-0aa50f7b83",
   "difficulty_scalar": 0.679768,
   "difficulty_tags": "hard;high-conflict;large-frontier;no-clear-win-win",
   "n_deals": 256,
   "n_ir_deals": 14,
   "feasible_all_ir": true,
   "ir_margin": 0.46875
  },
  {
   "instance_id": "scorable_negotiation-L0-a483b0d80d",
   "difficulty_scalar": 0.546303,
   "difficulty_tags": "easy",
   "n_deals": 256,
   "n_ir_deals": 40,
   "feasible_all_ir": true,
   "ir_margin": 0.4727272727272727
  },
  {
   "instance_id": "scorable_negotiation-L1-a9097927ce",
   "difficulty_scalar": 0.551691,
   "difficulty_tags": "easy",
   "n_deals": 256,
   "n_ir_deals": 37,
   "feasible_all_ir": true,
   "ir_margin": 0.4827586206896552
  },
  {
   "instance_id": "scorable_negotiation-L4-8a29217702",
   "difficulty_scalar": 0.68927,
   "difficulty_tags": "hard;high-conflict;no-clear-win-win;small-frontier",
   "n_deals": 256,
   "n_ir_deals": 4,
   "feasible_all_ir": true,
   "ir_margin": 0.49122807017543857
  },
  {
   "instance_id": "scorable_negotiation-L3-46e1252af7",
   "difficulty_scalar": 0.684076,
   "difficulty_tags": "hard;pivotal-seat",
   "n_deals": 256,
   "n_ir_deals": 8,
   "feasible_all_ir": true,
   "ir_margin": 0.49230769230769234
  },
  {
   "instance_id": "scorable_negotiation-L1-aabb4d986b",
   "difficulty_scalar": 0.614162,
   "difficulty_tags": "easy",
   "n_deals": 256,
   "n_ir_deals": 22,
   "feasible_all_ir": true,
   "ir_margin": 0.4959349593495935
  },
  {
   "instance_id": "scorable_negotiation-L1-282034699c",
   "difficulty_scalar": 0.600081,
   "difficulty_tags": "easy;large-frontier",
   "n_deals": 256,
   "n_ir_deals": 27,
   "feasible_all_ir": true,
   "ir_margin": 0.55
  },
  {
   "instance_id": "scorable_negotiation-L3-d9a0ef3c04",
   "difficulty_scalar": 0.7161,
   "difficulty_tags": "hard;no-clear-win-win;pivotal-seat",
   "n_deals": 256,
   "n_ir_deals": 5,
   "feasible_all_ir": true,
   "ir_margin": 0.651685393258427
  }
 ],
 "bank_margin_by_tag": {
  "easy": {
   "n_instances": 8,
   "mean_ir_margin": 0.44178923486561605,
   "min_ir_margin": 0.32926829268292684
  },
  "hard": {
   "n_instances": 8,
   "mean_ir_margin": 0.29679857232613394,
   "min_ir_margin": 0.0
  },
  "high-conflict": {
   "n_instances": 6,
   "mean_ir_margin": 0.35409559953339637,
   "min_ir_margin": 0.08620689655172414
  },
  "large-frontier": {
   "n_instances": 6,
   "mean_ir_margin": 0.4302459633278599,
   "min_ir_margin": 0.3103448275862069
  },
  "medium": {
   "n_instances": 8,
   "mean_ir_margin": 0.3935512475029476,
   "min_ir_margin": 0.2692307692307692
  },
  "no-clear-win-win": {
   "n_instances": 6,
   "mean_ir_margin": 0.32033471517001205,
   "min_ir_margin": 0.0
  },
  "pivotal-seat": {
   "n_instances": 6,
   "mean_ir_margin": 0.2357350847389388,
   "min_ir_margin": 0.0
  },
  "small-frontier": {
   "n_instances": 6,
   "mean_ir_margin": 0.330804442583027,
   "min_ir_margin": 0.0
  }
 },
 "walk_by_tag": {
  "all_llm": {
   "easy": {
    "n_no_deal": 2,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.44166666666666665
   },
   "hard": {
    "n_no_deal": 2,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.0
   },
   "high-conflict": {
    "n_no_deal": 0,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": NaN
   },
   "large-frontier": {
    "n_no_deal": 2,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.44166666666666665
   },
   "medium": {
    "n_no_deal": 1,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.2692307692307692
   },
   "no-clear-win-win": {
    "n_no_deal": 2,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.0
   },
   "pivotal-seat": {
    "n_no_deal": 2,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.0
   },
   "small-frontier": {
    "n_no_deal": 2,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.1346153846153846
   }
  },
  "one_rational": {
   "easy": {
    "n_no_deal": 6,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.411338766538169
   },
   "hard": {
    "n_no_deal": 16,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.27746280363555487
   },
   "high-conflict": {
    "n_no_deal": 6,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.3254813710228754
   },
   "large-frontier": {
    "n_no_deal": 7,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.4438350340136055
   },
   "medium": {
    "n_no_deal": 6,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.4505653677226427
   },
   "no-clear-win-win": {
    "n_no_deal": 11,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.30966021092055984
   },
   "pivotal-seat": {
    "n_no_deal": 13,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.22986143983215387
   },
   "small-frontier": {
    "n_no_deal": 6,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.3078039927404718
   }
  },
  "rational_advised_llm": {
   "easy": {
    "n_no_deal": 1,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.32926829268292684
   },
   "hard": {
    "n_no_deal": 9,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.21832358674463936
   },
   "high-conflict": {
    "n_no_deal": 6,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.4340875668284814
   },
   "large-frontier": {
    "n_no_deal": 2,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.3885057471264368
   },
   "medium": {
    "n_no_deal": 2,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.3885057471264368
   },
   "no-clear-win-win": {
    "n_no_deal": 10,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.2275257108287961
   },
   "pivotal-seat": {
    "n_no_deal": 5,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.0
   },
   "small-frontier": {
    "n_no_deal": 6,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.32748538011695905
   }
  },
  "interpreter_advised_llm": {
   "easy": {
    "n_no_deal": 0,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": NaN
   },
   "hard": {
    "n_no_deal": 4,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.1171875
   },
   "high-conflict": {
    "n_no_deal": 1,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.46875
   },
   "large-frontier": {
    "n_no_deal": 1,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.46875
   },
   "medium": {
    "n_no_deal": 1,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.36
   },
   "no-clear-win-win": {
    "n_no_deal": 4,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.1171875
   },
   "pivotal-seat": {
    "n_no_deal": 3,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.0
   },
   "small-frontier": {
    "n_no_deal": 2,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.18
   }
  },
  "one_oracle": {
   "easy": {
    "n_no_deal": 2,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.4351457000710732
   },
   "hard": {
    "n_no_deal": 5,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.03684210526315789
   },
   "high-conflict": {
    "n_no_deal": 1,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.4387755102040816
   },
   "large-frontier": {
    "n_no_deal": 2,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.45952380952380956
   },
   "medium": {
    "n_no_deal": 3,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.4454922198764564
   },
   "no-clear-win-win": {
    "n_no_deal": 4,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.0
   },
   "pivotal-seat": {
    "n_no_deal": 5,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.03684210526315789
   },
   "small-frontier": {
    "n_no_deal": 2,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.21551724137931033
   }
  },
  "all_oracle": {
   "easy": {
    "n_no_deal": 0,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": NaN
   },
   "hard": {
    "n_no_deal": 0,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": NaN
   },
   "high-conflict": {
    "n_no_deal": 0,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": NaN
   },
   "large-frontier": {
    "n_no_deal": 0,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": NaN
   },
   "medium": {
    "n_no_deal": 0,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": NaN
   },
   "no-clear-win-win": {
    "n_no_deal": 0,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": NaN
   },
   "pivotal-seat": {
    "n_no_deal": 0,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": NaN
   },
   "small-frontier": {
    "n_no_deal": 0,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": NaN
   }
  },
  "all_rational": {
   "easy": {
    "n_no_deal": 20,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.42783676535022835
   },
   "hard": {
    "n_no_deal": 39,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.30440879212936817
   },
   "high-conflict": {
    "n_no_deal": 26,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.3544311947248365
   },
   "large-frontier": {
    "n_no_deal": 22,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.42616388640095537
   },
   "medium": {
    "n_no_deal": 33,
    "n_episodes": 40,
    "justified_walks": 0,
    "mean_ir_margin": 0.39347498190463465
   },
   "no-clear-win-win": {
    "n_no_deal": 28,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.3321320224112198
   },
   "pivotal-seat": {
    "n_no_deal": 29,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.2438638807644195
   },
   "small-frontier": {
    "n_no_deal": 26,
    "n_episodes": 30,
    "justified_walks": 0,
    "mean_ir_margin": 0.32134240416384774
   }
  }
 },
 "margin_vs_no_deal_rate": {
  "all_llm": {
   "pearson_r": -0.46490335738860106,
   "ci_low": -0.8231415110480709,
   "ci_high": 0.08922968287703967,
   "n_instances": 24
  },
  "one_rational": {
   "pearson_r": -0.2492323190001127,
   "ci_low": -0.6984654747678015,
   "ci_high": 0.3083499966431045,
   "n_instances": 24
  },
  "rational_advised_llm": {
   "pearson_r": -0.3600032700086261,
   "ci_low": -0.8481456363867811,
   "ci_high": 0.1835409039145551,
   "n_instances": 24
  },
  "interpreter_advised_llm": {
   "pearson_r": -0.5460208528683343,
   "ci_low": -0.8154702739866616,
   "ci_high": 0.10560649031965162,
   "n_instances": 24
  },
  "one_oracle": {
   "pearson_r": -0.5063334214207315,
   "ci_low": -0.7823223392128961,
   "ci_high": 0.09759928568247297,
   "n_instances": 24
  },
  "all_oracle": {
   "pearson_r": NaN,
   "ci_low": null,
   "ci_high": null,
   "n_instances": 24
  },
  "all_rational": {
   "pearson_r": -0.25578659513352464,
   "ci_low": -0.544670415394607,
   "ci_high": 0.08202613376003876,
   "n_instances": 24
  }
 },
 "paired_strata": {
  "one_rational": {
   "easy": {
    "deal_rate": {
     "estimate": -0.1,
     "ci_low": -0.225,
     "ci_high": 0.025,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": -0.09625499999999998,
     "ci_low": -0.196425,
     "ci_high": 0.02597250000000001,
     "n": 40,
     "n_instances": 8
    }
   },
   "hard": {
    "deal_rate": {
     "estimate": -0.35,
     "ci_low": -0.45,
     "ci_high": -0.275,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": -0.3424175,
     "ci_low": -0.43495249999999996,
     "ci_high": -0.26295250000000003,
     "n": 40,
     "n_instances": 8
    }
   },
   "high-conflict": {
    "deal_rate": {
     "estimate": -0.2,
     "ci_low": -0.3333333333333333,
     "ci_high": -0.06666666666666667,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.21954333333333334,
     "ci_low": -0.32718,
     "ci_high": -0.10647666666666668,
     "n": 30,
     "n_instances": 6
    }
   },
   "large-frontier": {
    "deal_rate": {
     "estimate": -0.16666666666666666,
     "ci_low": -0.4,
     "ci_high": 0.03333333333333333,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.14880666666666667,
     "ci_low": -0.35865,
     "ci_high": 0.05763333333333332,
     "n": 30,
     "n_instances": 6
    }
   },
   "medium": {
    "deal_rate": {
     "estimate": -0.125,
     "ci_low": -0.275,
     "ci_high": 0.025,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": -0.11989000000000001,
     "ci_low": -0.27352231250000003,
     "ci_high": 0.009767500000000004,
     "n": 40,
     "n_instances": 8
    }
   },
   "no-clear-win-win": {
    "deal_rate": {
     "estimate": -0.3,
     "ci_low": -0.4666666666666667,
     "ci_high": -0.13333333333333333,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.30536333333333343,
     "ci_low": -0.4659666666666666,
     "ci_high": -0.15264025000000142,
     "n": 30,
     "n_instances": 6
    }
   },
   "pivotal-seat": {
    "deal_rate": {
     "estimate": -0.36666666666666664,
     "ci_low": -0.4666666666666667,
     "ci_high": -0.26666666666666666,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.35567333333333345,
     "ci_low": -0.46526666666666655,
     "ci_high": -0.26089666666666667,
     "n": 30,
     "n_instances": 6
    }
   },
   "small-frontier": {
    "deal_rate": {
     "estimate": -0.13333333333333333,
     "ci_low": -0.26666666666666666,
     "ci_high": 0.03333333333333333,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.13011999999999999,
     "ci_low": -0.26954,
     "ci_high": 0.020370000000000017,
     "n": 30,
     "n_instances": 6
    }
   }
  },
  "rational_advised_llm": {
   "easy": {
    "deal_rate": {
     "estimate": 0.025,
     "ci_low": -0.05,
     "ci_high": 0.1,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": 0.016370000000000003,
     "ci_low": -0.057419999999999985,
     "ci_high": 0.09564237499999999,
     "n": 40,
     "n_instances": 8
    }
   },
   "hard": {
    "deal_rate": {
     "estimate": -0.175,
     "ci_low": -0.375,
     "ci_high": -0.025,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": -0.17596499999999998,
     "ci_low": -0.38692843749999994,
     "ci_high": -0.017077500000000006,
     "n": 40,
     "n_instances": 8
    }
   },
   "high-conflict": {
    "deal_rate": {
     "estimate": -0.2,
     "ci_low": -0.4666666666666667,
     "ci_high": -0.03333333333333333,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.19425,
     "ci_low": -0.45588666666666666,
     "ci_high": -0.031279999999999995,
     "n": 30,
     "n_instances": 6
    }
   },
   "large-frontier": {
    "deal_rate": {
     "estimate": 0.0,
     "ci_low": -0.13333333333333333,
     "ci_high": 0.13333333333333333,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.004086666666666665,
     "ci_low": -0.11720333333333333,
     "ci_high": 0.10984,
     "n": 30,
     "n_instances": 6
    }
   },
   "medium": {
    "deal_rate": {
     "estimate": -0.025,
     "ci_low": -0.1,
     "ci_high": 0.05,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": -0.023792499999999994,
     "ci_low": -0.09841725,
     "ci_high": 0.051324999999999996,
     "n": 40,
     "n_instances": 8
    }
   },
   "no-clear-win-win": {
    "deal_rate": {
     "estimate": -0.26666666666666666,
     "ci_low": -0.5,
     "ci_high": -0.06666666666666667,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.27221000000000006,
     "ci_low": -0.4963033333333333,
     "ci_high": -0.08727333333333336,
     "n": 30,
     "n_instances": 6
    }
   },
   "pivotal-seat": {
    "deal_rate": {
     "estimate": -0.1,
     "ci_low": -0.23333333333333334,
     "ci_high": 0.0,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.10128666666666668,
     "ci_low": -0.22857333333333335,
     "ci_high": 0.001906666666666664,
     "n": 30,
     "n_instances": 6
    }
   },
   "small-frontier": {
    "deal_rate": {
     "estimate": -0.13333333333333333,
     "ci_low": -0.43333333333333335,
     "ci_high": 0.06666666666666667,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.1428133333333333,
     "ci_low": -0.42613333333333336,
     "ci_high": 0.058336666666666676,
     "n": 30,
     "n_instances": 6
    }
   }
  },
  "interpreter_advised_llm": {
   "easy": {
    "deal_rate": {
     "estimate": 0.05,
     "ci_low": 0.0,
     "ci_high": 0.125,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": 0.06315000000000001,
     "ci_low": 0.009039375000000004,
     "ci_high": 0.131635,
     "n": 40,
     "n_instances": 8
    }
   },
   "hard": {
    "deal_rate": {
     "estimate": -0.05,
     "ci_low": -0.125,
     "ci_high": 0.0,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": -0.0423225,
     "ci_low": -0.1108401875,
     "ci_high": 0.018985000000000005,
     "n": 40,
     "n_instances": 8
    }
   },
   "high-conflict": {
    "deal_rate": {
     "estimate": -0.03333333333333333,
     "ci_low": -0.1,
     "ci_high": 0.0,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.022353333333333343,
     "ci_low": -0.08896333333333332,
     "ci_high": 0.022286666666666656,
     "n": 30,
     "n_instances": 6
    }
   },
   "large-frontier": {
    "deal_rate": {
     "estimate": 0.03333333333333333,
     "ci_low": -0.06666666666666667,
     "ci_high": 0.13333333333333333,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": 0.04089666666666668,
     "ci_low": -0.06405000000000001,
     "ci_high": 0.1519333333333333,
     "n": 30,
     "n_instances": 6
    }
   },
   "medium": {
    "deal_rate": {
     "estimate": 0.0,
     "ci_low": -0.075,
     "ci_high": 0.075,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": 0.003822500000000001,
     "ci_low": -0.07040325,
     "ci_high": 0.0751875,
     "n": 40,
     "n_instances": 8
    }
   },
   "no-clear-win-win": {
    "deal_rate": {
     "estimate": -0.06666666666666667,
     "ci_low": -0.13333333333333333,
     "ci_high": 0.0,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.05902666666666668,
     "ci_low": -0.13702333333333333,
     "ci_high": 0.014743333333333337,
     "n": 30,
     "n_instances": 6
    }
   },
   "pivotal-seat": {
    "deal_rate": {
     "estimate": -0.03333333333333333,
     "ci_low": -0.1,
     "ci_high": 0.0,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.026766666666666668,
     "ci_low": -0.10735,
     "ci_high": 0.03741666666666667,
     "n": 30,
     "n_instances": 6
    }
   },
   "small-frontier": {
    "deal_rate": {
     "estimate": 0.0,
     "ci_low": -0.1,
     "ci_high": 0.1,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": 0.01621666666666667,
     "ci_low": -0.08424999999999999,
     "ci_high": 0.10593000000000001,
     "n": 30,
     "n_instances": 6
    }
   }
  },
  "one_oracle": {
   "easy": {
    "deal_rate": {
     "estimate": 0.0,
     "ci_low": -0.1,
     "ci_high": 0.1,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": -0.0034524999999999916,
     "ci_low": -0.09551056249999999,
     "ci_high": 0.09538250000000001,
     "n": 40,
     "n_instances": 8
    }
   },
   "hard": {
    "deal_rate": {
     "estimate": -0.075,
     "ci_low": -0.175,
     "ci_high": 0.0,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": -0.08085500000000001,
     "ci_low": -0.1945621875,
     "ci_high": 0.004245000000000001,
     "n": 40,
     "n_instances": 8
    }
   },
   "high-conflict": {
    "deal_rate": {
     "estimate": -0.03333333333333333,
     "ci_low": -0.1,
     "ci_high": 0.0,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.035946666666666675,
     "ci_low": -0.12113,
     "ci_high": 0.01865999999999999,
     "n": 30,
     "n_instances": 6
    }
   },
   "large-frontier": {
    "deal_rate": {
     "estimate": 0.0,
     "ci_low": -0.13333333333333333,
     "ci_high": 0.13333333333333333,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.006763333333333343,
     "ci_low": -0.11209333333333334,
     "ci_high": 0.11117333333333332,
     "n": 30,
     "n_instances": 6
    }
   },
   "medium": {
    "deal_rate": {
     "estimate": -0.05,
     "ci_low": -0.15,
     "ci_high": 0.05,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": -0.04694250000000001,
     "ci_low": -0.13748962500000003,
     "ci_high": 0.04340893749999998,
     "n": 40,
     "n_instances": 8
    }
   },
   "no-clear-win-win": {
    "deal_rate": {
     "estimate": -0.06666666666666667,
     "ci_low": -0.2,
     "ci_high": 0.0,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.06049666666666666,
     "ci_low": -0.19883,
     "ci_high": 0.014943333333333335,
     "n": 30,
     "n_instances": 6
    }
   },
   "pivotal-seat": {
    "deal_rate": {
     "estimate": -0.1,
     "ci_low": -0.23333333333333334,
     "ci_high": 0.0,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.10819666666666668,
     "ci_low": -0.24239,
     "ci_high": 0.005270000000000005,
     "n": 30,
     "n_instances": 6
    }
   },
   "small-frontier": {
    "deal_rate": {
     "estimate": 0.0,
     "ci_low": -0.1,
     "ci_high": 0.1,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": 0.012919999999999994,
     "ci_low": -0.07715333333333332,
     "ci_high": 0.09570333333333333,
     "n": 30,
     "n_instances": 6
    }
   }
  },
  "all_oracle": {
   "easy": {
    "deal_rate": {
     "estimate": 0.05,
     "ci_low": 0.0,
     "ci_high": 0.125,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": 0.016247500000000015,
     "ci_low": -0.028757499999999984,
     "ci_high": 0.06480250000000001,
     "n": 40,
     "n_instances": 8
    }
   },
   "hard": {
    "deal_rate": {
     "estimate": 0.05,
     "ci_low": 0.0,
     "ci_high": 0.125,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": 0.0649325,
     "ci_low": -0.0057200000000000055,
     "ci_high": 0.1556151875,
     "n": 40,
     "n_instances": 8
    }
   },
   "high-conflict": {
    "deal_rate": {
     "estimate": 0.0,
     "ci_low": 0.0,
     "ci_high": 0.0,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.02970666666666667,
     "ci_low": -0.06442666666666667,
     "ci_high": 0.01284333333333334,
     "n": 30,
     "n_instances": 6
    }
   },
   "large-frontier": {
    "deal_rate": {
     "estimate": 0.06666666666666667,
     "ci_low": 0.0,
     "ci_high": 0.13333333333333333,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": 0.04246666666666666,
     "ci_low": -0.014473333333333338,
     "ci_high": 0.09363666666666666,
     "n": 30,
     "n_instances": 6
    }
   },
   "medium": {
    "deal_rate": {
     "estimate": 0.025,
     "ci_low": 0.0,
     "ci_high": 0.075,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": 0.021552500000000002,
     "ci_low": -0.023887749999999996,
     "ci_high": 0.07073937499999998,
     "n": 40,
     "n_instances": 8
    }
   },
   "no-clear-win-win": {
    "deal_rate": {
     "estimate": 0.06666666666666667,
     "ci_low": 0.0,
     "ci_high": 0.13333333333333333,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": 0.08198333333333334,
     "ci_low": -0.016203333333333337,
     "ci_high": 0.1965866666666667,
     "n": 30,
     "n_instances": 6
    }
   },
   "pivotal-seat": {
    "deal_rate": {
     "estimate": 0.06666666666666667,
     "ci_low": 0.0,
     "ci_high": 0.13333333333333333,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": 0.07603666666666667,
     "ci_low": -0.016820000000000012,
     "ci_high": 0.19633666666666666,
     "n": 30,
     "n_instances": 6
    }
   },
   "small-frontier": {
    "deal_rate": {
     "estimate": 0.06666666666666667,
     "ci_low": 0.0,
     "ci_high": 0.13333333333333333,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": 0.08898000000000002,
     "ci_low": 0.005826666666666673,
     "ci_high": 0.19663666666666663,
     "n": 30,
     "n_instances": 6
    }
   }
  },
  "all_rational": {
   "easy": {
    "deal_rate": {
     "estimate": -0.45,
     "ci_low": -0.6,
     "ci_high": -0.275,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": -0.4468375,
     "ci_low": -0.5676945625,
     "ci_high": -0.32726999999999995,
     "n": 40,
     "n_instances": 8
    }
   },
   "hard": {
    "deal_rate": {
     "estimate": -0.925,
     "ci_low": -1.0,
     "ci_high": -0.825,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": -0.8691524999999999,
     "ci_low": -0.95555,
     "ci_high": -0.76901,
     "n": 40,
     "n_instances": 8
    }
   },
   "high-conflict": {
    "deal_rate": {
     "estimate": -0.8666666666666667,
     "ci_low": -0.9666666666666667,
     "ci_high": -0.7333333333333333,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.81754,
     "ci_low": -0.9271,
     "ci_high": -0.69025,
     "n": 30,
     "n_instances": 6
    }
   },
   "large-frontier": {
    "deal_rate": {
     "estimate": -0.6666666666666666,
     "ci_low": -0.9,
     "ci_high": -0.43333333333333335,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.6466466666666668,
     "ci_low": -0.8229299999999999,
     "ci_high": -0.45602525,
     "n": 30,
     "n_instances": 6
    }
   },
   "medium": {
    "deal_rate": {
     "estimate": -0.8,
     "ci_low": -0.925,
     "ci_high": -0.65,
     "n": 40,
     "n_instances": 8
    },
    "normalized_primary": {
     "estimate": -0.735275,
     "ci_low": -0.88693675,
     "ci_high": -0.5521585625000002,
     "n": 40,
     "n_instances": 8
    }
   },
   "no-clear-win-win": {
    "deal_rate": {
     "estimate": -0.8666666666666667,
     "ci_low": -0.9666666666666667,
     "ci_high": -0.7333333333333333,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.8241600000000001,
     "ci_low": -0.9412400000000001,
     "ci_high": -0.7067300000000001,
     "n": 30,
     "n_instances": 6
    }
   },
   "pivotal-seat": {
    "deal_rate": {
     "estimate": -0.9,
     "ci_low": -1.0,
     "ci_high": -0.7666666666666667,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.8493233333333333,
     "ci_low": -0.9584166666666666,
     "ci_high": -0.7356533333333334,
     "n": 30,
     "n_instances": 6
    }
   },
   "small-frontier": {
    "deal_rate": {
     "estimate": -0.8,
     "ci_low": -0.9666666666666667,
     "ci_high": -0.6,
     "n": 30,
     "n_instances": 6
    },
    "normalized_primary": {
     "estimate": -0.7377333333333334,
     "ci_low": -0.9399466666666666,
     "ci_high": -0.4833066666666666,
     "n": 30,
     "n_instances": 6
    }
   }
  }
 },
 "no_deal_scatter": {
  "all_llm": [
   [
    0.0,
    0.2
   ],
   [
    0.0,
    0.2
   ],
   [
    0.08620689655172414,
    0.0
   ],
   [
    0.18421052631578946,
    0.0
   ],
   [
    0.2692307692307692,
    0.2
   ],
   [
    0.3103448275862069,
    0.0
   ],
   [
    0.32926829268292684,
    0.0
   ],
   [
    0.3333333333333333,
    0.2
   ],
   [
    0.36,
    0.0
   ],
   [
    0.417910447761194,
    0.0
   ],
   [
    0.43103448275862066,
    0.0
   ],
   [
    0.43333333333333335,
    0.0
   ],
   [
    0.4387755102040816,
    0.0
   ],
   [
    0.43902439024390244,
    0.0
   ],
   [
    0.4523809523809524,
    0.0
   ],
   [
    0.4666666666666667,
    0.0
   ],
   [
    0.46875,
    0.0
   ],
   [
    0.4727272727272727,
    0.0
   ],
   [
    0.4827586206896552,
    0.0
   ],
   [
    0.49122807017543857,
    0.0
   ],
   [
    0.49230769230769234,
    0.0
   ],
   [
    0.4959349593495935,
    0.0
   ],
   [
    0.55,
    0.2
   ],
   [
    0.651685393258427,
    0.0
   ]
  ],
  "one_rational": [
   [
    0.0,
    0.4
   ],
   [
    0.0,
    0.6
   ],
   [
    0.08620689655172414,
    0.4
   ],
   [
    0.18421052631578946,
    0.4
   ],
   [
    0.2692307692307692,
    0.0
   ],
   [
    0.3103448275862069,
    0.0
   ],
   [
    0.32926829268292684,
    0.2
   ],
   [
    0.3333333333333333,
    0.2
   ],
   [
    0.36,
    0.0
   ],
   [
    0.417910447761194,
    0.2
   ],
   [
    0.43103448275862066,
    0.2
   ],
   [
    0.43333333333333335,
    0.2
   ],
   [
    0.4387755102040816,
    0.0
   ],
   [
    0.43902439024390244,
    0.2
   ],
   [
    0.4523809523809524,
    0.4
   ],
   [
    0.4666666666666667,
    0.6
   ],
   [
    0.46875,
    0.2
   ],
   [
    0.4727272727272727,
    0.0
   ],
   [
    0.4827586206896552,
    0.2
   ],
   [
    0.49122807017543857,
    0.4
   ],
   [
    0.49230769230769234,
    0.2
   ],
   [
    0.4959349593495935,
    0.0
   ],
   [
    0.55,
    0.0
   ],
   [
    0.651685393258427,
    0.6
   ]
  ],
  "rational_advised_llm": [
   [
    0.0,
    0.4
   ],
   [
    0.0,
    0.6
   ],
   [
    0.08620689655172414,
    0.0
   ],
   [
    0.18421052631578946,
    0.0
   ],
   [
    0.2692307692307692,
    0.0
   ],
   [
    0.3103448275862069,
    0.2
   ],
   [
    0.32926829268292684,
    0.2
   ],
   [
    0.3333333333333333,
    0.0
   ],
   [
    0.36,
    0.0
   ],
   [
    0.417910447761194,
    0.0
   ],
   [
    0.43103448275862066,
    0.0
   ],
   [
    0.43333333333333335,
    0.0
   ],
   [
    0.4387755102040816,
    0.0
   ],
   [
    0.43902439024390244,
    0.0
   ],
   [
    0.4523809523809524,
    0.0
   ],
   [
    0.4666666666666667,
    0.2
   ],
   [
    0.46875,
    0.0
   ],
   [
    0.4727272727272727,
    0.0
   ],
   [
    0.4827586206896552,
    0.0
   ],
   [
    0.49122807017543857,
    0.8
   ],
   [
    0.49230769230769234,
    0.0
   ],
   [
    0.4959349593495935,
    0.0
   ],
   [
    0.55,
    0.0
   ],
   [
    0.651685393258427,
    0.0
   ]
  ],
  "interpreter_advised_llm": [
   [
    0.0,
    0.2
   ],
   [
    0.0,
    0.4
   ],
   [
    0.08620689655172414,
    0.0
   ],
   [
    0.18421052631578946,
    0.0
   ],
   [
    0.2692307692307692,
    0.0
   ],
   [
    0.3103448275862069,
    0.0
   ],
   [
    0.32926829268292684,
    0.0
   ],
   [
    0.3333333333333333,
    0.0
   ],
   [
    0.36,
    0.2
   ],
   [
    0.417910447761194,
    0.0
   ],
   [
    0.43103448275862066,
    0.0
   ],
   [
    0.43333333333333335,
    0.0
   ],
   [
    0.4387755102040816,
    0.0
   ],
   [
    0.43902439024390244,
    0.0
   ],
   [
    0.4523809523809524,
    0.0
   ],
   [
    0.4666666666666667,
    0.0
   ],
   [
    0.46875,
    0.2
   ],
   [
    0.4727272727272727,
    0.0
   ],
   [
    0.4827586206896552,
    0.0
   ],
   [
    0.49122807017543857,
    0.0
   ],
   [
    0.49230769230769234,
    0.0
   ],
   [
    0.4959349593495935,
    0.0
   ],
   [
    0.55,
    0.0
   ],
   [
    0.651685393258427,
    0.0
   ]
  ],
  "one_oracle": [
   [
    0.0,
    0.2
   ],
   [
    0.0,
    0.6
   ],
   [
    0.08620689655172414,
    0.0
   ],
   [
    0.18421052631578946,
    0.2
   ],
   [
    0.2692307692307692,
    0.0
   ],
   [
    0.3103448275862069,
    0.0
   ],
   [
    0.32926829268292684,
    0.0
   ],
   [
    0.3333333333333333,
    0.0
   ],
   [
    0.36,
    0.0
   ],
   [
    0.417910447761194,
    0.2
   ],
   [
    0.43103448275862066,
    0.2
   ],
   [
    0.43333333333333335,
    0.0
   ],
   [
    0.4387755102040816,
    0.2
   ],
   [
    0.43902439024390244,
    0.0
   ],
   [
    0.4523809523809524,
    0.2
   ],
   [
    0.4666666666666667,
    0.2
   ],
   [
    0.46875,
    0.0
   ],
   [
    0.4727272727272727,
    0.0
   ],
   [
    0.4827586206896552,
    0.0
   ],
   [
    0.49122807017543857,
    0.0
   ],
   [
    0.49230769230769234,
    0.0
   ],
   [
    0.4959349593495935,
    0.0
   ],
   [
    0.55,
    0.0
   ],
   [
    0.651685393258427,
    0.0
   ]
  ],
  "all_oracle": [
   [
    0.0,
    0.0
   ],
   [
    0.0,
    0.0
   ],
   [
    0.08620689655172414,
    0.0
   ],
   [
    0.18421052631578946,
    0.0
   ],
   [
    0.2692307692307692,
    0.0
   ],
   [
    0.3103448275862069,
    0.0
   ],
   [
    0.32926829268292684,
    0.0
   ],
   [
    0.3333333333333333,
    0.0
   ],
   [
    0.36,
    0.0
   ],
   [
    0.417910447761194,
    0.0
   ],
   [
    0.43103448275862066,
    0.0
   ],
   [
    0.43333333333333335,
    0.0
   ],
   [
    0.4387755102040816,
    0.0
   ],
   [
    0.43902439024390244,
    0.0
   ],
   [
    0.4523809523809524,
    0.0
   ],
   [
    0.4666666666666667,
    0.0
   ],
   [
    0.46875,
    0.0
   ],
   [
    0.4727272727272727,
    0.0
   ],
   [
    0.4827586206896552,
    0.0
   ],
   [
    0.49122807017543857,
    0.0
   ],
   [
    0.49230769230769234,
    0.0
   ],
   [
    0.4959349593495935,
    0.0
   ],
   [
    0.55,
    0.0
   ],
   [
    0.651685393258427,
    0.0
   ]
  ],
  "all_rational": [
   [
    0.0,
    0.8
   ],
   [
    0.0,
    1.0
   ],
   [
    0.08620689655172414,
    1.0
   ],
   [
    0.18421052631578946,
    1.0
   ],
   [
    0.2692307692307692,
    0.8
   ],
   [
    0.3103448275862069,
    0.8
   ],
   [
    0.32926829268292684,
    0.6
   ],
   [
    0.3333333333333333,
    0.6
   ],
   [
    0.36,
    1.0
   ],
   [
    0.417910447761194,
    0.8
   ],
   [
    0.43103448275862066,
    1.0
   ],
   [
    0.43333333333333335,
    0.4
   ],
   [
    0.4387755102040816,
    0.8
   ],
   [
    0.43902439024390244,
    0.8
   ],
   [
    0.4523809523809524,
    0.6
   ],
   [
    0.4666666666666667,
    1.0
   ],
   [
    0.46875,
    1.0
   ],
   [
    0.4727272727272727,
    0.0
   ],
   [
    0.4827586206896552,
    0.6
   ],
   [
    0.49122807017543857,
    1.0
   ],
   [
    0.49230769230769234,
    1.0
   ],
   [
    0.4959349593495935,
    0.4
   ],
   [
    0.55,
    0.4
   ],
   [
    0.651685393258427,
    1.0
   ]
  ]
 },
 "plots": [
  ".claude/products/five-seat-advised-advocate-wave2/fairness_basket_vs_all_llm/fairness_basket.png",
  ".claude/products/five-seat-advised-advocate-wave2/fairness_basket_vs_all_llm/fairness_basket.pdf"
 ]
}
