04-Principal-Fairness.ipynb

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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import random\n",
    "import os\n",
    "\n",
    "DIVERSITY_UTILITY = float(os.environ.get('DIVERSITY_UTILITY'))\n",
    "FRAC_ADMIT = 0.5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   "source": [
    "\n",
    "\n",
    "###\n",
    "## Load dataframe where each row is a single applicant\n",
    "###\n",
    "\n",
    "df = pd.read_csv('./df_test.csv')\n",
    "df['key'] = df['R'].astype(str) + \"_\"  + df['T'].astype(str)\n",
    "\n",
    "###\n",
    "## Estimate E[Y(1)|T, A]\n",
    "###\n",
    "\n",
    "df_train = pd.read_csv('./df_train.csv')\n",
    "df_stratum_utility = df_train[['R','T','Y']].groupby(['R','T']).mean().reset_index()\n",
    "df_stratum_utility['stratum_utility'] = (df_stratum_utility['Y'] + DIVERSITY_UTILITY * df_stratum_utility['R']).round(2)\n",
    "df_stratum_utility['key'] = df_stratum_utility['R'].astype(str) + \"_\" + df_stratum_utility['T'].astype(str)\n",
    "\n",
    "df = df.merge(df_stratum_utility[['stratum_utility','key']], on='key')\n",
    "df['ml_outcomes'] = df['stratum_utility']"
   ]
  },
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   "execution_count": 3,
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    {
     "data": {
      "text/plain": [
       "0        1\n",
       "1        1\n",
       "2        1\n",
       "3        1\n",
       "4        1\n",
       "        ..\n",
       "99995    1\n",
       "99996    1\n",
       "99997    1\n",
       "99998    0\n",
       "99999    0\n",
       "Name: Y_reject, Length: 100000, dtype: int64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
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   ],
   "source": [
    "df['Y_reject']"
   ]
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   "outputs": [],
   "source": [
    "df['Y_stratum'] = df['Y'].astype(str) + df['Y_reject'].astype(str)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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    "execution": {
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    {
     "data": {
      "text/plain": [
       "00    55968\n",
       "11    35458\n",
       "10     8574\n",
       "Name: Y_stratum, dtype: int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Y_stratum'].value_counts()"
   ]
  },
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   "cell_type": "code",
   "execution_count": 6,
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    "execution": {
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   "outputs": [],
   "source": [
    "# = \n",
    "#df['Y_reject'] = df['Y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
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    "scrolled": true
   },
   "outputs": [],
   "source": [
    "FRAC_ADMIT = 0.5#df[['A']].sum()/len(df)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
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       "0.5"
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   "source": [
    "FRAC_ADMIT"
   ]
  },
  {
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   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2022-07-18T22:07:32.860120Z"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "100000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
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    }
   },
   "outputs": [],
   "source": [
    "#df['ml_outcomes'] = df['R']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>R</th>\n",
       "      <th>T</th>\n",
       "      <th>ml_outcomes</th>\n",
       "      <th>T_minority</th>\n",
       "      <th>T_majority</th>\n",
       "      <th>Y</th>\n",
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       "      <td>1.25</td>\n",
       "      <td>97</td>\n",
       "      <td>114</td>\n",
       "      <td>1</td>\n",
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       "<p>100000 rows × 6 columns</p>\n",
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       "       R    T  ml_outcomes  T_minority  T_majority  Y\n",
       "99974  0   12         0.02          10          12  0\n",
       "99914  0   16         0.03          10          16  0\n",
       "99913  0   16         0.03          12          16  0\n",
       "99650  0   17         0.06          14          17  0\n",
       "99653  0   17         0.06          13          17  0\n",
       "...   ..  ...          ...         ...         ... ..\n",
       "99940  1   94         1.21          94         107  0\n",
       "99949  1  101         1.23         101         118  1\n",
       "98552  1   98         1.25          98         114  1\n",
       "99977  1  112         1.25         112         129  1\n",
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       "\n",
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     "execution_count": 11,
     "metadata": {},
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   "source": [
    "##\n",
    "# R = race, T = test score, ml_outcomes = expected utility from admitting, \n",
    "# ml_outcomes_{} counterfactual utility given race \n",
    "##\n",
    "\n",
    "df[['R','T','ml_outcomes','T_minority','T_majority','Y']].sort_values(by='ml_outcomes')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:32.886682Z",
     "iopub.status.busy": "2022-07-18T22:07:32.886322Z",
     "iopub.status.idle": "2022-07-18T22:07:32.887619Z",
     "shell.execute_reply": "2022-07-18T22:07:32.887905Z"
    }
   },
   "outputs": [],
   "source": [
    "#df['ml_outcomes'] = df['ml_outcomes'] + 1*df['R']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
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   },
   "outputs": [],
   "source": [
    "###\n",
    "## Get total utility from admitting people in a stratum \n",
    "###\n",
    "\n",
    "df_ = df[['R','T','Y','Y_reject','ml_outcomes']].groupby(['R','T','Y','Y_reject']).sum().reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:32.902789Z",
     "iopub.status.busy": "2022-07-18T22:07:32.902412Z",
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     "shell.execute_reply": "2022-07-18T22:07:32.909040Z"
    }
   },
   "outputs": [],
   "source": [
    "###\n",
    "## Get number of people in each stratum\n",
    "###\n",
    "\n",
    "df_count = df[['R','T','ml_outcomes','Y','Y_reject']].groupby(['R','T','Y','Y_reject']).count().reset_index()\n",
    "df_count.columns = ['R','T','Y','Y_reject','Count']\n",
    "df_count['N'] = df_count['Count']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:32.913724Z",
     "iopub.status.busy": "2022-07-18T22:07:32.913350Z",
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     "shell.execute_reply": "2022-07-18T22:07:32.914982Z"
    }
   },
   "outputs": [],
   "source": [
    "###\n",
    "## Merge summary tables to get one table with Race, Test Score, SUM(Utility), COUNT(applicants) per stratum\n",
    "###\n",
    "\n",
    "dff = df_.merge(df_count[['N']],left_index=True,right_index=True).sort_values(by='ml_outcomes',ascending=False).reset_index().sort_values(by='index').reset_index()"
   ]
  },
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       "      <td>60</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>553.20</td>\n",
       "      <td>922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>131</th>\n",
       "      <td>3</td>\n",
       "      <td>131</td>\n",
       "      <td>0</td>\n",
       "      <td>61</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>563.58</td>\n",
       "      <td>909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>134</th>\n",
       "      <td>2</td>\n",
       "      <td>134</td>\n",
       "      <td>0</td>\n",
       "      <td>62</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>563.84</td>\n",
       "      <td>881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>105</th>\n",
       "      <td>1</td>\n",
       "      <td>105</td>\n",
       "      <td>0</td>\n",
       "      <td>53</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>564.42</td>\n",
       "      <td>1227</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>140</th>\n",
       "      <td>0</td>\n",
       "      <td>140</td>\n",
       "      <td>0</td>\n",
       "      <td>64</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>576.87</td>\n",
       "      <td>861</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>479 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     level_0  index  R   T  Y  Y_reject  ml_outcomes     N\n",
       "0        478      0  0  12  0         0         0.02     1\n",
       "3        477      3  0  16  0         0         0.06     2\n",
       "5        476      5  0  17  1         1         0.06     1\n",
       "2        474      2  0  15  0         0         0.07     1\n",
       "11       473     11  0  20  1         1         0.07     1\n",
       "..       ...    ... ..  .. ..       ...          ...   ...\n",
       "128        4    128  0  60  1         1       553.20   922\n",
       "131        3    131  0  61  1         1       563.58   909\n",
       "134        2    134  0  62  1         1       563.84   881\n",
       "105        1    105  0  53  0         0       564.42  1227\n",
       "140        0    140  0  64  1         1       576.87   861\n",
       "\n",
       "[479 rows x 8 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# final info table\n",
    "dff.sort_values(by='ml_outcomes')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup optimization problem "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:32.925308Z",
     "iopub.status.busy": "2022-07-18T22:07:32.924951Z",
     "iopub.status.idle": "2022-07-18T22:07:32.948810Z",
     "shell.execute_reply": "2022-07-18T22:07:32.949026Z"
    }
   },
   "outputs": [],
   "source": [
    "from ortools.linear_solver import pywraplp\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:32.951558Z",
     "iopub.status.busy": "2022-07-18T22:07:32.951201Z",
     "iopub.status.idle": "2022-07-18T22:07:32.952502Z",
     "shell.execute_reply": "2022-07-18T22:07:32.952736Z"
    }
   },
   "outputs": [],
   "source": [
    "solver = pywraplp.Solver.CreateSolver('GLOP')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:32.955051Z",
     "iopub.status.busy": "2022-07-18T22:07:32.954659Z",
     "iopub.status.idle": "2022-07-18T22:07:32.956956Z",
     "shell.execute_reply": "2022-07-18T22:07:32.957233Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "479"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(dff[['R','T','Y','Y_reject']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:32.963351Z",
     "iopub.status.busy": "2022-07-18T22:07:32.962958Z",
     "iopub.status.idle": "2022-07-18T22:07:32.964570Z",
     "shell.execute_reply": "2022-07-18T22:07:32.964864Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>level_0</th>\n",
       "      <th>index</th>\n",
       "      <th>R</th>\n",
       "      <th>T</th>\n",
       "      <th>Y</th>\n",
       "      <th>Y_reject</th>\n",
       "      <th>ml_outcomes</th>\n",
       "      <th>N</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>478</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.02</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>468</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>13</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.10</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>474</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.07</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>477</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.06</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>454</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.42</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>474</th>\n",
       "      <td>418</td>\n",
       "      <td>474</td>\n",
       "      <td>1</td>\n",
       "      <td>95</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1.19</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>475</th>\n",
       "      <td>409</td>\n",
       "      <td>475</td>\n",
       "      <td>1</td>\n",
       "      <td>97</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1.25</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>476</th>\n",
       "      <td>410</td>\n",
       "      <td>476</td>\n",
       "      <td>1</td>\n",
       "      <td>98</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1.25</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>477</th>\n",
       "      <td>413</td>\n",
       "      <td>477</td>\n",
       "      <td>1</td>\n",
       "      <td>101</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1.23</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>478</th>\n",
       "      <td>411</td>\n",
       "      <td>478</td>\n",
       "      <td>1</td>\n",
       "      <td>112</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1.25</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>479 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     level_0  index  R    T  Y  Y_reject  ml_outcomes  N\n",
       "0        478      0  0   12  0         0         0.02  1\n",
       "1        468      1  0   13  0         0         0.10  1\n",
       "2        474      2  0   15  0         0         0.07  1\n",
       "3        477      3  0   16  0         0         0.06  2\n",
       "4        454      4  0   17  0         0         0.42  7\n",
       "..       ...    ... ..  ... ..       ...          ... ..\n",
       "474      418    474  1   95  1         1         1.19  1\n",
       "475      409    475  1   97  1         1         1.25  1\n",
       "476      410    476  1   98  1         1         1.25  1\n",
       "477      413    477  1  101  1         1         1.23  1\n",
       "478      411    478  1  112  1         1         1.25  1\n",
       "\n",
       "[479 rows x 8 columns]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:32.982900Z",
     "iopub.status.busy": "2022-07-18T22:07:32.982532Z",
     "iopub.status.idle": "2022-07-18T22:07:32.983769Z",
     "shell.execute_reply": "2022-07-18T22:07:32.984056Z"
    }
   },
   "outputs": [],
   "source": [
    "applicant_stratum = []\n",
    "vars_cache = {}\n",
    "\n",
    "# Objective: Maximize the expected utility of the admitted students\n",
    "objective = solver.Objective()\n",
    "\n",
    "# For each stratum\n",
    "for ix, row in dff.iterrows():\n",
    "    # probability of admission\n",
    "    numvar = solver.NumVar(0.0, 1.0, str(ix))\n",
    "    \n",
    "    # store variable by index, and also by stratum R, T\n",
    "    applicant_stratum.append(numvar)\n",
    "    vars_cache[(row['R'],row['T'],row['Y'], row['Y_reject'])] = numvar\n",
    "    \n",
    "    # Benefit of admitting people is total utility in that stratum\n",
    "    objective.SetCoefficient(applicant_stratum[ix], float(row['ml_outcomes']))\n",
    "objective.SetMaximization()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:32.986363Z",
     "iopub.status.busy": "2022-07-18T22:07:32.985976Z",
     "iopub.status.idle": "2022-07-18T22:07:32.987568Z",
     "shell.execute_reply": "2022-07-18T22:07:32.987924Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Currently we have no constraints \n",
    "solver.NumConstraints()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.000400Z",
     "iopub.status.busy": "2022-07-18T22:07:33.000034Z",
     "iopub.status.idle": "2022-07-18T22:07:33.001569Z",
     "shell.execute_reply": "2022-07-18T22:07:33.001811Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50000\n"
     ]
    }
   ],
   "source": [
    "# Constraint: At most K applicants\n",
    "K = int(len(df)*FRAC_ADMIT)\n",
    "print(K)\n",
    "admit_quota = solver.Constraint(0, K)\n",
    "\n",
    "# Total applicants cannot exceed K \n",
    "for ix, row in dff.iterrows():\n",
    "    admit_quota.SetCoefficient(applicant_stratum[ix], float(row['N']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.004068Z",
     "iopub.status.busy": "2022-07-18T22:07:33.003709Z",
     "iopub.status.idle": "2022-07-18T22:07:33.005200Z",
     "shell.execute_reply": "2022-07-18T22:07:33.005468Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we have one constraint\n",
    "solver.NumConstraints()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Add Equalized Odds Constraints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.035615Z",
     "iopub.status.busy": "2022-07-18T22:07:33.035207Z",
     "iopub.status.idle": "2022-07-18T22:07:33.036832Z",
     "shell.execute_reply": "2022-07-18T22:07:33.037114Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(593, 844)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Make sure that you have to add all people in Y stratum or none\n",
    "## i.e. you can't add only people who pass boards and reject those who fail boards from same T, R stratum\n",
    "didntexist, exists = 0, 0 \n",
    "\n",
    "for ix, row in dff.iterrows():\n",
    "    \n",
    "    \n",
    "    var1 = vars_cache[(row['R'],row['T'],row['Y'], row['Y_reject'])]\n",
    "    key2s = [(row['R'],row['T'], 1-row['Y'], 1-row['Y_reject']), (row['R'],row['T'], row['Y'], 1-row['Y_reject']), (row['R'],row['T'], 1-row['Y'], row['Y_reject'])]\n",
    "    \n",
    "    for key2 in key2s:\n",
    "        constrain_bp = solver.Constraint(0.0, 0.0)\n",
    "        \n",
    "        if key2 not in vars_cache:\n",
    "            didntexist+=1\n",
    "            continue\n",
    "            \n",
    "        var2 = vars_cache[key2]\n",
    "        \n",
    "        constrain_bp.SetCoefficient(var1, -1.0)\n",
    "        constrain_bp.SetCoefficient(var2, 1.0)\n",
    "        exists+=1\n",
    "\n",
    "didntexist, exists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.043814Z",
     "iopub.status.busy": "2022-07-18T22:07:33.043435Z",
     "iopub.status.idle": "2022-07-18T22:07:33.045084Z",
     "shell.execute_reply": "2022-07-18T22:07:33.045453Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(97, 0, 80, 0)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "majority_pass_boards_pass_boards_reject = []\n",
    "majority_fail_boards_pass_boards_reject = []\n",
    "minority_pass_boards_pass_boards_reject = []\n",
    "minority_fail_boards_pass_boards_reject = []\n",
    "majority_pass_boards_fail_boards_reject = []\n",
    "majority_fail_boards_fail_boards_reject = []\n",
    "minority_pass_boards_fail_boards_reject = []\n",
    "minority_fail_boards_fail_boards_reject = []\n",
    "\n",
    "\n",
    "for key in vars_cache:\n",
    "    r, t, Y, Y_reject = key\n",
    "    if Y == 1 and r==0 and Y_reject==1:\n",
    "        majority_pass_boards_pass_boards_reject.append(key)\n",
    "    elif Y == 0 and r==0 and Y_reject==1:\n",
    "        majority_fail_boards_pass_boards_reject.append(key)\n",
    "    elif Y == 1 and r==1 and Y_reject==1:\n",
    "        minority_pass_boards_pass_boards_reject.append(key)\n",
    "    elif Y == 0 and r==1 and Y_reject==1:\n",
    "        minority_fail_boards_pass_boards_reject.append(key)\n",
    "        \n",
    "    if Y == 1 and r==0 and Y_reject==0:\n",
    "        majority_pass_boards_fail_boards_reject.append(key)\n",
    "    elif Y == 0 and r==0 and Y_reject==0:\n",
    "        majority_fail_boards_fail_boards_reject.append(key)\n",
    "    elif Y == 1 and r==1 and Y_reject==0:\n",
    "        minority_pass_boards_fail_boards_reject.append(key)\n",
    "    elif Y == 0 and r==1 and Y_reject==0:\n",
    "        minority_fail_boards_fail_boards_reject.append(key)\n",
    "\n",
    "len(majority_pass_boards_pass_boards_reject),len(majority_fail_boards_pass_boards_reject),len(minority_pass_boards_pass_boards_reject),len(minority_fail_boards_pass_boards_reject)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.063922Z",
     "iopub.status.busy": "2022-07-18T22:07:33.063578Z",
     "iopub.status.idle": "2022-07-18T22:07:33.064862Z",
     "shell.execute_reply": "2022-07-18T22:07:33.065161Z"
    }
   },
   "outputs": [],
   "source": [
    "NUM_TOTALS = {}\n",
    "df_totals = dff[['N','R','Y','Y_reject']].groupby(['R','Y','Y_reject']).sum().reset_index()\n",
    "for ix, row in df_totals.iterrows():\n",
    "    NUM_TOTALS[(row['R'],row['Y'],row['Y_reject'])] = row['N']\n",
    "    \n",
    "N_IN_STRATAS = {}\n",
    "for ix, row in dff.iterrows():\n",
    "    N_IN_STRATAS[(row['R'],row['T'],row['Y'],row['Y_reject'])] = row['N']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.067495Z",
     "iopub.status.busy": "2022-07-18T22:07:33.067055Z",
     "iopub.status.idle": "2022-07-18T22:07:33.068709Z",
     "shell.execute_reply": "2022-07-18T22:07:33.068991Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1438"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we have one constraint\n",
    "solver.NumConstraints()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.073443Z",
     "iopub.status.busy": "2022-07-18T22:07:33.073089Z",
     "iopub.status.idle": "2022-07-18T22:07:33.074340Z",
     "shell.execute_reply": "2022-07-18T22:07:33.074677Z"
    }
   },
   "outputs": [],
   "source": [
    "#Of those who pass the boards exams, pass boards exams if rejected\n",
    "#Frac majority admitted and frac minority admitted should be the same\n",
    "\n",
    "constrain_pass_boards_pass_boards_reject = solver.Constraint(0.0, 0.0)\n",
    "\n",
    "for key in majority_pass_boards_pass_boards_reject:\n",
    "    r, t, Y, Y_reject = key\n",
    "    N_IN_STRATUM = N_IN_STRATAS[(r,t,Y, Y_reject)]\n",
    "    N_TOTAL = NUM_TOTALS[(r,Y, Y_reject)]\n",
    "    \n",
    "    constrain_pass_boards_pass_boards_reject.SetCoefficient(vars_cache[key], float(N_IN_STRATUM) / float(N_TOTAL))\n",
    "\n",
    "for key in minority_pass_boards_pass_boards_reject:\n",
    "    r, t, Y, Y_reject = key\n",
    "    N_IN_STRATUM = N_IN_STRATAS[(r,t,Y, Y_reject)]\n",
    "    N_TOTAL = NUM_TOTALS[(r,Y, Y_reject)]\n",
    "    \n",
    "    constrain_pass_boards_pass_boards_reject.SetCoefficient(vars_cache[key], -1.0 * (float(N_IN_STRATUM) / float(N_TOTAL)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.078126Z",
     "iopub.status.busy": "2022-07-18T22:07:33.077766Z",
     "iopub.status.idle": "2022-07-18T22:07:33.079147Z",
     "shell.execute_reply": "2022-07-18T22:07:33.079506Z"
    }
   },
   "outputs": [],
   "source": [
    "#Of those who fail the boards exams, pass boards exams if rejected\n",
    "#Frac majority admitted and frac minority admitted should be the same\n",
    "\n",
    "constrain_fail_boards_pass_boards_reject = solver.Constraint(0.0, 0.0)\n",
    "\n",
    "for key in majority_fail_boards_pass_boards_reject:\n",
    "    r, t, Y, Y_reject = key\n",
    "    N_IN_STRATUM = N_IN_STRATAS[(r,t,Y, Y_reject)]\n",
    "    N_TOTAL = NUM_TOTALS[(r,Y, Y_reject)]\n",
    "    \n",
    "    constrain_fail_boards_pass_boards_reject.SetCoefficient(vars_cache[key], float(N_IN_STRATUM) / float(N_TOTAL))\n",
    "\n",
    "for key in minority_fail_boards_pass_boards_reject:\n",
    "    r, t, Y, Y_reject = key\n",
    "    N_IN_STRATUM = N_IN_STRATAS[(r,t,Y, Y_reject)]\n",
    "    N_TOTAL = NUM_TOTALS[(r,Y, Y_reject)]\n",
    "    \n",
    "    constrain_fail_boards_pass_boards_reject.SetCoefficient(vars_cache[key], -1.0 * (float(N_IN_STRATUM) / float(N_TOTAL)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.086032Z",
     "iopub.status.busy": "2022-07-18T22:07:33.085672Z",
     "iopub.status.idle": "2022-07-18T22:07:33.086988Z",
     "shell.execute_reply": "2022-07-18T22:07:33.087274Z"
    }
   },
   "outputs": [],
   "source": [
    "constrain_pass_boards_fail_boards_reject = solver.Constraint(0.0, 0.0)\n",
    "\n",
    "for key in majority_pass_boards_fail_boards_reject:\n",
    "    r, t, Y, Y_reject = key\n",
    "    N_IN_STRATUM = N_IN_STRATAS[(r,t,Y, Y_reject)]\n",
    "    N_TOTAL = NUM_TOTALS[(r,Y, Y_reject)]\n",
    "    \n",
    "    constrain_pass_boards_fail_boards_reject.SetCoefficient(vars_cache[key], float(N_IN_STRATUM) / float(N_TOTAL))\n",
    "\n",
    "for key in minority_pass_boards_fail_boards_reject:\n",
    "    r, t, Y, Y_reject = key\n",
    "    N_IN_STRATUM = N_IN_STRATAS[(r,t,Y, Y_reject)]\n",
    "    N_TOTAL = NUM_TOTALS[(r,Y, Y_reject)]\n",
    "    \n",
    "    constrain_pass_boards_fail_boards_reject.SetCoefficient(vars_cache[key], -1.0 * (float(N_IN_STRATUM) / float(N_TOTAL)))\n",
    "\n",
    "    \n",
    "#Of those who fail the boards exams, fail boards exams if rejected\n",
    "#Frac majority admitted and frac minority admitted should be the same\n",
    "\n",
    "constrain_fail_boards_fail_boards_reject = solver.Constraint(0.0, 0.0)\n",
    "\n",
    "for key in majority_fail_boards_fail_boards_reject:\n",
    "    r, t, Y, Y_reject = key\n",
    "    N_IN_STRATUM = N_IN_STRATAS[(r,t,Y, Y_reject)]\n",
    "    N_TOTAL = NUM_TOTALS[(r,Y, Y_reject)]\n",
    "    \n",
    "    constrain_fail_boards_fail_boards_reject.SetCoefficient(vars_cache[key], float(N_IN_STRATUM) / float(N_TOTAL))\n",
    "\n",
    "for key in minority_fail_boards_fail_boards_reject:\n",
    "    r, t, Y, Y_reject = key\n",
    "    N_IN_STRATUM = N_IN_STRATAS[(r,t,Y, Y_reject)]\n",
    "    N_TOTAL = NUM_TOTALS[(r,Y, Y_reject)]\n",
    "    \n",
    "    constrain_fail_boards_fail_boards_reject.SetCoefficient(vars_cache[key], -1.0 * (float(N_IN_STRATUM) / float(N_TOTAL)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Add constraints on people who fail boards exams"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve linear program"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.089749Z",
     "iopub.status.busy": "2022-07-18T22:07:33.089388Z",
     "iopub.status.idle": "2022-07-18T22:07:33.090959Z",
     "shell.execute_reply": "2022-07-18T22:07:33.091240Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solver.ABNORMAL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.095401Z",
     "iopub.status.busy": "2022-07-18T22:07:33.095048Z",
     "iopub.status.idle": "2022-07-18T22:07:33.096254Z",
     "shell.execute_reply": "2022-07-18T22:07:33.096543Z"
    }
   },
   "outputs": [],
   "source": [
    "status = solver.Solve()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.098719Z",
     "iopub.status.busy": "2022-07-18T22:07:33.098326Z",
     "iopub.status.idle": "2022-07-18T22:07:33.100009Z",
     "shell.execute_reply": "2022-07-18T22:07:33.100289Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "status"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.102505Z",
     "iopub.status.busy": "2022-07-18T22:07:33.102129Z",
     "iopub.status.idle": "2022-07-18T22:07:33.103724Z",
     "shell.execute_reply": "2022-07-18T22:07:33.103991Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solver.OPTIMAL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.109978Z",
     "iopub.status.busy": "2022-07-18T22:07:33.109488Z",
     "iopub.status.idle": "2022-07-18T22:07:33.111190Z",
     "shell.execute_reply": "2022-07-18T22:07:33.111430Z"
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    {
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      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "applicant_stratum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.114877Z",
     "iopub.status.busy": "2022-07-18T22:07:33.114522Z",
     "iopub.status.idle": "2022-07-18T22:07:33.115602Z",
     "shell.execute_reply": "2022-07-18T22:07:33.115995Z"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "row = []\n",
    "admit = []\n",
    "\n",
    "for i in applicant_stratum:\n",
    "    row.append(int(str(i)))\n",
    "    admit.append(i.solution_value())\n",
    "\n",
    "df_decisions = pd.DataFrame({'row_id':row,'decision':admit})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.120922Z",
     "iopub.status.busy": "2022-07-18T22:07:33.120548Z",
     "iopub.status.idle": "2022-07-18T22:07:33.122089Z",
     "shell.execute_reply": "2022-07-18T22:07:33.122378Z"
    }
   },
   "outputs": [
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       "     row_id  decision\n",
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       "[479 rows x 2 columns]"
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     "execution_count": 38,
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       "     level_0  index  R   T  Y  Y_reject  ml_outcomes     N  row_id  decision\n",
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       "..       ...    ... ..  .. ..       ...          ...   ...     ...       ...\n",
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       "13       475     13  0  21  1         1         0.07     1      13       0.0\n",
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       "0        478      0  0  12  0         0         0.02     1       0       0.0\n",
       "\n",
       "[479 rows x 10 columns]"
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   "source": [
    "dff.merge(df_decisions,left_index=True,right_index=True).sort_values(by='ml_outcomes',ascending=False)"
   ]
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      ],
      "text/plain": [
       "     level_0  index  R    T  Y  Y_reject  ml_outcomes  N  row_id  decision\n",
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       "..       ...    ... ..  ... ..       ...          ... ..     ...       ...\n",
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       "258      431    258  0  130  1         1         1.00  1     258       0.0\n",
       "\n",
       "[479 rows x 10 columns]"
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     "execution_count": 40,
     "metadata": {},
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    "xxx_ = dff.merge(df_decisions,left_index=True,right_index=True).sort_values(by='ml_outcomes',ascending=False)\n",
    "xxx_.sort_values(by='T')"
   ]
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     "shell.execute_reply": "2022-07-18T22:07:33.150945Z"
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       "      <td>1</td>\n",
       "      <td>576.87</td>\n",
       "      <td>861</td>\n",
       "      <td>140</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>105</th>\n",
       "      <td>1</td>\n",
       "      <td>105</td>\n",
       "      <td>0</td>\n",
       "      <td>53</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>564.42</td>\n",
       "      <td>1227</td>\n",
       "      <td>105</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>134</th>\n",
       "      <td>2</td>\n",
       "      <td>134</td>\n",
       "      <td>0</td>\n",
       "      <td>62</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>563.84</td>\n",
       "      <td>881</td>\n",
       "      <td>134</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>131</th>\n",
       "      <td>3</td>\n",
       "      <td>131</td>\n",
       "      <td>0</td>\n",
       "      <td>61</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>563.58</td>\n",
       "      <td>909</td>\n",
       "      <td>131</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>128</th>\n",
       "      <td>4</td>\n",
       "      <td>128</td>\n",
       "      <td>0</td>\n",
       "      <td>60</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>553.20</td>\n",
       "      <td>922</td>\n",
       "      <td>128</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>474</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.07</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>475</td>\n",
       "      <td>13</td>\n",
       "      <td>0</td>\n",
       "      <td>21</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.07</td>\n",
       "      <td>1</td>\n",
       "      <td>13</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>476</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.06</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>477</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.06</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>478</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.02</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>479 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     level_0  index  R   T  Y  Y_reject  ml_outcomes     N  row_id  decision\n",
       "140        0    140  0  64  1         1       576.87   861     140       1.0\n",
       "105        1    105  0  53  0         0       564.42  1227     105       0.0\n",
       "134        2    134  0  62  1         1       563.84   881     134       1.0\n",
       "131        3    131  0  61  1         1       563.58   909     131       1.0\n",
       "128        4    128  0  60  1         1       553.20   922     128       1.0\n",
       "..       ...    ... ..  .. ..       ...          ...   ...     ...       ...\n",
       "2        474      2  0  15  0         0         0.07     1       2       0.0\n",
       "13       475     13  0  21  1         1         0.07     1      13       0.0\n",
       "5        476      5  0  17  1         1         0.06     1       5       0.0\n",
       "3        477      3  0  16  0         0         0.06     2       3       0.0\n",
       "0        478      0  0  12  0         0         0.02     1       0       0.0\n",
       "\n",
       "[479 rows x 10 columns]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xxx = dff.merge(df_decisions,left_index=True,right_index=True).sort_values(by='ml_outcomes',ascending=False)\n",
    "xxx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.153350Z",
     "iopub.status.busy": "2022-07-18T22:07:33.152930Z",
     "iopub.status.idle": "2022-07-18T22:07:33.154591Z",
     "shell.execute_reply": "2022-07-18T22:07:33.154881Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "479"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(xxx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.210673Z",
     "iopub.status.busy": "2022-07-18T22:07:33.210292Z",
     "iopub.status.idle": "2022-07-18T22:07:33.394437Z",
     "shell.execute_reply": "2022-07-18T22:07:33.394134Z"
    }
   },
   "outputs": [],
   "source": [
    "df['key'] = df['R'].astype(str)+'_'+df['T'].astype(str)+'_'+df['Y'].astype(str)+'_'+df['Y_reject'].astype(str)\n",
    "xxx['key'] = xxx['R'].astype(str)+'_'+xxx['T'].astype(str)+'_'+xxx['Y'].astype(str)+'_'+xxx['Y_reject'].astype(str)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.406277Z",
     "iopub.status.busy": "2022-07-18T22:07:33.405864Z",
     "iopub.status.idle": "2022-07-18T22:07:33.448187Z",
     "shell.execute_reply": "2022-07-18T22:07:33.448461Z"
    }
   },
   "outputs": [],
   "source": [
    "admit_decisions = df.merge(xxx[['key','decision']],how='left',on='key')\n",
    "admit_decisions['decision_random'] = pd.Series([random.random() for x in range(0,len(admit_decisions))]) < FRAC_ADMIT\n",
    "\n",
    "FRAC_minority_POLICY = (admit_decisions['R'] * admit_decisions['decision']).sum()/admit_decisions['decision'].sum()\n",
    "SUM_BP_POLICY = ( admit_decisions['Y'] * admit_decisions['decision']).sum()\n",
    "\n",
    "FRAC_RANDOM_POLICY = (admit_decisions['R'] * admit_decisions['decision_random']).sum()/admit_decisions['decision_random'].sum()\n",
    "SUM_BP_RAND_POLICY = ( admit_decisions['Y'] * admit_decisions['decision_random']).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.451901Z",
     "iopub.status.busy": "2022-07-18T22:07:33.451429Z",
     "iopub.status.idle": "2022-07-18T22:07:33.453341Z",
     "shell.execute_reply": "2022-07-18T22:07:33.453580Z"
    }
   },
   "outputs": [],
   "source": [
    "file = open('./lp_results.csv','a')\n",
    "file.write('{}\\t{}\\t{}\\n'.format('Principal Fairness',str(FRAC_minority_POLICY),str(SUM_BP_POLICY)))\n",
    "file.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:07:33.456972Z",
     "iopub.status.busy": "2022-07-18T22:07:33.456489Z",
     "iopub.status.idle": "2022-07-18T22:07:33.458394Z",
     "shell.execute_reply": "2022-07-18T22:07:33.458648Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49999999999999983"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(xxx['N']*xxx['decision']).sum()/len(df)"
   ]
  }
 ],
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