00-Maximize-Utility.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 = float(os.environ.get('FRAC_ADMIT'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
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    }
   },
   "outputs": [],
   "source": [
    "###\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']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
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    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>99974</th>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>0.02</td>\n",
       "      <td>10</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99914</th>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>0.03</td>\n",
       "      <td>10</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99913</th>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>0.03</td>\n",
       "      <td>12</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99650</th>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>0.06</td>\n",
       "      <td>14</td>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99653</th>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>0.06</td>\n",
       "      <td>13</td>\n",
       "      <td>17</td>\n",
       "      <td>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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99940</th>\n",
       "      <td>1</td>\n",
       "      <td>94</td>\n",
       "      <td>1.21</td>\n",
       "      <td>94</td>\n",
       "      <td>107</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99949</th>\n",
       "      <td>1</td>\n",
       "      <td>101</td>\n",
       "      <td>1.23</td>\n",
       "      <td>101</td>\n",
       "      <td>118</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98552</th>\n",
       "      <td>1</td>\n",
       "      <td>98</td>\n",
       "      <td>1.25</td>\n",
       "      <td>98</td>\n",
       "      <td>114</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99977</th>\n",
       "      <td>1</td>\n",
       "      <td>112</td>\n",
       "      <td>1.25</td>\n",
       "      <td>112</td>\n",
       "      <td>129</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99976</th>\n",
       "      <td>1</td>\n",
       "      <td>97</td>\n",
       "      <td>1.25</td>\n",
       "      <td>97</td>\n",
       "      <td>114</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100000 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       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",
       "99976  1   97         1.25          97         114  1\n",
       "\n",
       "[100000 rows x 6 columns]"
      ]
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     "execution_count": 3,
     "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": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.274453Z",
     "iopub.status.busy": "2022-07-18T22:06:15.274111Z",
     "iopub.status.idle": "2022-07-18T22:06:15.275392Z",
     "shell.execute_reply": "2022-07-18T22:06:15.275687Z"
    }
   },
   "outputs": [],
   "source": [
    "#df['ml_outcomes'] = df['ml_outcomes'] + 1*df['R']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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','ml_outcomes']].groupby(['R','T']).sum().reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2022-07-18T22:06:15.293111Z"
    }
   },
   "outputs": [],
   "source": [
    "###\n",
    "## Get number of people in each stratum\n",
    "###\n",
    "\n",
    "df_count = df[['R','T','ml_outcomes']].groupby(['R','T']).count().reset_index()\n",
    "df_count.columns = ['R','T','Count']\n",
    "df_count['N'] = df_count['Count']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.297711Z",
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     "shell.execute_reply": "2022-07-18T22:06:15.298687Z"
    }
   },
   "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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   "cell_type": "code",
   "execution_count": 8,
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    "execution": {
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       "      <th>level_0</th>\n",
       "      <th>index</th>\n",
       "      <th>R</th>\n",
       "      <th>T</th>\n",
       "      <th>ml_outcomes</th>\n",
       "      <th>N</th>\n",
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       "      <td>0.06</td>\n",
       "      <td>2</td>\n",
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       "      <th>2</th>\n",
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       "      <th>104</th>\n",
       "      <td>187</td>\n",
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       "      <td>7</td>\n",
       "      <td>0.25</td>\n",
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       "      <th>...</th>\n",
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       "      <th>49</th>\n",
       "      <td>4</td>\n",
       "      <td>49</td>\n",
       "      <td>0</td>\n",
       "      <td>62</td>\n",
       "      <td>1074.56</td>\n",
       "      <td>1679</td>\n",
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       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>3</td>\n",
       "      <td>42</td>\n",
       "      <td>0</td>\n",
       "      <td>55</td>\n",
       "      <td>1091.00</td>\n",
       "      <td>2182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>2</td>\n",
       "      <td>44</td>\n",
       "      <td>0</td>\n",
       "      <td>57</td>\n",
       "      <td>1107.54</td>\n",
       "      <td>2051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>1</td>\n",
       "      <td>46</td>\n",
       "      <td>0</td>\n",
       "      <td>59</td>\n",
       "      <td>1115.34</td>\n",
       "      <td>1923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>0</td>\n",
       "      <td>45</td>\n",
       "      <td>0</td>\n",
       "      <td>58</td>\n",
       "      <td>1123.36</td>\n",
       "      <td>2006</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>192 rows × 6 columns</p>\n",
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      ],
      "text/plain": [
       "     level_0  index  R   T  ml_outcomes     N\n",
       "0        191      0  0  12         0.02     1\n",
       "3        190      3  0  16         0.06     2\n",
       "2        189      2  0  15         0.07     1\n",
       "1        188      1  0  13         0.10     1\n",
       "104      187    104  1   7         0.25     1\n",
       "..       ...    ... ..  ..          ...   ...\n",
       "49         4     49  0  62      1074.56  1679\n",
       "42         3     42  0  55      1091.00  2182\n",
       "44         2     44  0  57      1107.54  2051\n",
       "46         1     46  0  59      1115.34  1923\n",
       "45         0     45  0  58      1123.36  2006\n",
       "\n",
       "[192 rows x 6 columns]"
      ]
     },
     "execution_count": 8,
     "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": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.308839Z",
     "iopub.status.busy": "2022-07-18T22:06:15.308480Z",
     "iopub.status.idle": "2022-07-18T22:06:15.332207Z",
     "shell.execute_reply": "2022-07-18T22:06:15.332426Z"
    }
   },
   "outputs": [],
   "source": [
    "from ortools.linear_solver import pywraplp\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.334991Z",
     "iopub.status.busy": "2022-07-18T22:06:15.334638Z",
     "iopub.status.idle": "2022-07-18T22:06:15.335988Z",
     "shell.execute_reply": "2022-07-18T22:06:15.336273Z"
    }
   },
   "outputs": [],
   "source": [
    "solver = pywraplp.Solver.CreateSolver('GLOP')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.342083Z",
     "iopub.status.busy": "2022-07-18T22:06:15.341719Z",
     "iopub.status.idle": "2022-07-18T22:06:15.343788Z",
     "shell.execute_reply": "2022-07-18T22:06:15.343537Z"
    }
   },
   "outputs": [
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       "      <th>T</th>\n",
       "      <th>ml_outcomes</th>\n",
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       "      <th>3</th>\n",
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       "      <td>3</td>\n",
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       "      <td>16</td>\n",
       "      <td>0.06</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>183</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>0.48</td>\n",
       "      <td>8</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>172</td>\n",
       "      <td>187</td>\n",
       "      <td>1</td>\n",
       "      <td>95</td>\n",
       "      <td>1.19</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>188</th>\n",
       "      <td>166</td>\n",
       "      <td>188</td>\n",
       "      <td>1</td>\n",
       "      <td>97</td>\n",
       "      <td>1.25</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>189</th>\n",
       "      <td>167</td>\n",
       "      <td>189</td>\n",
       "      <td>1</td>\n",
       "      <td>98</td>\n",
       "      <td>1.25</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>190</th>\n",
       "      <td>169</td>\n",
       "      <td>190</td>\n",
       "      <td>1</td>\n",
       "      <td>101</td>\n",
       "      <td>1.23</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>191</th>\n",
       "      <td>168</td>\n",
       "      <td>191</td>\n",
       "      <td>1</td>\n",
       "      <td>112</td>\n",
       "      <td>1.25</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>192 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     level_0  index  R    T  ml_outcomes  N\n",
       "0        191      0  0   12         0.02  1\n",
       "1        188      1  0   13         0.10  1\n",
       "2        189      2  0   15         0.07  1\n",
       "3        190      3  0   16         0.06  2\n",
       "4        183      4  0   17         0.48  8\n",
       "..       ...    ... ..  ...          ... ..\n",
       "187      172    187  1   95         1.19  1\n",
       "188      166    188  1   97         1.25  1\n",
       "189      167    189  1   98         1.25  1\n",
       "190      169    190  1  101         1.23  1\n",
       "191      168    191  1  112         1.25  1\n",
       "\n",
       "[192 rows x 6 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.352624Z",
     "iopub.status.busy": "2022-07-18T22:06:15.352240Z",
     "iopub.status.idle": "2022-07-18T22:06:15.353517Z",
     "shell.execute_reply": "2022-07-18T22:06:15.353803Z"
    }
   },
   "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'])] = 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": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.356111Z",
     "iopub.status.busy": "2022-07-18T22:06:15.355676Z",
     "iopub.status.idle": "2022-07-18T22:06:15.357395Z",
     "shell.execute_reply": "2022-07-18T22:06:15.357634Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Currently we have no constraints \n",
    "solver.NumConstraints()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.364309Z",
     "iopub.status.busy": "2022-07-18T22:06:15.363957Z",
     "iopub.status.idle": "2022-07-18T22:06:15.365513Z",
     "shell.execute_reply": "2022-07-18T22:06:15.365799Z"
    },
    "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 admits 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": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.368028Z",
     "iopub.status.busy": "2022-07-18T22:06:15.367670Z",
     "iopub.status.idle": "2022-07-18T22:06:15.369362Z",
     "shell.execute_reply": "2022-07-18T22:06:15.369607Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we have one constraint\n",
    "solver.NumConstraints()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve linear program"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.371977Z",
     "iopub.status.busy": "2022-07-18T22:06:15.371599Z",
     "iopub.status.idle": "2022-07-18T22:06:15.373134Z",
     "shell.execute_reply": "2022-07-18T22:06:15.373414Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solver.ABNORMAL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.376053Z",
     "iopub.status.busy": "2022-07-18T22:06:15.375711Z",
     "iopub.status.idle": "2022-07-18T22:06:15.376824Z",
     "shell.execute_reply": "2022-07-18T22:06:15.377183Z"
    }
   },
   "outputs": [],
   "source": [
    "status = solver.Solve()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.379400Z",
     "iopub.status.busy": "2022-07-18T22:06:15.379027Z",
     "iopub.status.idle": "2022-07-18T22:06:15.380514Z",
     "shell.execute_reply": "2022-07-18T22:06:15.380797Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "status"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.382979Z",
     "iopub.status.busy": "2022-07-18T22:06:15.382609Z",
     "iopub.status.idle": "2022-07-18T22:06:15.384032Z",
     "shell.execute_reply": "2022-07-18T22:06:15.384382Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solver.OPTIMAL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.387393Z",
     "iopub.status.busy": "2022-07-18T22:06:15.387035Z",
     "iopub.status.idle": "2022-07-18T22:06:15.388235Z",
     "shell.execute_reply": "2022-07-18T22:06:15.388463Z"
    },
    "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": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.393204Z",
     "iopub.status.busy": "2022-07-18T22:06:15.392783Z",
     "iopub.status.idle": "2022-07-18T22:06:15.394423Z",
     "shell.execute_reply": "2022-07-18T22:06:15.394706Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>row_id</th>\n",
       "      <th>decision</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
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       "      <th>2</th>\n",
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       "      <th>3</th>\n",
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       "      <th>4</th>\n",
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       "    <tr>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>187</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>188</th>\n",
       "      <td>188</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>189</th>\n",
       "      <td>189</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>190</th>\n",
       "      <td>190</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>191</th>\n",
       "      <td>191</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>192 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     row_id  decision\n",
       "0         0       0.0\n",
       "1         1       0.0\n",
       "2         2       0.0\n",
       "3         3       0.0\n",
       "4         4       0.0\n",
       "..      ...       ...\n",
       "187     187       1.0\n",
       "188     188       1.0\n",
       "189     189       1.0\n",
       "190     190       1.0\n",
       "191     191       1.0\n",
       "\n",
       "[192 rows x 2 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_decisions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.401992Z",
     "iopub.status.busy": "2022-07-18T22:06:15.401558Z",
     "iopub.status.idle": "2022-07-18T22:06:15.403242Z",
     "shell.execute_reply": "2022-07-18T22:06:15.403477Z"
    }
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\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>ml_outcomes</th>\n",
       "      <th>N</th>\n",
       "      <th>row_id</th>\n",
       "      <th>decision</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>0</td>\n",
       "      <td>45</td>\n",
       "      <td>0</td>\n",
       "      <td>58</td>\n",
       "      <td>1123.36</td>\n",
       "      <td>2006</td>\n",
       "      <td>45</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>1</td>\n",
       "      <td>46</td>\n",
       "      <td>0</td>\n",
       "      <td>59</td>\n",
       "      <td>1115.34</td>\n",
       "      <td>1923</td>\n",
       "      <td>46</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>2</td>\n",
       "      <td>44</td>\n",
       "      <td>0</td>\n",
       "      <td>57</td>\n",
       "      <td>1107.54</td>\n",
       "      <td>2051</td>\n",
       "      <td>44</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>3</td>\n",
       "      <td>42</td>\n",
       "      <td>0</td>\n",
       "      <td>55</td>\n",
       "      <td>1091.00</td>\n",
       "      <td>2182</td>\n",
       "      <td>42</td>\n",
       "      <td>0.27681</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>4</td>\n",
       "      <td>49</td>\n",
       "      <td>0</td>\n",
       "      <td>62</td>\n",
       "      <td>1074.56</td>\n",
       "      <td>1679</td>\n",
       "      <td>49</td>\n",
       "      <td>1.00000</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>104</th>\n",
       "      <td>187</td>\n",
       "      <td>104</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>0.25</td>\n",
       "      <td>1</td>\n",
       "      <td>104</td>\n",
       "      <td>0.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>188</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>13</td>\n",
       "      <td>0.10</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>189</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>15</td>\n",
       "      <td>0.07</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>190</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>0.06</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>0.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>191</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>0.02</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>192 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     level_0  index  R   T  ml_outcomes     N  row_id  decision\n",
       "45         0     45  0  58      1123.36  2006      45   1.00000\n",
       "46         1     46  0  59      1115.34  1923      46   1.00000\n",
       "44         2     44  0  57      1107.54  2051      44   1.00000\n",
       "42         3     42  0  55      1091.00  2182      42   0.27681\n",
       "49         4     49  0  62      1074.56  1679      49   1.00000\n",
       "..       ...    ... ..  ..          ...   ...     ...       ...\n",
       "104      187    104  1   7         0.25     1     104   0.00000\n",
       "1        188      1  0  13         0.10     1       1   0.00000\n",
       "2        189      2  0  15         0.07     1       2   0.00000\n",
       "3        190      3  0  16         0.06     2       3   0.00000\n",
       "0        191      0  0  12         0.02     1       0   0.00000\n",
       "\n",
       "[192 rows x 8 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
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    "dff.merge(df_decisions,left_index=True,right_index=True).sort_values(by='ml_outcomes',ascending=False)"
   ]
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   "execution_count": 23,
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     "iopub.status.idle": "2022-07-18T22:06:15.412399Z",
     "shell.execute_reply": "2022-07-18T22:06:15.412701Z"
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       "     level_0  index  R    T  ml_outcomes  N  row_id  decision\n",
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       "..       ...    ... ..  ...          ... ..     ...       ...\n",
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       "103      175    103  0  130         1.00  1     103       1.0\n",
       "\n",
       "[192 rows x 8 columns]"
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     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "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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  {
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     "shell.execute_reply": "2022-07-18T22:06:15.421699Z"
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       "     level_0  index  R   T  ml_outcomes     N  row_id  decision\n",
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       "44         2     44  0  57      1107.54  2051      44   1.00000\n",
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       "49         4     49  0  62      1074.56  1679      49   1.00000\n",
       "..       ...    ... ..  ..          ...   ...     ...       ...\n",
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       "0        191      0  0  12         0.02     1       0   0.00000\n",
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     "execution_count": 24,
     "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"
   ]
  },
  {
   "cell_type": "code",
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    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.424147Z",
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     "shell.execute_reply": "2022-07-18T22:06:15.425382Z"
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    {
     "data": {
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       "192"
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     "execution_count": 25,
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    "len(xxx_)"
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  {
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   "execution_count": 26,
   "metadata": {
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     "iopub.execute_input": "2022-07-18T22:06:15.431562Z",
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     "shell.execute_reply": "2022-07-18T22:06:15.433103Z"
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      "text/plain": [
       "     level_0  index  R   T  ml_outcomes     N  row_id  decision\n",
       "45         0     45  0  58      1123.36  2006      45   1.00000\n",
       "46         1     46  0  59      1115.34  1923      46   1.00000\n",
       "44         2     44  0  57      1107.54  2051      44   1.00000\n",
       "42         3     42  0  55      1091.00  2182      42   0.27681\n",
       "49         4     49  0  62      1074.56  1679      49   1.00000\n",
       "..       ...    ... ..  ..          ...   ...     ...       ...\n",
       "104      187    104  1   7         0.25     1     104   0.00000\n",
       "1        188      1  0  13         0.10     1       1   0.00000\n",
       "2        189      2  0  15         0.07     1       2   0.00000\n",
       "3        190      3  0  16         0.06     2       3   0.00000\n",
       "0        191      0  0  12         0.02     1       0   0.00000\n",
       "\n",
       "[192 rows x 8 columns]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xxx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.435856Z",
     "iopub.status.busy": "2022-07-18T22:06:15.435438Z",
     "iopub.status.idle": "2022-07-18T22:06:15.437088Z",
     "shell.execute_reply": "2022-07-18T22:06:15.437381Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "34190.23000000001"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(xxx['ml_outcomes']*xxx['decision']).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.440580Z",
     "iopub.status.busy": "2022-07-18T22:06:15.440220Z",
     "iopub.status.idle": "2022-07-18T22:06:15.441460Z",
     "shell.execute_reply": "2022-07-18T22:06:15.441753Z"
    }
   },
   "outputs": [],
   "source": [
    "def maxMLOutcomes(frac_minority=0.01):\n",
    "    minority_admits = int(K*frac_minority)\n",
    "    majority_admits = int(K*(1-frac_minority))\n",
    "    \n",
    "    b = df[df['R']==1].sort_values(by='ml_outcomes',ascending=False).head(n=minority_admits)\n",
    "    w = df[df['R']==0].sort_values(by='ml_outcomes',ascending=False).head(n=majority_admits)\n",
    "    \n",
    "    return b['Y'].sum() + w['Y'].sum()    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.444777Z",
     "iopub.status.busy": "2022-07-18T22:06:15.444414Z",
     "iopub.status.idle": "2022-07-18T22:06:15.445604Z",
     "shell.execute_reply": "2022-07-18T22:06:15.445890Z"
    }
   },
   "outputs": [],
   "source": [
    "def maxMLOutcomesminority(frac_minority=0.01):\n",
    "    minority_admits = int(K*frac_minority)\n",
    "    majority_admits = int(K*(1-frac_minority))\n",
    "    \n",
    "    b = df[df['R']==1].sort_values(by='ml_outcomes',ascending=False).head(n=minority_admits)\n",
    "    w = df[df['R']==0].sort_values(by='ml_outcomes',ascending=False).head(n=majority_admits)\n",
    "    \n",
    "    return b['Y'].sum()   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.556535Z",
     "iopub.status.busy": "2022-07-18T22:06:15.556156Z",
     "iopub.status.idle": "2022-07-18T22:06:15.557328Z",
     "shell.execute_reply": "2022-07-18T22:06:15.557613Z"
    }
   },
   "outputs": [],
   "source": [
    "df['key'] = df['R'].astype(str)+'_'+df['T'].astype(str)\n",
    "xxx['key'] = xxx['R'].astype(str)+'_'+xxx['T'].astype(str)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.560086Z",
     "iopub.status.busy": "2022-07-18T22:06:15.559664Z",
     "iopub.status.idle": "2022-07-18T22:06:15.561216Z",
     "shell.execute_reply": "2022-07-18T22:06:15.561511Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "192"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(xxx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.571167Z",
     "iopub.status.busy": "2022-07-18T22:06:15.570794Z",
     "iopub.status.idle": "2022-07-18T22:06:15.606129Z",
     "shell.execute_reply": "2022-07-18T22:06:15.606380Z"
    }
   },
   "outputs": [],
   "source": [
    "admit_decisions = df.merge(xxx,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",
    "\n",
    "FRAC_minority_POLICY = (admit_decisions['R_y'] * 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_y'] * admit_decisions['decision_random']).sum()/admit_decisions['decision_random'].sum()\n",
    "SUM_BP_RAND_POLICY = ( admit_decisions['Y'] * admit_decisions['decision_random']).sum()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-18T22:06:15.609757Z",
     "iopub.status.busy": "2022-07-18T22:06:15.609396Z",
     "iopub.status.idle": "2022-07-18T22:06:15.610617Z",
     "shell.execute_reply": "2022-07-18T22:06:15.610899Z"
    }
   },
   "outputs": [],
   "source": [
    "file = open('./lp_results.csv','w')\n",
    "file.write('{}\\t{}\\t{}\\n'.format('Policy Name','Frac Diverse Candidates','Total Graduated'))\n",
    "file.write('{}\\t{}\\t{}\\n'.format('Random',str(FRAC_RANDOM_POLICY),str(SUM_BP_RAND_POLICY)))\n",
    "file.write('{}\\t{}\\t{}\\n'.format('Maximize Utility',str(FRAC_minority_POLICY),str(SUM_BP_POLICY)))\n",
    "file.close()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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