Experiment 2 Toy Example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "72fad733",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.utils import shuffle\n",
    "from rules import *\n",
    "import warnings; warnings.simplefilter('ignore')\n",
    "\n",
    "def get_kendall(x, c1, c2):\n",
    "    return pd.DataFrame([x[c1],x[c2]]).T.corr(method='kendall')[1].values[0]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6860d67b",
   "metadata": {},
   "source": [
    "# This is a toy example for the experiment 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "af17cc02",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize your experiments\n",
    "METHOD = 'UM10'\n",
    "N_PROFILES = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "aa8b81d8",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running profile:  0\n"
     ]
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    {
     "name": "stderr",
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     ]
    }
   ],
   "source": [
    "results = []\n",
    "\n",
    "\n",
    "for profile in range(N_PROFILES):\n",
    "    \n",
    "    print(\"Running profile: \", profile)\n",
    "\n",
    "    for number_issues in range(3,6):\n",
    "\n",
    "        for number_agents in [100]:\n",
    "        \n",
    "            individuals = []\n",
    "            all_rankings = using_preflib(number_issues, number_agents+1, type_=METHOD)\n",
    "            for perc_rows in np.arange(0.10, 1.05, 0.01):\n",
    "\n",
    "                total_rows = calculate_number_of_rows_for_complete_information(number_issues,2)\n",
    "                number_rows = math.ceil(total_rows * perc_rows)+1\n",
    "                \n",
    "                output = data_transform_with_pairwise(individuals, \n",
    "                                                      all_rankings, \n",
    "                                     number_individuals=number_agents, \n",
    "                                     number_proposals=number_issues, \n",
    "                                     number_rows=number_rows, \n",
    "                                     number_preferences=2)\n",
    "\n",
    "                data = pd.DataFrame(output)\n",
    "                data.columns = [\"uuid\", \"option_a\", \"option_b\", \"selected\"]\n",
    "                data[\"id\"] = range(1, data.shape[0] + 1)\n",
    "                data[\"option_a\"] = data[\"option_a\"].astype(int)\n",
    "                data[\"option_b\"] = data[\"option_b\"].astype(int)\n",
    "                data[\"selected\"] = data[\"selected\"].astype(int)\n",
    "                data[\"option_a_sorted\"] = data[[\"option_a\", \"option_b\"]].min(axis=1).astype(int)\n",
    "                data[\"option_b_sorted\"] = data[[\"option_a\", \"option_b\"]].max(axis=1).astype(int)\n",
    "                data[\"card_id\"] = data[\"option_a_sorted\"].astype(str) + \"_\" + data[\"option_b_sorted\"].astype(str)\n",
    "                a = data[[\"option_a\", \"option_b\", \"selected\"]].values\n",
    "                data[\"option_source\"] = np.where(a[:, 1] == a[:, 2], a[:, 0], a[:, 1])\n",
    "                data[\"option_target\"] = np.where(a[:, 0] == a[:, 2], a[:, 0], a[:, 1])\n",
    "\n",
    "                df_win_rate = bootstrap4(data, win_rate, iterations=1, \n",
    "                                     aggregate=False, rank=True, rank_column=\"rank\")\n",
    "                ranked_win_rate = list(df_win_rate.sort_values(by='value', ascending=False)['id'].values)\n",
    "    \n",
    "                df_copeland = bootstrap4(data, copeland, iterations=1, \n",
    "                                         aggregate=False, rank=True, rank_column=\"rank\")\n",
    "                ranked_copeland = list(df_copeland.sort_values(by='value', ascending=False)['id'].values)\n",
    "\n",
    "                df_divisiveness_win_rate = bootstrap4(data, divisiveness, iterations=1, \n",
    "                                             aggregate=False, rank=True, rank_column=\"rank\")\n",
    "                ranked_divisiveness_win_rate = list(df_divisiveness_win_rate.sort_values(by='value', ascending=False)['id'].values)\n",
    "\n",
    "\n",
    "                df_divisiveness_copeland = bootstrap4(data, divisiveness_copeland, iterations=1, \n",
    "                                             aggregate=False, rank=True, rank_column=\"rank\")\n",
    "                ranked_divisiveness_copeland = list(df_divisiveness_copeland.sort_values(by='value', ascending=False)['id'].values)\n",
    "\n",
    "                df_std = standard_deviation_rankings(all_rankings)\n",
    "                ranked_std = list(df_std.sort_values(by='value', ascending=False)['id'].values)\n",
    "\n",
    "                results.append([perc_rows,\n",
    "                                number_rows,\n",
    "                                number_issues, \n",
    "                                number_agents,\n",
    "                                profile,\n",
    "                                ranked_win_rate,\\\n",
    "                                ranked_copeland,\\\n",
    "                                ranked_std,\\\n",
    "                                ranked_divisiveness_win_rate,\\\n",
    "                                ranked_divisiveness_copeland\n",
    "                ])\n",
    "\n",
    "    plot = pd.DataFrame(results, \n",
    "                        columns=['perc_rows',\n",
    "                                 'number_rows',\n",
    "                                 'number_issues',\n",
    "                                 'number_agents',\n",
    "                                 'profile',\\\n",
    "                                 'RANK(WR)',\n",
    "                                 'RANK(COP)',\n",
    "                                 'RANK(STD)',\n",
    "                                 'RANK(DIV(WR))',\n",
    "                                 'RANK(DIV(COP))'])\n",
    "    plot.to_csv(\"data/results_incomplete_method_%s_profile_%s.csv\"%(METHOD,N_PROFILES), index=False)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f9803564",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"data/results_incomplete_method_%s_profile_%s.csv\"%(METHOD,N_PROFILES))\n",
    "df['RANK(WR)'] = df['RANK(WR)'].apply(lambda x: eval(x))\n",
    "df['RANK(STD)'] = df['RANK(STD)'].apply(lambda x: eval(x))\n",
    "df['RANK(COP)'] = df['RANK(COP)'].apply(lambda x: eval(x))\n",
    "df['RANK(DIV(WR))'] = df['RANK(DIV(WR))'].apply(lambda x: eval(x))\n",
    "df['RANK(DIV(COP))'] = df['RANK(DIV(COP))'].apply(lambda x: eval(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "18764342",
   "metadata": {},
   "outputs": [],
   "source": [
    "df['KT(WR,STD)'] = df.apply(lambda x: get_kendall(x, c1='RANK(WR)', c2='RANK(STD)'), axis=1)\n",
    "df['KT(WR,COP)'] = df.apply(lambda x: get_kendall(x, c1='RANK(WR)', c2='RANK(COP)'), axis=1)\n",
    "df['KT(WR,RANK(DIV(WR)))'] = df.apply(lambda x: get_kendall(x, c1='RANK(WR)', c2='RANK(DIV(WR))'), axis=1)\n",
    "df['KT(WR,RANK(DIV(COP)))'] = df.apply(lambda x: get_kendall(x, c1='RANK(WR)', c2='RANK(DIV(COP))'), axis=1)\n",
    "df['KT(RANK(DIV(WR)),STD)'] = df.apply(lambda x: get_kendall(x, c1='RANK(DIV(WR))', c2='RANK(STD)'), axis=1)\n",
    "df['KT(RANK(DIV(WR)),COP)'] = df.apply(lambda x: get_kendall(x, c1='RANK(DIV(WR))', c2='RANK(COP)'), axis=1)\n",
    "df['KT(RANK(DIV(WR)),RANK(DIV(COP)))'] = df.apply(lambda x: get_kendall(x, c1='RANK(DIV(WR))', c2='RANK(DIV(COP))'), axis=1)\n",
    "df['KT(RANK(DIV(COP)),STD)'] = df.apply(lambda x: get_kendall(x, c1='RANK(DIV(COP))', c2='RANK(STD)'), axis=1)\n",
    "df['KT(RANK(DIV(COP)),COP)'] = df.apply(lambda x: get_kendall(x, c1='RANK(DIV(COP))', c2='RANK(COP)'), axis=1)\n",
    "df['KT(RANK(DIV(COP)),RANK(DIV(WR)))'] = df.apply(lambda x: get_kendall(x, c1='RANK(DIV(COP))', c2='RANK(DIV(WR))'), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e795d6a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>perc_rows</th>\n",
       "      <th>number_rows</th>\n",
       "      <th>number_issues</th>\n",
       "      <th>number_agents</th>\n",
       "      <th>profile</th>\n",
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       "      <th>KT(RANK(DIV(WR)),STD)</th>\n",
       "      <th>KT(RANK(DIV(WR)),COP)</th>\n",
       "      <th>KT(RANK(DIV(WR)),RANK(DIV(COP)))</th>\n",
       "      <th>KT(RANK(DIV(COP)),STD)</th>\n",
       "      <th>KT(RANK(DIV(COP)),COP)</th>\n",
       "      <th>KT(RANK(DIV(COP)),RANK(DIV(WR)))</th>\n",
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       "    <tr>\n",
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       "      <td>0.11</td>\n",
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       "    <tr>\n",
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       "      <td>1.0</td>\n",
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       "      <td>-0.333333</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>-0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.13</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>100</td>\n",
       "      <td>0</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[2, 0, 1]</td>\n",
       "      <td>[2, 1, 0]</td>\n",
       "      <td>[2, 0, 1]</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.14</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>100</td>\n",
       "      <td>0</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[2, 0, 1]</td>\n",
       "      <td>[2, 0, 1]</td>\n",
       "      <td>[2, 0, 1]</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   perc_rows  number_rows  number_issues  number_agents  profile   RANK(WR)  \\\n",
       "0       0.10            2              3            100        0  [0, 1, 2]   \n",
       "1       0.11            2              3            100        0  [0, 1, 2]   \n",
       "2       0.12            2              3            100        0  [0, 1, 2]   \n",
       "3       0.13            2              3            100        0  [0, 1, 2]   \n",
       "4       0.14            2              3            100        0  [0, 1, 2]   \n",
       "\n",
       "   RANK(COP)  RANK(STD) RANK(DIV(WR)) RANK(DIV(COP))  KT(WR,STD)  KT(WR,COP)  \\\n",
       "0  [0, 1, 2]  [2, 0, 1]     [0, 1, 2]      [0, 1, 2]   -0.333333         1.0   \n",
       "1  [0, 1, 2]  [2, 0, 1]     [2, 1, 0]      [0, 1, 2]   -0.333333         1.0   \n",
       "2  [0, 1, 2]  [2, 0, 1]     [2, 1, 0]      [0, 2, 1]   -0.333333         1.0   \n",
       "3  [0, 1, 2]  [2, 0, 1]     [2, 1, 0]      [2, 0, 1]   -0.333333         1.0   \n",
       "4  [0, 1, 2]  [2, 0, 1]     [2, 0, 1]      [2, 0, 1]   -0.333333         1.0   \n",
       "\n",
       "   KT(WR,RANK(DIV(WR)))  KT(WR,RANK(DIV(COP)))  KT(RANK(DIV(WR)),STD)  \\\n",
       "0              1.000000               1.000000              -0.333333   \n",
       "1             -1.000000               1.000000               0.333333   \n",
       "2             -1.000000               0.333333               0.333333   \n",
       "3             -1.000000              -0.333333               0.333333   \n",
       "4             -0.333333              -0.333333               1.000000   \n",
       "\n",
       "   KT(RANK(DIV(WR)),COP)  KT(RANK(DIV(WR)),RANK(DIV(COP)))  \\\n",
       "0               1.000000                          1.000000   \n",
       "1              -1.000000                         -1.000000   \n",
       "2              -1.000000                         -0.333333   \n",
       "3              -1.000000                          0.333333   \n",
       "4              -0.333333                          1.000000   \n",
       "\n",
       "   KT(RANK(DIV(COP)),STD)  KT(RANK(DIV(COP)),COP)  \\\n",
       "0               -0.333333                1.000000   \n",
       "1               -0.333333                1.000000   \n",
       "2               -1.000000                0.333333   \n",
       "3                1.000000               -0.333333   \n",
       "4                1.000000               -0.333333   \n",
       "\n",
       "   KT(RANK(DIV(COP)),RANK(DIV(WR)))  \n",
       "0                          1.000000  \n",
       "1                         -1.000000  \n",
       "2                         -0.333333  \n",
       "3                          0.333333  \n",
       "4                          1.000000  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e3ffc9bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "df['Robusteness(WR)'] = -1\n",
    "df['Robusteness(COP)'] = -1\n",
    "df['Robusteness(DIV,WR)'] = -1\n",
    "df['Robusteness(DIV,COP)'] = -1\n",
    "\n",
    "for each_row in df.iterrows():\n",
    "    \n",
    "    rank_wr = df[(df['number_issues']==each_row[1]['number_issues'])\n",
    "          & (df['number_agents']==each_row[1]['number_agents'])\n",
    "          & (df['profile']==each_row[1]['profile'])\n",
    "          ].sort_values(by='perc_rows').tail(1)['RANK(WR)'].values[0]\n",
    "    \n",
    "    \n",
    "    rank_wr1 = float(df[(df['number_issues']==each_row[1]['number_issues'])\n",
    "          & (df['number_agents']==each_row[1]['number_agents'])\n",
    "          & (df['profile']==each_row[1]['profile'])\n",
    "            & (df['perc_rows']<=each_row[1]['perc_rows'])\n",
    "          ].sort_values(by='perc_rows')['Robusteness(WR)'].max())\n",
    "    \n",
    "    kt_wr = float(pd.DataFrame([each_row[1]['RANK(WR)'], rank_wr]).T.corr(method='kendall')[1].values[0])\n",
    "    \n",
    "    if kt_wr < rank_wr1:\n",
    "        kt_wr = rank_wr1\n",
    "    df.loc[df.index == each_row[0], 'Robusteness(WR)'] = kt_wr\n",
    "    \n",
    "    rank_cop = df[(df['number_issues']==each_row[1]['number_issues'])\n",
    "          & (df['number_agents']==each_row[1]['number_agents'])\n",
    "          & (df['profile']==each_row[1]['profile'])\n",
    "          ].sort_values(by='perc_rows').tail(1)['RANK(COP)'].values[0]\n",
    "    \n",
    "    rank_cop1 = float(df[(df['number_issues']==each_row[1]['number_issues'])\n",
    "          & (df['number_agents']==each_row[1]['number_agents'])\n",
    "          & (df['profile']==each_row[1]['profile'])\n",
    "            & (df['perc_rows']<=each_row[1]['perc_rows'])\n",
    "          ].sort_values(by='perc_rows')['Robusteness(COP)'].max())\n",
    "    \n",
    "    kt_wr = float(pd.DataFrame([each_row[1]['RANK(COP)'], rank_cop]).T.corr(method='kendall')[1].values[0])\n",
    "    \n",
    "    if kt_wr < rank_cop1:\n",
    "        kt_wr = rank_cop1\n",
    "    df.loc[df.index == each_row[0], 'Robusteness(COP)'] = kt_wr\n",
    "    \n",
    "    \n",
    "    \n",
    "    rank_div_wr = df[(df['number_issues']==each_row[1]['number_issues'])\n",
    "          & (df['number_agents']==each_row[1]['number_agents'])\n",
    "          & (df['profile']==each_row[1]['profile'])\n",
    "          ].sort_values(by='perc_rows').tail(1)['RANK(DIV(WR))'].values[0]\n",
    "    \n",
    "    rank_div_cop =df[(df['number_issues']==each_row[1]['number_issues'])\n",
    "          & (df['number_agents']==each_row[1]['number_agents'])\n",
    "          & (df['profile']==each_row[1]['profile'])\n",
    "          ].sort_values(by='perc_rows').tail(1)['RANK(DIV(COP))'].values[0]\n",
    "    \n",
    "    rank_div_wr1 = float(df[(df['number_issues']==each_row[1]['number_issues'])\n",
    "          & (df['number_agents']==each_row[1]['number_agents'])\n",
    "          & (df['profile']==each_row[1]['profile'])\n",
    "            & (df['perc_rows']<=each_row[1]['perc_rows'])\n",
    "          ].sort_values(by='perc_rows')['Robusteness(DIV,WR)'].max())\n",
    "        \n",
    "    rank_div_cop1 = float(df[(df['number_issues']==each_row[1]['number_issues'])\n",
    "          & (df['number_agents']==each_row[1]['number_agents'])\n",
    "          & (df['profile']==each_row[1]['profile'])\n",
    "            & (df['perc_rows']<=each_row[1]['perc_rows'])\n",
    "          ].sort_values(by='perc_rows')['Robusteness(DIV,COP)'].max())\n",
    "\n",
    "        \n",
    "    kt_wr = float(pd.DataFrame([each_row[1]['RANK(DIV(WR))'], rank_div_wr]).T.corr(method='kendall')[1].values[0])\n",
    "    \n",
    "    if kt_wr < rank_div_wr1:\n",
    "        kt_wr = rank_div_wr1\n",
    "    df.loc[df.index == each_row[0], 'Robusteness(DIV,WR)'] = kt_wr\n",
    "    \n",
    "    kt_cop = float(pd.DataFrame([each_row[1]['RANK(DIV(COP))'], rank_div_cop]).T.corr(method='kendall')[1].values[0])\n",
    "    \n",
    "    if kt_cop < rank_div_cop1:\n",
    "        kt_cop = rank_div_cop1\n",
    "    df.loc[df.index ==each_row[0], 'Robusteness(DIV,COP)'] = kt_cop\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7c084b9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.to_csv(\"data/results_incomplete_method_%s_profile_%s_kendall.csv\"%(METHOD,N_PROFILES), index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a9f6179e",
   "metadata": {},
   "outputs": [],
   "source": [
    "df['Robusteness(WR)'] = df['Robusteness(WR)'].astype(float)\n",
    "df['Robusteness(COP)'] = df['Robusteness(COP)'].astype(float)\n",
    "df['Robusteness(DIV,WR)'] = df['Robusteness(DIV,WR)'].astype(float)\n",
    "df['Robusteness(DIV,COP)'] = df['Robusteness(DIV,COP)'].astype(float)\n",
    "df['perc_rows'] = df['perc_rows'].astype(float)*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8787803c",
   "metadata": {},
   "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>perc_rows</th>\n",
       "      <th>number_rows</th>\n",
       "      <th>number_issues</th>\n",
       "      <th>number_agents</th>\n",
       "      <th>profile</th>\n",
       "      <th>RANK(WR)</th>\n",
       "      <th>RANK(COP)</th>\n",
       "      <th>RANK(STD)</th>\n",
       "      <th>RANK(DIV(WR))</th>\n",
       "      <th>RANK(DIV(COP))</th>\n",
       "      <th>...</th>\n",
       "      <th>KT(RANK(DIV(WR)),STD)</th>\n",
       "      <th>KT(RANK(DIV(WR)),COP)</th>\n",
       "      <th>KT(RANK(DIV(WR)),RANK(DIV(COP)))</th>\n",
       "      <th>KT(RANK(DIV(COP)),STD)</th>\n",
       "      <th>KT(RANK(DIV(COP)),COP)</th>\n",
       "      <th>KT(RANK(DIV(COP)),RANK(DIV(WR)))</th>\n",
       "      <th>Robusteness(WR)</th>\n",
       "      <th>Robusteness(COP)</th>\n",
       "      <th>Robusteness(DIV,WR)</th>\n",
       "      <th>Robusteness(DIV,COP)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10.0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>100</td>\n",
       "      <td>0</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[2, 0, 1]</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>-0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11.0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>100</td>\n",
       "      <td>0</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[2, 0, 1]</td>\n",
       "      <td>[2, 1, 0]</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>...</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12.0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>100</td>\n",
       "      <td>0</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[2, 0, 1]</td>\n",
       "      <td>[2, 1, 0]</td>\n",
       "      <td>[0, 2, 1]</td>\n",
       "      <td>...</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>13.0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>100</td>\n",
       "      <td>0</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[2, 0, 1]</td>\n",
       "      <td>[2, 1, 0]</td>\n",
       "      <td>[2, 0, 1]</td>\n",
       "      <td>...</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>14.0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>100</td>\n",
       "      <td>0</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[0, 1, 2]</td>\n",
       "      <td>[2, 0, 1]</td>\n",
       "      <td>[2, 0, 1]</td>\n",
       "      <td>[2, 0, 1]</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.333333</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 24 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   perc_rows  number_rows  number_issues  number_agents  profile   RANK(WR)  \\\n",
       "0       10.0            2              3            100        0  [0, 1, 2]   \n",
       "1       11.0            2              3            100        0  [0, 1, 2]   \n",
       "2       12.0            2              3            100        0  [0, 1, 2]   \n",
       "3       13.0            2              3            100        0  [0, 1, 2]   \n",
       "4       14.0            2              3            100        0  [0, 1, 2]   \n",
       "\n",
       "   RANK(COP)  RANK(STD) RANK(DIV(WR)) RANK(DIV(COP))  ...  \\\n",
       "0  [0, 1, 2]  [2, 0, 1]     [0, 1, 2]      [0, 1, 2]  ...   \n",
       "1  [0, 1, 2]  [2, 0, 1]     [2, 1, 0]      [0, 1, 2]  ...   \n",
       "2  [0, 1, 2]  [2, 0, 1]     [2, 1, 0]      [0, 2, 1]  ...   \n",
       "3  [0, 1, 2]  [2, 0, 1]     [2, 1, 0]      [2, 0, 1]  ...   \n",
       "4  [0, 1, 2]  [2, 0, 1]     [2, 0, 1]      [2, 0, 1]  ...   \n",
       "\n",
       "   KT(RANK(DIV(WR)),STD)  KT(RANK(DIV(WR)),COP)  \\\n",
       "0              -0.333333               1.000000   \n",
       "1               0.333333              -1.000000   \n",
       "2               0.333333              -1.000000   \n",
       "3               0.333333              -1.000000   \n",
       "4               1.000000              -0.333333   \n",
       "\n",
       "   KT(RANK(DIV(WR)),RANK(DIV(COP)))  KT(RANK(DIV(COP)),STD)  \\\n",
       "0                          1.000000               -0.333333   \n",
       "1                         -1.000000               -0.333333   \n",
       "2                         -0.333333               -1.000000   \n",
       "3                          0.333333                1.000000   \n",
       "4                          1.000000                1.000000   \n",
       "\n",
       "   KT(RANK(DIV(COP)),COP)  KT(RANK(DIV(COP)),RANK(DIV(WR)))  Robusteness(WR)  \\\n",
       "0                1.000000                          1.000000              1.0   \n",
       "1                1.000000                         -1.000000              1.0   \n",
       "2                0.333333                         -0.333333              1.0   \n",
       "3               -0.333333                          0.333333              1.0   \n",
       "4               -0.333333                          1.000000              1.0   \n",
       "\n",
       "   Robusteness(COP)  Robusteness(DIV,WR)  Robusteness(DIV,COP)  \n",
       "0               1.0                 -1.0             -0.333333  \n",
       "1               1.0                  1.0             -0.333333  \n",
       "2               1.0                  1.0             -0.333333  \n",
       "3               1.0                  1.0              1.000000  \n",
       "4               1.0                  1.0              1.000000  \n",
       "\n",
       "[5 rows x 24 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6a8c81eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "subp = df.melt(id_vars=['perc_rows','number_issues','number_agents','profile'],\\\n",
    "                 value_vars=[\"Robusteness(DIV,WR)\",\n",
    "                             \"Robusteness(DIV,COP)\",\n",
    "                            \"KT(RANK(DIV(COP)),RANK(DIV(WR)))\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b0b2aade",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Figure1: kendall-tau on the vertical axis, \n",
    "# number of individuals on horiz axis (fix number of items=20)\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(4,4), dpi=150)\n",
    "\n",
    "subp['size'] = 1500\n",
    "g = sns.lineplot(data=subp[(subp['number_agents'].isin([10])) & \n",
    "                           (subp['variable'].isin([\"Robusteness(DIV,WR)\"])) & \n",
    "                          (subp['number_issues'].isin([4,6,8,10,14,18]))].dropna(), \\\n",
    "             x='perc_rows', y='value',\\\n",
    "                 hue='number_issues',\n",
    "             linewidth=2, \n",
    "                 style='number_issues',\\\n",
    "                 markers = True, \n",
    "                 alpha=0.9, palette='Dark2', legend=True,\n",
    "              ax=ax)\n",
    "leg = g.legend(title=\"# issues\", frameon=False, fontsize=7, ncol=3, loc='lower right')\n",
    "leg.get_title().set_position((-10, 0))\n",
    "for line in leg.get_lines():\n",
    "    line.set_linewidth(1.4)\n",
    "    \n",
    "# for dots in g.collections:\n",
    "#     dots.set_alpha(1)\n",
    "#     dots.set_s(1500)\n",
    "\n",
    "\n",
    "ax.spines[\"left\"].set_linewidth(1.2)\n",
    "ax.spines[\"bottom\"].set_linewidth(1.2)\n",
    "ax.spines[\"right\"].set_visible(False)\n",
    "ax.spines[\"top\"].set_visible(False)\n",
    "ax.set_ylim(-0.25,1.05)\n",
    "plt.title(\"UM10\")\n",
    "# import matplotlib.ticker as mticker\n",
    "# ax.xaxis.set_major_locator(mticker.MultipleLocator(100))\n",
    "ax.set_ylabel(\"KT($\\mathit{Div}^\\mathit{Borda}(x\\%)$,$\\mathit{Div}^\\mathit{Borda}(100\\%)$)\")\n",
    "ax.set_xlabel(\"% of pairs\")\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"figures/figure_experiment_2.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "68f7772f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7360bdba",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a1eedd01",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8 (tags/v3.10.8:aaaf517, Oct 11 2022, 16:50:30) [MSC v.1933 64 bit (AMD64)]"
  },
  "vscode": {
   "interpreter": {
    "hash": "369f2c481f4da34e4445cda3fffd2e751bd1c4d706f27375911949ba6bb62e1c"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}