{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dynamic Process: Robustness to the Initial Poll (C.4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-16T11:20:03.222937Z",
     "start_time": "2021-02-16T11:20:01.167004Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from poisson_approval import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-16T11:20:03.228589Z",
     "start_time": "2021-02-16T11:20:03.224598Z"
    }
   },
   "outputs": [],
   "source": [
    "N_SAMPLES = 10000\n",
    "N_MAX_EPISODES = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-16T11:20:03.243548Z",
     "start_time": "2021-02-16T11:20:03.229585Z"
    }
   },
   "outputs": [],
   "source": [
    "inits = {\n",
    "    'uniform undominated': 'random_tau_undominated',\n",
    "    'expressive': 'fanatic',\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Condorcet Consistency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-16T14:42:35.701243Z",
     "start_time": "2021-02-16T11:20:03.244545Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Approval</th>\n",
       "      <th>Plurality</th>\n",
       "      <th>Anti-plurality</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Distribution of tau^0</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>uniform undominated</th>\n",
       "      <td>0.999974</td>\n",
       "      <td>0.8170</td>\n",
       "      <td>0.489474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>expressive</th>\n",
       "      <td>0.999990</td>\n",
       "      <td>0.9681</td>\n",
       "      <td>0.488994</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       Approval  Plurality  Anti-plurality\n",
       "Distribution of tau^0                                     \n",
       "uniform undominated    0.999974     0.8170        0.489474\n",
       "expressive             0.999990     0.9681        0.488994"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_cond = pd.DataFrame()\n",
    "table_cond.index.name = 'Distribution of tau^0'\n",
    "for init_name, init in inits.items():\n",
    "    rand_profile = RandConditional(\n",
    "        RandProfileHistogramUniform(n_bins=1), \n",
    "        test=is_condorcet, n_trials_max=None\n",
    "    )\n",
    "    results = monte_carlo_fictitious_play(\n",
    "        factory=rand_profile,\n",
    "        n_samples=N_SAMPLES,\n",
    "        n_max_episodes=N_MAX_EPISODES,\n",
    "        voting_rules=VOTING_RULES,\n",
    "        init=init,\n",
    "        monte_carlo_settings=[\n",
    "            MCS_FREQUENCY_CW_WINS,\n",
    "        ],\n",
    "        file_save='sav/init_%s_with_CW.sav' % init_name,\n",
    "    )\n",
    "    for voting_rule in VOTING_RULES:\n",
    "        table_cond.loc[init_name, voting_rule] = float(results[voting_rule]['mean_frequency_cw_wins'])\n",
    "table_cond"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Welfare Loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-16T19:07:50.719809Z",
     "start_time": "2021-02-16T14:42:35.702241Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th {\n",
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       "    }\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>Approval</th>\n",
       "      <th>Plurality</th>\n",
       "      <th>Anti-plurality</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Distribution of tau^0</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>uniform undominated</th>\n",
       "      <td>0.006502</td>\n",
       "      <td>0.030931</td>\n",
       "      <td>0.099204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>expressive</th>\n",
       "      <td>0.006553</td>\n",
       "      <td>0.008550</td>\n",
       "      <td>0.099098</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       Approval  Plurality  Anti-plurality\n",
       "Distribution of tau^0                                     \n",
       "uniform undominated    0.006502   0.030931        0.099204\n",
       "expressive             0.006553   0.008550        0.099098"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_welfare_loss = pd.DataFrame()\n",
    "table_welfare_loss.index.name = 'Distribution of tau^0'\n",
    "for init_name, init in inits.items():\n",
    "    rand_profile = RandProfileHistogramUniform(n_bins=1)\n",
    "    results = monte_carlo_fictitious_play(\n",
    "        factory=rand_profile,\n",
    "        n_samples=N_SAMPLES,\n",
    "        n_max_episodes=N_MAX_EPISODES,\n",
    "        voting_rules=VOTING_RULES,\n",
    "        init=init,\n",
    "        monte_carlo_settings=[\n",
    "            MCS_WELFARE_LOSSES,\n",
    "        ],\n",
    "        file_save='sav/init_%s.sav' % init_name,\n",
    "    )\n",
    "    for voting_rule in VOTING_RULES:\n",
    "        table_welfare_loss.loc[init_name, voting_rule] = float(\n",
    "            results[voting_rule]['mean_utilitarian_welfare_loss'])\n",
    "table_welfare_loss"
   ]
  }
 ],
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