{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dynamic Process: Robustness to the Distribution of Preference Intensities (C.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T13:45:47.970067Z",
     "start_time": "2021-02-09T13:45:41.514789Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from poisson_approval import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T13:45:47.978333Z",
     "start_time": "2021-02-09T13:45:47.973346Z"
    }
   },
   "outputs": [],
   "source": [
    "N_SAMPLES = 10000\n",
    "N_MAX_EPISODES = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T13:45:48.010248Z",
     "start_time": "2021-02-09T13:45:47.981427Z"
    }
   },
   "outputs": [],
   "source": [
    "distributions = {\n",
    "    'U([0.09, .11])': RandProfileNoisyDiscreteUniform(\n",
    "        types=[(ranking, 0.1, 0.01) for ranking in RANKINGS]),\n",
    "    'U([0.89, .91])': RandProfileNoisyDiscreteUniform(\n",
    "        types=[(ranking, 0.9, 0.01) for ranking in RANKINGS]),\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Condorcet Consistency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T13:45:49.661510Z",
     "start_time": "2021-02-09T13:45:48.014239Z"
    }
   },
   "outputs": [
    {
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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>rho_o</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>U([0.09, .11])</th>\n",
       "      <td>0.984800</td>\n",
       "      <td>0.6649</td>\n",
       "      <td>0.492624</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>U([0.89, .91])</th>\n",
       "      <td>0.984975</td>\n",
       "      <td>0.6600</td>\n",
       "      <td>0.489420</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Approval  Plurality  Anti-plurality\n",
       "rho_o                                              \n",
       "U([0.09, .11])  0.984800     0.6649        0.492624\n",
       "U([0.89, .91])  0.984975     0.6600        0.489420"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_cond = pd.DataFrame()\n",
    "table_cond.index.name = 'rho_o'\n",
    "for distribution_name, distribution in distributions.items():\n",
    "    rand_profile = RandConditional(\n",
    "        distribution, \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='random_tau',\n",
    "        monte_carlo_settings=[\n",
    "            MCS_FREQUENCY_CW_WINS,\n",
    "        ],\n",
    "        file_save='sav/distribution_%s_with_CW.sav' % distribution_name,\n",
    "    )\n",
    "    for voting_rule in VOTING_RULES:\n",
    "        table_cond.loc[distribution_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": "2021-02-09T13:45:51.128669Z",
     "start_time": "2021-02-09T13:45:49.666359Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\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>rho_o</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>U([0.09, .11])</th>\n",
       "      <td>0.010898</td>\n",
       "      <td>0.085809</td>\n",
       "      <td>0.115399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>U([0.89, .91])</th>\n",
       "      <td>0.033006</td>\n",
       "      <td>0.061998</td>\n",
       "      <td>0.113344</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Approval  Plurality  Anti-plurality\n",
       "rho_o                                              \n",
       "U([0.09, .11])  0.010898   0.085809        0.115399\n",
       "U([0.89, .91])  0.033006   0.061998        0.113344"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_welfare_loss = pd.DataFrame()\n",
    "table_welfare_loss.index.name = 'rho_o'\n",
    "for distribution_name, distribution in distributions.items():\n",
    "    results = monte_carlo_fictitious_play(\n",
    "        factory=distribution,\n",
    "        n_samples=N_SAMPLES,\n",
    "        n_max_episodes=N_MAX_EPISODES,\n",
    "        voting_rules=VOTING_RULES,\n",
    "        init='random_tau',\n",
    "        monte_carlo_settings=[\n",
    "            MCS_WELFARE_LOSSES,\n",
    "        ],\n",
    "        file_save='sav/distribution_%s.sav' % distribution_name,\n",
    "    )\n",
    "    for voting_rule in VOTING_RULES:\n",
    "        table_welfare_loss.loc[distribution_name, voting_rule] = float(\n",
    "            results[voting_rule]['mean_utilitarian_welfare_loss'])\n",
    "table_welfare_loss"
   ]
  }
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