{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dynamic Process: Robustness to the Share of Updating Voters (with CW) (C.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T13:45:45.469003Z",
     "start_time": "2021-02-09T13:45:39.185427Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "from poisson_approval import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T13:45:45.479931Z",
     "start_time": "2021-02-09T13:45:45.474307Z"
    }
   },
   "outputs": [],
   "source": [
    "N_SAMPLES = 10000\n",
    "N_MAX_EPISODES = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T13:45:45.519824Z",
     "start_time": "2021-02-09T13:45:45.485914Z"
    }
   },
   "outputs": [],
   "source": [
    "update_ratios = {\n",
    "    '1': 1,\n",
    "    '0.5': 0.5,\n",
    "    'one_over_log_log_t_plus_fourteen': one_over_log_log_t_plus_fourteen,\n",
    "    'one_over_log_t_plus_one': one_over_log_t_plus_one,\n",
    "    'one_over_sqrt_t': one_over_sqrt_t,\n",
    "    'one_over_t': one_over_t, \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T13:45:45.534344Z",
     "start_time": "2021-02-09T13:45:45.523812Z"
    }
   },
   "outputs": [],
   "source": [
    "rand_profile = RandConditional(\n",
    "    RandProfileHistogramUniform(n_bins=1), \n",
    "    test=is_condorcet, n_trials_max=None\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Condorcet consistency:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T13:45:50.392888Z",
     "start_time": "2021-02-09T13:45:45.538641Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "    }\n",
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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>Share of updating voters</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.997838</td>\n",
       "      <td>0.6670</td>\n",
       "      <td>0.102871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.5</th>\n",
       "      <td>0.999552</td>\n",
       "      <td>0.6697</td>\n",
       "      <td>0.267519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>one_over_log_log_t_plus_fourteen</th>\n",
       "      <td>0.999749</td>\n",
       "      <td>0.6730</td>\n",
       "      <td>0.257903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>one_over_log_t_plus_one</th>\n",
       "      <td>0.999908</td>\n",
       "      <td>0.6628</td>\n",
       "      <td>0.496961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>one_over_sqrt_t</th>\n",
       "      <td>0.999800</td>\n",
       "      <td>0.6697</td>\n",
       "      <td>0.570528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>one_over_t</th>\n",
       "      <td>0.999700</td>\n",
       "      <td>0.6573</td>\n",
       "      <td>0.603082</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  Approval  Plurality  Anti-plurality\n",
       "Share of updating voters                                             \n",
       "1                                 0.997838     0.6670        0.102871\n",
       "0.5                               0.999552     0.6697        0.267519\n",
       "one_over_log_log_t_plus_fourteen  0.999749     0.6730        0.257903\n",
       "one_over_log_t_plus_one           0.999908     0.6628        0.496961\n",
       "one_over_sqrt_t                   0.999800     0.6697        0.570528\n",
       "one_over_t                        0.999700     0.6573        0.603082"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_cond = pd.DataFrame()\n",
    "table_cond.index.name = 'Share of updating voters'\n",
    "for update_ratio_name, update_ratio in update_ratios.items():\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",
    "        ballot_update_ratio=update_ratio,\n",
    "        monte_carlo_settings=[\n",
    "            MCS_FREQUENCY_CW_WINS,\n",
    "        ],\n",
    "        file_save='sav/ballot_update_%s_with_CW.sav' % update_ratio_name,\n",
    "    )\n",
    "    for voting_rule in VOTING_RULES:\n",
    "        table_cond.loc[update_ratio_name, voting_rule] = float(results[voting_rule]['mean_frequency_cw_wins'])\n",
    "table_cond"
   ]
  }
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