{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dynamic Process: Robustness to the Belief Updating Parameter (with CW) (C.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T13:45:39.550486Z",
     "start_time": "2021-02-09T13:45:33.326091Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from poisson_approval import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T13:45:39.568440Z",
     "start_time": "2021-02-09T13:45:39.559531Z"
    }
   },
   "outputs": [],
   "source": [
    "N_SAMPLES = 10000\n",
    "N_MAX_EPISODES = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T13:45:39.623686Z",
     "start_time": "2021-02-09T13:45:39.575419Z"
    }
   },
   "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": "2021-02-09T13:45:39.635723Z",
     "start_time": "2021-02-09T13:45:39.628741Z"
    }
   },
   "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": "2021-02-09T13:45:44.236406Z",
     "start_time": "2021-02-09T13:45:39.638714Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
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       "    }\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>Belief updating parameter</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.999385</td>\n",
       "      <td>0.6616</td>\n",
       "      <td>0.547106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.5</th>\n",
       "      <td>0.999765</td>\n",
       "      <td>0.6721</td>\n",
       "      <td>0.527511</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>one_over_log_log_t_plus_fourteen</th>\n",
       "      <td>0.999898</td>\n",
       "      <td>0.6735</td>\n",
       "      <td>0.531112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>one_over_log_t_plus_one</th>\n",
       "      <td>0.999729</td>\n",
       "      <td>0.6700</td>\n",
       "      <td>0.492881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>one_over_sqrt_t</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.6599</td>\n",
       "      <td>0.462096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>one_over_t</th>\n",
       "      <td>0.999500</td>\n",
       "      <td>0.6645</td>\n",
       "      <td>0.446902</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  Approval  Plurality  Anti-plurality\n",
       "Belief updating parameter                                            \n",
       "1                                 0.999385     0.6616        0.547106\n",
       "0.5                               0.999765     0.6721        0.527511\n",
       "one_over_log_log_t_plus_fourteen  0.999898     0.6735        0.531112\n",
       "one_over_log_t_plus_one           0.999729     0.6700        0.492881\n",
       "one_over_sqrt_t                   1.000000     0.6599        0.462096\n",
       "one_over_t                        0.999500     0.6645        0.446902"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_cond = pd.DataFrame()\n",
    "table_cond.index.name = 'Belief updating parameter'\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",
    "        perception_update_ratio=update_ratio,\n",
    "        monte_carlo_settings=[\n",
    "            MCS_FREQUENCY_CW_WINS,\n",
    "        ],\n",
    "        file_save='sav/perception_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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