{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Dynamic Process: Robustness to the Share of Updating Voters (C.2)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2021-02-09T13:45:42.597524Z",
"start_time": "2021-02-09T13:45:36.046941Z"
}
},
"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": "2021-02-09T13:45:42.609297Z",
"start_time": "2021-02-09T13:45:42.603312Z"
}
},
"outputs": [],
"source": [
"N_SAMPLES = 10000\n",
"N_MAX_EPISODES = 1000"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2021-02-09T13:45:42.642208Z",
"start_time": "2021-02-09T13:45:42.614283Z"
}
},
"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": "2021-02-09T13:45:42.724481Z",
"start_time": "2021-02-09T13:45:42.647194Z"
}
},
"outputs": [],
"source": [
"update_ratios_legend = {\n",
" '1': '1', \n",
" '0.5': '0.5',\n",
" 'one_over_log_log_t_plus_fourteen': '1 / log(log(t + 14))',\n",
" 'one_over_log_t_plus_one': '1 / log(t + 1)',\n",
" 'one_over_sqrt_t': '1 / sqrt(t)',\n",
" 'one_over_t': '1 / t', \n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"ExecuteTime": {
"end_time": "2021-02-09T13:45:42.738719Z",
"start_time": "2021-02-09T13:45:42.728675Z"
}
},
"outputs": [],
"source": [
"rand_profile = RandProfileHistogramUniform(n_bins=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Convergence Rate"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"ExecuteTime": {
"end_time": "2021-02-09T13:45:47.508841Z",
"start_time": "2021-02-09T13:45:42.743002Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" Approval | \n",
" Plurality | \n",
" Anti-plurality | \n",
"
\n",
" \n",
" | Share of updating voters | \n",
" | \n",
" | \n",
" | \n",
"
\n",
" \n",
" \n",
" \n",
" | 1 | \n",
" 0.9390 | \n",
" 1.0 | \n",
" 0.0 | \n",
"
\n",
" \n",
" | 0.5 | \n",
" 0.9461 | \n",
" 1.0 | \n",
" 0.0 | \n",
"
\n",
" \n",
" | one_over_log_log_t_plus_fourteen | \n",
" 0.9492 | \n",
" 1.0 | \n",
" 0.0 | \n",
"
\n",
" \n",
" | one_over_log_t_plus_one | \n",
" 0.9472 | \n",
" 1.0 | \n",
" 0.0 | \n",
"
\n",
" \n",
" | one_over_sqrt_t | \n",
" 0.9503 | \n",
" 1.0 | \n",
" 0.0 | \n",
"
\n",
" \n",
" | one_over_t | \n",
" 0.0558 | \n",
" 1.0 | \n",
" 0.0 | \n",
"
\n",
" \n",
"
\n",
"