{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binary Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:49:35.686265Z",
     "start_time": "2021-02-15T09:49:30.602781Z"
    }
   },
   "outputs": [],
   "source": [
    "import poisson_approval as pa\n",
    "from fractions import Fraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## XyyToProfile"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Poisson Approval, we call *binary plot* a graphical study of some profiles that are based on two rankings, denoted *left_ranking* and *right_ranking*, in various proportions, and where the utility of the voters for their second candidate also varies. To achieve this, we need an *XyyToProfile* object that will generate the profiles:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:49:35.696894Z",
     "start_time": "2021-02-15T09:49:35.688914Z"
    }
   },
   "outputs": [],
   "source": [
    "xyy_to_profile = pa.XyyToProfile(\n",
    "    pa.ProfileNoisyDiscrete,\n",
    "    left_ranking='abc',\n",
    "    right_ranking='cba',\n",
    "    d_type_fixed_share={('bac', 0.1, 0.01): Fraction(1, 12),\n",
    "                        ('bac', 0.9, 0.01): Fraction(1, 12)},\n",
    "    noise=0.01\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above syntax defines a function ``xyy_to_profile``  that maps a tuple $(x, y1, y2)$ to a profile defined as:\n",
    "\n",
    "* The class of profile is *ProfileNoisyDiscrete*,\n",
    "* A fixed share 1/12 of voters are of type $(bac, 0.1, 0.01)$, and a fixed share 1/12 of voters are of type $(bac, 0.9, 0.01)$,\n",
    "* The other voters, i.e. a share 5/6, are distributed between *left_ranking* and *right_ranking*, in respective proportions $1 - x$ and $x$.\n",
    "* The voters with preference order *left_ranking* have a utility $y1$ for their second candidate,\n",
    "* The voters with preference order *right_ranking* have a utility $y2$ for their second candidate.\n",
    "\n",
    "For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:49:35.722825Z",
     "start_time": "2021-02-15T09:49:35.699885Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<abc 0.42 ± 0.01: 2/3, bac 0.1 ± 0.01: 1/12, bac 0.9 ± 0.01: 1/12, cba 0.51 ± 0.01: 1/6> (Condorcet winner: a)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xyy_to_profile(x=Fraction(1, 5), y1=0.42, y2=0.51)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All the plots require two resolution parameters called *xscale* and *yscale*. For example, if *xscale = yscale = 10*, then the x-axis and the y-axis are divided into cells of diameter 1/10 and the value of the plotted function is computed at the center of each cell. In this tutorial, we define global parameters *XSCALE* and *YSCALE* and we will use them for all the plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:49:35.762718Z",
     "start_time": "2021-02-15T09:49:35.726813Z"
    }
   },
   "outputs": [],
   "source": [
    "XSCALE = 10\n",
    "YSCALE = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Number of Equilibria"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, the function *binary_plot_n_equilibria* computes the ordinal equilibria, i.e. those where all voters having the same ranking cast the same ballot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:49:42.060851Z",
     "start_time": "2021-02-15T09:49:35.766707Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 414x288 with 3 Axes>,\n",
       " <poisson_approval.meta_analysis.binary_plots.BinaryAxesSubplotPoisson at 0x1e2d1f355f8>)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 414x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pa.binary_plot_n_equilibria(\n",
    "    xyy_to_profile,\n",
    "    xscale=XSCALE, yscale=YSCALE,\n",
    "    title='Number of ordinal equilibria')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the option *meth*, you can investigate other kinds of equilibria:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:49:49.086401Z",
     "start_time": "2021-02-15T09:49:42.064840Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 414x288 with 3 Axes>,\n",
       " <poisson_approval.meta_analysis.binary_plots.BinaryAxesSubplotPoisson at 0x1e2d1d4ddd8>)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 414x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pa.binary_plot_n_equilibria(\n",
    "    xyy_to_profile,\n",
    "    xscale=XSCALE, yscale=YSCALE,\n",
    "    title='Number of group equilibria', \n",
    "    meth='analyzed_strategies_group')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Depending on the class of profile, the possible values of the option ``meth`` may be:\n",
    "\n",
    "* ``'analyzed_strategies_ordinal'`` (the default),\n",
    "* ``'analyzed_strategies_group'``,\n",
    "* ``'analyzed_strategies_pure'`` (for *ProfileDiscrete* only)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Winners at Equilibrium"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function *binary_plot_n_equilibria* works similarly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:49:55.382520Z",
     "start_time": "2021-02-15T09:49:49.089399Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 288x288 with 2 Axes>,\n",
       " <poisson_approval.meta_analysis.binary_plots.BinaryAxesSubplotPoisson at 0x1e2d2346a20>)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pa.binary_plot_winners_at_equilibrium(\n",
    "    xyy_to_profile,\n",
    "    xscale=XSCALE, yscale=YSCALE,\n",
    "    title='Winners in ordinal equilibria')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:50:05.179853Z",
     "start_time": "2021-02-15T09:49:55.389505Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 288x288 with 2 Axes>,\n",
       " <poisson_approval.meta_analysis.binary_plots.BinaryAxesSubplotPoisson at 0x1e2d24b4dd8>)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pa.binary_plot_winners_at_equilibrium(\n",
    "    xyy_to_profile,\n",
    "    xscale=XSCALE, yscale=YSCALE,\n",
    "    title='Winners in group equilibria',\n",
    "    legend_title='Winners', \n",
    "    meth='analyzed_strategies_group')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Winning Frequencies in Fictitious Play or Iterated Voting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, the function *binary_plot_winning_frequencies computes the winning frequencies in fictitious play, with an initialization in sincere strategy, and with all update ratios in $1 / \\log(t + 1)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:50:34.545545Z",
     "start_time": "2021-02-15T09:50:05.182844Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 288x288 with 3 Axes>,\n",
       " <poisson_approval.meta_analysis.binary_plots.BinaryAxesSubplotPoisson at 0x1e2d26dd860>)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pa.binary_plot_winning_frequencies(\n",
    "    xyy_to_profile,\n",
    "    xscale=XSCALE, yscale=YSCALE,\n",
    "    n_max_episodes=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can change this behavior with the optional parameters of the function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:50:55.449175Z",
     "start_time": "2021-02-15T09:50:34.548591Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 288x288 with 3 Axes>,\n",
       " <poisson_approval.meta_analysis.binary_plots.BinaryAxesSubplotPoisson at 0x1e2d2973198>)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pa.binary_plot_winning_frequencies(\n",
    "    xyy_to_profile,\n",
    "    xscale=XSCALE, yscale=YSCALE,\n",
    "    meth='iterated_voting',\n",
    "    init='random_tau_undominated',\n",
    "    samples_per_point=10, \n",
    "    perception_update_ratio=1,\n",
    "    ballot_update_ratio=1,\n",
    "    winning_frequency_update_ratio=pa.one_over_t,\n",
    "    n_max_episodes=100, \n",
    "    title='Winning frequencies in iterated voting',\n",
    "    legend_title='Winners'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence Rate in Fictitious Play or Iterated Voting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function *binary_plot_convergence* computes the convergence frequency in fictitious play or iterated voting, which is defined as the proportion of initializations that lead to convergence within *n_max_episodes* iterations. Its syntax is similar to *binary_plot_winning_frequencies*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:54:56.037030Z",
     "start_time": "2021-02-15T09:50:55.452630Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 414x288 with 3 Axes>,\n",
       " <poisson_approval.meta_analysis.binary_plots.BinaryAxesSubplotPoisson at 0x1e2d288de10>)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 414x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pa.binary_plot_convergence(xyy_to_profile,\n",
    "                           xscale=XSCALE, yscale=YSCALE,\n",
    "                           n_max_episodes=100, init='random_tau', samples_per_point=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Advanced Intensity Heat Maps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, define a function that maps a point $(x, y1, y2)$ to a number:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:54:56.049060Z",
     "start_time": "2021-02-15T09:54:56.041440Z"
    }
   },
   "outputs": [],
   "source": [
    "def f(x, y1, y2):\n",
    "    return (x**2 + y1) / (y2 + 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then use the method *heatmap_intensity*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:54:56.715045Z",
     "start_time": "2021-02-15T09:54:56.053518Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 414x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure, tax = pa.binary_figure(xscale=XSCALE, yscale=YSCALE)\n",
    "tax.heatmap_intensity(f, \n",
    "                      x_left_label='x-left',\n",
    "                      x_right_label='x-right',\n",
    "                      y_left_label='y-left',\n",
    "                      y_right_label='y-right')\n",
    "tax.set_title('An intensity heat map')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Advanced Candidate Heat Maps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, define a function that maps a point $(x, y1, y2)$ to a list of size 3 (associated with candidates *a*, *b*, *c*):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:54:56.727043Z",
     "start_time": "2021-02-15T09:54:56.718991Z"
    }
   },
   "outputs": [],
   "source": [
    "def g(x, y1, y2):\n",
    "    a = x**.5\n",
    "    b = y1**2\n",
    "    c = 1 - a - b\n",
    "    return [a, b, c]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then use the method *heatmap_candidates*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-15T09:54:57.650872Z",
     "start_time": "2021-02-15T09:54:56.731056Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure, tax = pa.binary_figure(xscale=XSCALE, yscale=YSCALE)\n",
    "tax.heatmap_candidates(g, \n",
    "                       x_left_label='x-left',\n",
    "                       x_right_label='x-right',\n",
    "                       y_left_label='y-left',\n",
    "                       y_right_label='y-right',\n",
    "                       legend_title='Candidates',\n",
    "                       legend_style='palette')\n",
    "tax.set_title('A candidate heat map')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  },
  "nbsphinx": {
   "execute": "never"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": false,
   "sideBar": true,
   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}