{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Election"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-28T09:17:34.424997Z",
     "start_time": "2023-09-28T09:17:32.776871Z"
    }
   },
   "outputs": [],
   "source": [
    "import svvamp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a population of 9 voters with preferences over 5 candidates, using the Spheroid model (which extends Impartial Culture to utilities):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-28T09:17:34.451807Z",
     "start_time": "2023-09-28T09:17:34.427746Z"
    }
   },
   "outputs": [],
   "source": [
    "random_profile = svvamp.GeneratorProfileSpheroid(n_v=9, n_c=5)\n",
    "profile = random_profile()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Preference rankings of the voters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-28T09:17:34.483948Z",
     "start_time": "2023-09-28T09:17:34.451807Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 4, 2, 3],\n",
       "       [3, 0, 4, 1, 2],\n",
       "       [4, 2, 3, 1, 0],\n",
       "       [2, 3, 0, 4, 1],\n",
       "       [0, 1, 4, 3, 2],\n",
       "       [2, 1, 4, 3, 0],\n",
       "       [4, 2, 0, 3, 1],\n",
       "       [4, 2, 0, 1, 3],\n",
       "       [1, 4, 0, 2, 3]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "profile.preferences_rk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a voting rule:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-28T09:17:34.499827Z",
     "start_time": "2023-09-28T09:17:34.483948Z"
    }
   },
   "outputs": [],
   "source": [
    "rule = svvamp.RulePlurality()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the profile into the voting rule:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-28T09:17:34.515938Z",
     "start_time": "2023-09-28T09:17:34.499827Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<svvamp.rules.rule_plurality.RulePlurality at 0x2061f15e9a0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rule(profile)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ballots:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-28T09:17:34.531822Z",
     "start_time": "2023-09-28T09:17:34.515938Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 3, 4, 2, 0, 2, 4, 4, 1])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rule.ballots_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scores:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-28T09:17:34.548084Z",
     "start_time": "2023-09-28T09:17:34.532952Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1, 2, 1, 3])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rule.scores_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Order the candidates according to their scores:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-28T09:17:34.564088Z",
     "start_time": "2023-09-28T09:17:34.548084Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 0, 2, 1, 3], dtype=int64)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rule.candidates_by_scores_best_to_worst_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-28T09:17:34.585641Z",
     "start_time": "2023-09-28T09:17:34.564808Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 2, 2, 1, 1])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rule.scores_best_to_worst_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The winner, her score and her total utility:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-28T09:17:34.601764Z",
     "start_time": "2023-09-28T09:17:34.585641Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rule.w_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-28T09:17:34.618155Z",
     "start_time": "2023-09-28T09:17:34.602521Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rule.score_w_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-28T09:17:34.634047Z",
     "start_time": "2023-09-28T09:17:34.618155Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5038515767548695"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rule.total_utility_w_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Decide whether the winner of the election is a Condorcet winner:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-09-28T09:17:34.650174Z",
     "start_time": "2023-09-28T09:17:34.634047Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rule.w_is_condorcet_winner_ut_abs_"
   ]
  }
 ],
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