SupremeCourtDimensionReduction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Supreme Court Dimension Reduction\n",
    "\n",
    "Using dimensionaility reduction and spectral value decomposition (SVD), I will complete an analysis of Supreme Court Decisions. \n",
    "\n",
    "The inspiration come from [this paper](https://pdfs.semanticscholar.org/dac3/bde9a6605cf81969a5b4d0d53627013a5145.pdf) which I will be recreating the first 3 tables from. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import numpy as np\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loading the Data\n",
    "\n",
    "First, I am going to load the csv file into a pandas dataframe. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Breyer</th>\n",
       "      <th>Ginsburg</th>\n",
       "      <th>Kennedy</th>\n",
       "      <th>O'Conner</th>\n",
       "      <th>Rehnquist</th>\n",
       "      <th>Scalia</th>\n",
       "      <th>Souter</th>\n",
       "      <th>Stevens</th>\n",
       "      <th>Thomas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
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       "      <td>-1</td>\n",
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       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
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       "      <td>1</td>\n",
       "      <td>-1</td>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Breyer  Ginsburg  Kennedy  O'Conner  Rehnquist  Scalia  Souter  Stevens  \\\n",
       "0      -1        -1        1         1          1       1      -1       -1   \n",
       "1       1         1        1         1         -1      -1       1        1   \n",
       "2      -1        -1        1         1          1       1      -1       -1   \n",
       "3       1        -1        1        -1          1       1      -1       -1   \n",
       "4       1         1        1        -1         -1       1       1        1   \n",
       "\n",
       "   Thomas  \n",
       "0       1  \n",
       "1      -1  \n",
       "2       1  \n",
       "3       1  \n",
       "4       1  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decisions = pd.read_csv('Supreme_Court.csv')\n",
    "decisions.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data I receive is a list of Supreme Court justices with their decisions on individual court cases. Each row is a distinct court case and the entry, either 1 or -1, corresponds to whether or not the justice was in the majority or not. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of court cases: 468\n"
     ]
    }
   ],
   "source": [
    "print('Number of court cases:', len(decisions))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Recreating the Tables\n",
    "\n",
    "## Table 1 - Most Frequent Decisions\n",
    "\n",
    "I want to recreate the tables that were shown in the paper. The first table shows the most frequent decisions of the justices. The table can be seen below.\n",
    "\n",
    "<img src=\"tables/table1.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[-1, -1, 1, 1, 1, 1, -1, -1, 1],\n",
       " [1, 1, 1, 1, -1, -1, 1, 1, -1],\n",
       " [-1, -1, 1, 1, 1, 1, -1, -1, 1],\n",
       " [1, -1, 1, -1, 1, 1, -1, -1, 1],\n",
       " [1, 1, 1, -1, -1, 1, 1, 1, 1],\n",
       " [1, 1, 1, 1, 1, 1, 1, 1, 1]]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decFreq= [list(decisions.iloc[i]) for i in range(len(decisions))]\n",
    "decFreq[:6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'[-1, -1, 1, -1, 1, 1, -1, 1, 1]': 2,\n",
       " '[-1, -1, 1, -1, 1, 1, 1, -1, 1]': 2,\n",
       " '[-1, -1, 1, -1, 1, 1, 1, 1, 1]': 1,\n",
       " '[-1, -1, 1, 1, -1, 1, 1, -1, 1]': 1,\n",
       " '[-1, -1, 1, 1, 1, -1, 1, 1, -1]': 1,\n",
       " '[-1, -1, 1, 1, 1, 1, -1, -1, 1]': 45,\n",
       " '[-1, -1, 1, 1, 1, 1, -1, 1, 1]': 1,\n",
       " '[-1, -1, 1, 1, 1, 1, 1, -1, 1]': 4,\n",
       " '[-1, 1, -1, -1, -1, 1, 1, 1, 1]': 2,\n",
       " '[-1, 1, -1, 1, 1, 1, -1, -1, 1]': 1,\n",
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       " '[-1, 1, 1, -1, 1, 1, -1, 1, 1]': 1,\n",
       " '[-1, 1, 1, -1, 1, 1, 1, -1, 1]': 1,\n",
       " '[-1, 1, 1, -1, 1, 1, 1, 1, 1]': 1,\n",
       " '[-1, 1, 1, 1, 1, -1, 1, -1, -1]': 1,\n",
       " '[-1, 1, 1, 1, 1, -1, 1, 1, 1]': 3,\n",
       " '[-1, 1, 1, 1, 1, 1, 1, -1, 1]': 9,\n",
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       " '[1, -1, -1, -1, -1, 1, 1, 1, 1]': 1,\n",
       " '[1, -1, -1, -1, 1, 1, 1, 1, 1]': 1,\n",
       " '[1, -1, -1, 1, -1, 1, 1, 1, 1]': 2,\n",
       " '[1, -1, -1, 1, 1, 1, -1, -1, 1]': 1,\n",
       " '[1, -1, 1, -1, 1, 1, -1, -1, 1]': 1,\n",
       " '[1, -1, 1, 1, -1, -1, -1, 1, 1]': 1,\n",
       " '[1, -1, 1, 1, -1, -1, 1, 1, -1]': 2,\n",
       " '[1, -1, 1, 1, -1, -1, 1, 1, 1]': 1,\n",
       " '[1, -1, 1, 1, 1, -1, -1, -1, 1]': 2,\n",
       " '[1, -1, 1, 1, 1, -1, -1, 1, -1]': 1,\n",
       " '[1, -1, 1, 1, 1, 1, -1, -1, -1]': 1,\n",
       " '[1, -1, 1, 1, 1, 1, -1, -1, 1]': 6,\n",
       " '[1, -1, 1, 1, 1, 1, -1, 1, 1]': 1,\n",
       " '[1, -1, 1, 1, 1, 1, 1, -1, -1]': 1,\n",
       " '[1, -1, 1, 1, 1, 1, 1, -1, 1]': 11,\n",
       " '[1, -1, 1, 1, 1, 1, 1, 1, 1]': 1,\n",
       " '[1, 1, -1, -1, -1, -1, 1, 1, 1]': 1,\n",
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       " '[1, 1, -1, 1, -1, -1, 1, 1, -1]': 18,\n",
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       " '[1, 1, -1, 1, 1, 1, 1, -1, 1]': 3,\n",
       " '[1, 1, -1, 1, 1, 1, 1, 1, -1]': 1,\n",
       " '[1, 1, -1, 1, 1, 1, 1, 1, 1]': 1,\n",
       " '[1, 1, 1, -1, -1, -1, 1, 1, -1]': 9,\n",
       " '[1, 1, 1, -1, -1, 1, -1, 1, 1]': 1,\n",
       " '[1, 1, 1, -1, -1, 1, 1, 1, -1]': 1,\n",
       " '[1, 1, 1, -1, -1, 1, 1, 1, 1]': 1,\n",
       " '[1, 1, 1, -1, 1, -1, -1, 1, -1]': 1,\n",
       " '[1, 1, 1, -1, 1, -1, 1, -1, 1]': 1,\n",
       " '[1, 1, 1, -1, 1, -1, 1, 1, -1]': 7,\n",
       " '[1, 1, 1, -1, 1, -1, 1, 1, 1]': 1,\n",
       " '[1, 1, 1, -1, 1, 1, -1, -1, 1]': 1,\n",
       " '[1, 1, 1, -1, 1, 1, -1, 1, -1]': 1,\n",
       " '[1, 1, 1, -1, 1, 1, 1, 1, 1]': 1,\n",
       " '[1, 1, 1, 1, -1, -1, -1, 1, -1]': 2,\n",
       " '[1, 1, 1, 1, -1, -1, 1, -1, -1]': 1,\n",
       " '[1, 1, 1, 1, -1, -1, 1, 1, -1]': 12,\n",
       " '[1, 1, 1, 1, -1, -1, 1, 1, 1]': 2,\n",
       " '[1, 1, 1, 1, -1, 1, 1, 1, -1]': 3,\n",
       " '[1, 1, 1, 1, -1, 1, 1, 1, 1]': 3,\n",
       " '[1, 1, 1, 1, 1, -1, -1, 1, -1]': 2,\n",
       " '[1, 1, 1, 1, 1, -1, 1, -1, -1]': 2,\n",
       " '[1, 1, 1, 1, 1, -1, 1, -1, 1]': 1,\n",
       " '[1, 1, 1, 1, 1, -1, 1, 1, -1]': 14,\n",
       " '[1, 1, 1, 1, 1, -1, 1, 1, 1]': 3,\n",
       " '[1, 1, 1, 1, 1, 1, -1, -1, 1]': 4,\n",
       " '[1, 1, 1, 1, 1, 1, 1, -1, -1]': 1,\n",
       " '[1, 1, 1, 1, 1, 1, 1, -1, 1]': 21,\n",
       " '[1, 1, 1, 1, 1, 1, 1, 1, -1]': 3,\n",
       " '[1, 1, 1, 1, 1, 1, 1, 1, 1]': 220}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freq = {}\n",
    "for i in range(len(decFreq)):\n",
    "    try:\n",
    "        freq[str(decFreq[i])] += 1\n",
    "    except:\n",
    "        freq[str(decFreq[i])] = 1\n",
    "freq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "    0   1   2  3   4   5   6   7   8\n",
       "0   1   1   1  1   1   1   1   1   1\n",
       "1  -1  -1   1  1   1   1  -1  -1   1\n",
       "2   1   1   1  1   1   1   1  -1   1\n",
       "3   1   1  -1  1  -1  -1   1   1  -1\n",
       "4   1   1   1  1   1  -1   1   1  -1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigDecisions = sorted(freq, key=freq.get,reverse=True)[0:12]\n",
    "freqDecisions = [[j[0][1:],j[1],j[2],j[3],j[4],j[5],j[6],j[7],j[8][:-1]] for j in [i.split(', ') for i in sigDecisions]]\n",
    "table1 = pd.DataFrame(freqDecisions)\n",
    "table1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
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       "      <td>1</td>\n",
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       "      <td>-1</td>\n",
       "      <td>1</td>\n",
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       "      <th>9</th>\n",
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       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Br  Gi  Ke 0'C  Re  Sc  So  St  Th\n",
       "0    1   1   1   1   1   1   1   1   1\n",
       "1   -1  -1   1   1   1   1  -1  -1   1\n",
       "2    1   1   1   1   1   1   1  -1   1\n",
       "3    1   1  -1   1  -1  -1   1   1  -1\n",
       "4    1   1   1   1   1  -1   1   1  -1\n",
       "5    1   1   1   1  -1  -1   1   1  -1\n",
       "6    1  -1   1   1   1   1   1  -1   1\n",
       "7    1   1   1  -1  -1  -1   1   1  -1\n",
       "8   -1   1   1   1   1   1   1  -1   1\n",
       "9    1   1   1  -1   1  -1   1   1  -1\n",
       "10   1  -1   1   1   1   1  -1  -1   1\n",
       "11   1   1  -1   1   1  -1   1   1  -1"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col_names = ['Br','Gi','Ke',\"0'C\",'Re','Sc','So','St','Th']\n",
    "table1.columns = col_names\n",
    "table1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</table>\n",
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      ],
      "text/plain": [
       "    Br  Gi  Ke 0'C  Re  Sc  So  St  Th  margin\n",
       "0    1   1   1   1   1   1   1   1   1       9\n",
       "1   -1  -1   1   1   1   1  -1  -1   1       1\n",
       "2    1   1   1   1   1   1   1  -1   1       7\n",
       "3    1   1  -1   1  -1  -1   1   1  -1       1\n",
       "4    1   1   1   1   1  -1   1   1  -1       5\n",
       "5    1   1   1   1  -1  -1   1   1  -1       3\n",
       "6    1  -1   1   1   1   1   1  -1   1       5\n",
       "7    1   1   1  -1  -1  -1   1   1  -1       1\n",
       "8   -1   1   1   1   1   1   1  -1   1       5\n",
       "9    1   1   1  -1   1  -1   1   1  -1       3\n",
       "10   1  -1   1   1   1   1  -1  -1   1       3\n",
       "11   1   1  -1   1   1  -1   1   1  -1       3"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "newTable1 = table1.copy()\n",
    "margin = []\n",
    "for i in range(len(table1)):\n",
    "    margin.append(sum(int(j) for j in table1.iloc[i]))\n",
    "newTable1['margin'] = margin\n",
    "newTable1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[220, 45, 21, 18, 14, 12, 11, 9, 9, 7, 6, 5]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numCases = [freq[i] for i in sigDecisions]\n",
    "numCases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.47,\n",
       " 0.096,\n",
       " 0.045,\n",
       " 0.038,\n",
       " 0.03,\n",
       " 0.026,\n",
       " 0.024,\n",
       " 0.019,\n",
       " 0.019,\n",
       " 0.015,\n",
       " 0.013,\n",
       " 0.011]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "percent = [round(i/len(decisions),3) for i in numCases]\n",
    "percent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['47 (220)',\n",
       " '9.6 (45)',\n",
       " '4.5 (21)',\n",
       " '3.8 (18)',\n",
       " '3.0 (14)',\n",
       " '2.6 (12)',\n",
       " '2.4 (11)',\n",
       " '1.9 (9)',\n",
       " '1.9 (9)',\n",
       " '1.5 (7)',\n",
       " '1.3 (6)',\n",
       " '1.1 (5)']"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freqCol = []\n",
    "for i in range(len(newTable1)):\n",
    "    if str(percent[i])[2] == '0':\n",
    "        try:\n",
    "            per = str(percent[i])[3] + '.' + str(percent[i])[4]\n",
    "        except IndexError:\n",
    "            per = str(percent[i])[3] + '.' + '0'\n",
    "    else:\n",
    "        per = str(percent[i])[2:4]\n",
    "        \n",
    "    appendFreq = per + ' (' + str(numCases[i]) +')'\n",
    "    freqCol.append(appendFreq)\n",
    "freqCol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 1. Most frequent decisions of the 2nd Reinquist Court\n",
      "Br, Breyer; Gi, Ginsburg; Ke, Kennedy; O'C, O'Connor;Re, Rehnquist;Sc,Scalia;So, Souter; St, Stevens; Th, Thomas\n"
     ]
    },
    {
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       "      <td>2.6 (12)</td>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1.3 (6)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>3</td>\n",
       "      <td>1.1 (5)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Br  Gi  Ke 0'C  Re  Sc  So  St  Th  margin Frequency, %\n",
       "0    1   1   1   1   1   1   1   1   1       9     47 (220)\n",
       "1   -1  -1   1   1   1   1  -1  -1   1       1     9.6 (45)\n",
       "2    1   1   1   1   1   1   1  -1   1       7     4.5 (21)\n",
       "3    1   1  -1   1  -1  -1   1   1  -1       1     3.8 (18)\n",
       "4    1   1   1   1   1  -1   1   1  -1       5     3.0 (14)\n",
       "5    1   1   1   1  -1  -1   1   1  -1       3     2.6 (12)\n",
       "6    1  -1   1   1   1   1   1  -1   1       5     2.4 (11)\n",
       "7    1   1   1  -1  -1  -1   1   1  -1       1      1.9 (9)\n",
       "8   -1   1   1   1   1   1   1  -1   1       5      1.9 (9)\n",
       "9    1   1   1  -1   1  -1   1   1  -1       3      1.5 (7)\n",
       "10   1  -1   1   1   1   1  -1  -1   1       3      1.3 (6)\n",
       "11   1   1  -1   1   1  -1   1   1  -1       3      1.1 (5)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "finalTable1 = newTable1.copy()\n",
    "finalTable1['Frequency, %'] = freqCol\n",
    "print('Table 1. Most frequent decisions of the 2nd Reinquist Court')\n",
    "print(\"Br, Breyer; Gi, Ginsburg; Ke, Kennedy; O'C, O'Connor;Re, Rehnquist;Sc,Scalia;So, Souter; St, Stevens; Th, Thomas\")\n",
    "finalTable1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table 2 - Joint Probabilites\n",
    "\n",
    "Next, I am going to analyze the joint probabilites of each judge to disagree with another given judge.\n",
    "\n",
    "The table I am recreating looks like this: \n",
    "\n",
    "<img src = tables/table2.png>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#P(breyer|ginsburg) = P(Ginsburg|breyer)*P(Ginsburg)\n",
    "a = len(decisions[decisions['Breyer'] != decisions['Kennedy']])/len(decisions)\n",
    "round(a, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0.0,\n",
       "  0.11966,\n",
       "  0.25,\n",
       "  0.2094,\n",
       "  0.29915,\n",
       "  0.35256,\n",
       "  0.11752,\n",
       "  0.16239,\n",
       "  0.35897,\n",
       "  1.86965],\n",
       " [0.11966,\n",
       "  0.0,\n",
       "  0.26709,\n",
       "  0.25214,\n",
       "  0.30769,\n",
       "  0.36966,\n",
       "  0.09615,\n",
       "  0.1453,\n",
       "  0.36752,\n",
       "  1.92521],\n",
       " [0.25,\n",
       "  0.26709,\n",
       "  0.0,\n",
       "  0.15598,\n",
       "  0.12179,\n",
       "  0.18803,\n",
       "  0.24786,\n",
       "  0.32692,\n",
       "  0.17735,\n",
       "  1.73502],\n",
       " [0.2094,\n",
       "  0.25214,\n",
       "  0.15598,\n",
       "  0.0,\n",
       "  0.16239,\n",
       "  0.20726,\n",
       "  0.22009,\n",
       "  0.32906,\n",
       "  0.20513,\n",
       "  1.74145],\n",
       " [0.29915,\n",
       "  0.30769,\n",
       "  0.12179,\n",
       "  0.16239,\n",
       "  0.0,\n",
       "  0.14316,\n",
       "  0.29274,\n",
       "  0.40171,\n",
       "  0.13675,\n",
       "  1.86538],\n",
       " [0.35256,\n",
       "  0.36966,\n",
       "  0.18803,\n",
       "  0.20726,\n",
       "  0.14316,\n",
       "  0.0,\n",
       "  0.33761,\n",
       "  0.43803,\n",
       "  0.06624,\n",
       "  2.10255],\n",
       " [0.11752,\n",
       "  0.09615,\n",
       "  0.24786,\n",
       "  0.22009,\n",
       "  0.29274,\n",
       "  0.33761,\n",
       "  0.0,\n",
       "  0.1688,\n",
       "  0.3312,\n",
       "  1.81197],\n",
       " [0.16239,\n",
       "  0.1453,\n",
       "  0.32692,\n",
       "  0.32906,\n",
       "  0.40171,\n",
       "  0.43803,\n",
       "  0.1688,\n",
       "  0.0,\n",
       "  0.4359,\n",
       "  2.40811],\n",
       " [0.35897,\n",
       "  0.36752,\n",
       "  0.17735,\n",
       "  0.20513,\n",
       "  0.13675,\n",
       "  0.06624,\n",
       "  0.3312,\n",
       "  0.4359,\n",
       "  0.0,\n",
       "  2.07906]]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probabilities = list()\n",
    "justices = list(decisions.columns)\n",
    "for justice1 in justices:\n",
    "    for justice2 in justices:\n",
    "        prob = len(decisions[decisions[justice1] != decisions[justice2]])/len(decisions)\n",
    "        probabilities.append(round(prob,5))\n",
    "jointProb = []\n",
    "start= 0\n",
    "stop = 9\n",
    "for i in range(0,9):\n",
    "    jointProb.append(probabilities[start:stop])\n",
    "    start += 9\n",
    "    stop += 9\n",
    "for i in range(0,9):\n",
    "    jointProb[i].append(round(sum(jointProb[i]),5))\n",
    "jointProb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Br</th>\n",
       "      <th>Gi</th>\n",
       "      <th>Ke</th>\n",
       "      <th>0'C</th>\n",
       "      <th>Re</th>\n",
       "      <th>Sc</th>\n",
       "      <th>So</th>\n",
       "      <th>St</th>\n",
       "      <th>Th</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Br</th>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.11966</td>\n",
       "      <td>0.25000</td>\n",
       "      <td>0.20940</td>\n",
       "      <td>0.29915</td>\n",
       "      <td>0.35256</td>\n",
       "      <td>0.11752</td>\n",
       "      <td>0.16239</td>\n",
       "      <td>0.35897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gi</th>\n",
       "      <td>0.11966</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.26709</td>\n",
       "      <td>0.25214</td>\n",
       "      <td>0.30769</td>\n",
       "      <td>0.36966</td>\n",
       "      <td>0.09615</td>\n",
       "      <td>0.14530</td>\n",
       "      <td>0.36752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ke</th>\n",
       "      <td>0.25000</td>\n",
       "      <td>0.26709</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.15598</td>\n",
       "      <td>0.12179</td>\n",
       "      <td>0.18803</td>\n",
       "      <td>0.24786</td>\n",
       "      <td>0.32692</td>\n",
       "      <td>0.17735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0'C</th>\n",
       "      <td>0.20940</td>\n",
       "      <td>0.25214</td>\n",
       "      <td>0.15598</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.16239</td>\n",
       "      <td>0.20726</td>\n",
       "      <td>0.22009</td>\n",
       "      <td>0.32906</td>\n",
       "      <td>0.20513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Re</th>\n",
       "      <td>0.29915</td>\n",
       "      <td>0.30769</td>\n",
       "      <td>0.12179</td>\n",
       "      <td>0.16239</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.14316</td>\n",
       "      <td>0.29274</td>\n",
       "      <td>0.40171</td>\n",
       "      <td>0.13675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sc</th>\n",
       "      <td>0.35256</td>\n",
       "      <td>0.36966</td>\n",
       "      <td>0.18803</td>\n",
       "      <td>0.20726</td>\n",
       "      <td>0.14316</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.33761</td>\n",
       "      <td>0.43803</td>\n",
       "      <td>0.06624</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>So</th>\n",
       "      <td>0.11752</td>\n",
       "      <td>0.09615</td>\n",
       "      <td>0.24786</td>\n",
       "      <td>0.22009</td>\n",
       "      <td>0.29274</td>\n",
       "      <td>0.33761</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.16880</td>\n",
       "      <td>0.33120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>St</th>\n",
       "      <td>0.16239</td>\n",
       "      <td>0.14530</td>\n",
       "      <td>0.32692</td>\n",
       "      <td>0.32906</td>\n",
       "      <td>0.40171</td>\n",
       "      <td>0.43803</td>\n",
       "      <td>0.16880</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.43590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Th</th>\n",
       "      <td>0.35897</td>\n",
       "      <td>0.36752</td>\n",
       "      <td>0.17735</td>\n",
       "      <td>0.20513</td>\n",
       "      <td>0.13675</td>\n",
       "      <td>0.06624</td>\n",
       "      <td>0.33120</td>\n",
       "      <td>0.43590</td>\n",
       "      <td>0.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Dissent</th>\n",
       "      <td>1.86965</td>\n",
       "      <td>1.92521</td>\n",
       "      <td>1.73502</td>\n",
       "      <td>1.74145</td>\n",
       "      <td>1.86538</td>\n",
       "      <td>2.10255</td>\n",
       "      <td>1.81197</td>\n",
       "      <td>2.40811</td>\n",
       "      <td>2.07906</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Br       Gi       Ke      0'C       Re       Sc       So  \\\n",
       "Br       0.00000  0.11966  0.25000  0.20940  0.29915  0.35256  0.11752   \n",
       "Gi       0.11966  0.00000  0.26709  0.25214  0.30769  0.36966  0.09615   \n",
       "Ke       0.25000  0.26709  0.00000  0.15598  0.12179  0.18803  0.24786   \n",
       "0'C      0.20940  0.25214  0.15598  0.00000  0.16239  0.20726  0.22009   \n",
       "Re       0.29915  0.30769  0.12179  0.16239  0.00000  0.14316  0.29274   \n",
       "Sc       0.35256  0.36966  0.18803  0.20726  0.14316  0.00000  0.33761   \n",
       "So       0.11752  0.09615  0.24786  0.22009  0.29274  0.33761  0.00000   \n",
       "St       0.16239  0.14530  0.32692  0.32906  0.40171  0.43803  0.16880   \n",
       "Th       0.35897  0.36752  0.17735  0.20513  0.13675  0.06624  0.33120   \n",
       "Dissent  1.86965  1.92521  1.73502  1.74145  1.86538  2.10255  1.81197   \n",
       "\n",
       "              St       Th  \n",
       "Br       0.16239  0.35897  \n",
       "Gi       0.14530  0.36752  \n",
       "Ke       0.32692  0.17735  \n",
       "0'C      0.32906  0.20513  \n",
       "Re       0.40171  0.13675  \n",
       "Sc       0.43803  0.06624  \n",
       "So       0.16880  0.33120  \n",
       "St       0.00000  0.43590  \n",
       "Th       0.43590  0.00000  \n",
       "Dissent  2.40811  2.07906  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table2 = pd.DataFrame(np.array(jointProb).transpose())\n",
    "table2.columns = col_names\n",
    "table2.rename(index={0: 'Br', 1:'Gi',2:'Ke',3:\"0'C\",4:'Re',5:'Sc',6:'So',7:'St',8:'Th',9:'Dissent'})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table 3\n",
    "\n",
    "<img src= tables/table3.png>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "      <th>V5</th>\n",
       "      <th>V6</th>\n",
       "      <th>V7</th>\n",
       "      <th>V8</th>\n",
       "      <th>V9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.341083</td>\n",
       "      <td>-0.327401</td>\n",
       "      <td>0.122481</td>\n",
       "      <td>0.242601</td>\n",
       "      <td>-0.142766</td>\n",
       "      <td>0.818428</td>\n",
       "      <td>-0.037204</td>\n",
       "      <td>-0.020455</td>\n",
       "      <td>-0.102976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.332609</td>\n",
       "      <td>-0.367567</td>\n",
       "      <td>-0.110215</td>\n",
       "      <td>0.073447</td>\n",
       "      <td>0.427827</td>\n",
       "      <td>-0.193473</td>\n",
       "      <td>0.212646</td>\n",
       "      <td>0.685597</td>\n",
       "      <td>-0.031553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.363366</td>\n",
       "      <td>0.174192</td>\n",
       "      <td>0.346174</td>\n",
       "      <td>-0.579431</td>\n",
       "      <td>0.101478</td>\n",
       "      <td>0.039381</td>\n",
       "      <td>-0.583564</td>\n",
       "      <td>0.165764</td>\n",
       "      <td>0.046610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.362987</td>\n",
       "      <td>0.104212</td>\n",
       "      <td>0.527083</td>\n",
       "      <td>0.382865</td>\n",
       "      <td>-0.513640</td>\n",
       "      <td>-0.384338</td>\n",
       "      <td>0.103697</td>\n",
       "      <td>0.103361</td>\n",
       "      <td>-0.000622</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.346547</td>\n",
       "      <td>0.304502</td>\n",
       "      <td>0.221575</td>\n",
       "      <td>-0.255128</td>\n",
       "      <td>0.335368</td>\n",
       "      <td>0.102670</td>\n",
       "      <td>0.665052</td>\n",
       "      <td>-0.327666</td>\n",
       "      <td>0.018063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.312679</td>\n",
       "      <td>0.403145</td>\n",
       "      <td>-0.458959</td>\n",
       "      <td>0.168381</td>\n",
       "      <td>-0.114938</td>\n",
       "      <td>0.115622</td>\n",
       "      <td>-0.047714</td>\n",
       "      <td>0.122879</td>\n",
       "      <td>0.675836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.348709</td>\n",
       "      <td>-0.312700</td>\n",
       "      <td>-0.075215</td>\n",
       "      <td>0.295861</td>\n",
       "      <td>0.366213</td>\n",
       "      <td>-0.300389</td>\n",
       "      <td>-0.330139</td>\n",
       "      <td>-0.587015</td>\n",
       "      <td>0.097500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.264479</td>\n",
       "      <td>-0.445911</td>\n",
       "      <td>-0.347320</td>\n",
       "      <td>-0.511823</td>\n",
       "      <td>-0.509594</td>\n",
       "      <td>-0.166624</td>\n",
       "      <td>0.191138</td>\n",
       "      <td>-0.155812</td>\n",
       "      <td>0.018946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.315957</td>\n",
       "      <td>0.405752</td>\n",
       "      <td>-0.434937</td>\n",
       "      <td>0.102405</td>\n",
       "      <td>-0.054563</td>\n",
       "      <td>-0.039616</td>\n",
       "      <td>-0.109552</td>\n",
       "      <td>0.007046</td>\n",
       "      <td>-0.720612</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         V1        V2        V3        V4        V5        V6        V7  \\\n",
       "0  0.341083 -0.327401  0.122481  0.242601 -0.142766  0.818428 -0.037204   \n",
       "1  0.332609 -0.367567 -0.110215  0.073447  0.427827 -0.193473  0.212646   \n",
       "2  0.363366  0.174192  0.346174 -0.579431  0.101478  0.039381 -0.583564   \n",
       "3  0.362987  0.104212  0.527083  0.382865 -0.513640 -0.384338  0.103697   \n",
       "4  0.346547  0.304502  0.221575 -0.255128  0.335368  0.102670  0.665052   \n",
       "5  0.312679  0.403145 -0.458959  0.168381 -0.114938  0.115622 -0.047714   \n",
       "6  0.348709 -0.312700 -0.075215  0.295861  0.366213 -0.300389 -0.330139   \n",
       "7  0.264479 -0.445911 -0.347320 -0.511823 -0.509594 -0.166624  0.191138   \n",
       "8  0.315957  0.405752 -0.434937  0.102405 -0.054563 -0.039616 -0.109552   \n",
       "\n",
       "         V8        V9  \n",
       "0 -0.020455 -0.102976  \n",
       "1  0.685597 -0.031553  \n",
       "2  0.165764  0.046610  \n",
       "3  0.103361 -0.000622  \n",
       "4 -0.327666  0.018063  \n",
       "5  0.122879  0.675836  \n",
       "6 -0.587015  0.097500  \n",
       "7 -0.155812  0.018946  \n",
       "8  0.007046 -0.720612  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U,s,V = np.linalg.svd(decisions)\n",
    "c1 = V.T[:,0]\n",
    "c2 = V.T[:,1]\n",
    "c3 = V.T[:,2]\n",
    "c4 = V.T[:,3]\n",
    "c5 = V.T[:,4]\n",
    "c6 = V.T[:,5]\n",
    "c7 = V.T[:,6]\n",
    "c8 = V.T[:,7]\n",
    "c9 = V.T[:,8]\n",
    "table3 = pd.DataFrame({'V1':c1,'V2':c2,'V3':c3,'V4':c4,'V5':c5,'V6':c6,'V7':c7,'V8':c8,'V9':c9})\n",
    "table3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Figure 1 - 2D Projection of 2nd Reinquist Court"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/QwhBYeFT3LuXjMzMdIjF4lb7mJqawd19JIYPH9Fv7/FSrenrG8DLazS8vEaj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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119b1c160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "firstComp = np.dot(np.array(decisions),c1)\n",
    "secComp = np.dot(np.array(decisions),c2)\n",
    "\n",
    "circle1 = plt.Circle((0, 0), 2, color='black',fill=False,lw = 3, alpha=.5)\n",
    "circle2 = plt.Circle((0, 0), 3, color='black',fill=False,lw = 3, alpha=.5)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.add_artist(circle1)\n",
    "ax.add_artist(circle2)\n",
    "\n",
    "i = 0\n",
    "for dec in decFreq:\n",
    "    if freq[str(dec)] == 1:\n",
    "        mark='+'\n",
    "        c = 'red'\n",
    "        lab = 'visited once'\n",
    "    elif str(dec) in sigDecisions:\n",
    "        mark= '*'\n",
    "        c = 'blue'\n",
    "        lab = '12 most visited'\n",
    "    else: \n",
    "        mark = '.'\n",
    "        c = 'green'\n",
    "        lab = 'next 12 most visited'\n",
    "    plt.scatter(secComp[i], firstComp[i], marker = mark, color= c, label = lab)        \n",
    "    i += 1\n",
    "\n",
    "plt.axvline(0, linestyle = '--', color = 'black',alpha = .5)\n",
    "plt.title('Figure 1: 2D Projection of 2nd Reinquist Court. V1 in horizontal,V2 in vertical')\n",
    "plt.show()\n"
   ]
  }
 ],
 "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}