CS146 Session 7.2 Pre-Class Work

CS146 Session 7.2 Pre-Class Work.ipynb

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      "cell_type": "markdown",
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        "id": "bt3Ls8Fo_Sqw",
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      "source": [
        "# Modeling elections"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pwLS6xJ8_Sqz",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import scipy.stats as sts\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pystan"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I9s-ScIh_Sq7",
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      "source": [
        "## Data\n",
        "\n",
        "The `electoral_votes` variable is a dictionary containing the number of Electoral College votes for each state. For example\n",
        "```\n",
        "  >>> electoral_votes['Indiana']\n",
        "  11\n",
        "```\n",
        "Data from [Wikipedia: United_States_Electoral_College](https://en.wikipedia.org/wiki/United_States_Electoral_College)\n",
        "\n",
        "The `survey_results` variable is a dictionary mapping from states to an array of survey results for each candidate. Each row in a survey results array represents one survey and each column represents one candidate. There are 4 columns, representing Clinton, Trump, Johnson, and Stein in that order. In the example below, Clinton got 340 votes in the first survey, Trump got 258, Johnson got 27, and Stein got 13.\n",
        "```\n",
        "  >>> survey_results['Indiana']\n",
        "  array([[340, 258,  27,  13],\n",
        "         [240, 155,   5,   5],\n",
        "         [235, 155,  50,  20],\n",
        "         [308, 266,  49,  35],\n",
        "         [222, 161,  80,  30]])\n",
        "```\n",
        "Data from [Wikipedia: Statewide opinion polling for the United States presidential election, 2016](https://en.wikipedia.org/wiki/Statewide_opinion_polling_for_the_United_States_presidential_election,_2016)\n"
      ]
    },
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      "cell_type": "code",
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      "source": [
        "electoral_votes = {\n",
        "    'Alabama': 9,\n",
        "    'Alaska': 3,\n",
        "    'Arizona': 11,\n",
        "    'Arkansas': 6,\n",
        "    'Colorado': 9,\n",
        "}\n",
        "\n",
        "survey_results = {\n",
        "    'Alabama': np.array([], dtype=int).reshape(0, 4),\n",
        "    'Alaska': np.array([400 * np.array([.47, .43, .07, .03]), 500 * np.array([.36, .37, .07, .03]), 500 * np.array([.34, .37, .10, .02]), 660 * np.array([.31, .36, .18, .06])], dtype=int),\n",
        "    'Arizona': np.array([392 * np.array([.45, .47, .05, .02]), 550 * np.array([.39, .47, .04, .03]), 719 * np.array([.40, .45, .09, .03]), 769 * np.array([.44, .49, .05, .01]), 2229 * np.array([.45, .44, .07, .01]), 700 * np.array([.43, .47, .02, .02]), 550 * np.array([.41, .45, .03, .01]), 994 * np.array([.42, .44, .04, .01]), 550 * np.array([.40, .42, .05, .02]), 2385 * np.array([.48, .46, .05, .01]), 401 * np.array([.45, .46, .04, .01]), 550 * np.array([.41, .41, .05, .02]), 1538 * np.array([.39, .44, .06, .02]), 713 * np.array([.43, .38, .06, .01]), 400 * np.array([.39, .37, .08, .03]), 600 * np.array([.44, .42, .09, .01]), 718 * np.array([.42, .42, .05, .01]), 484 * np.array([.41, .46, .09, .01]), 649 * np.array([.38, .40, .12, .03])], dtype=int),\n",
        "    'Arkansas': np.array([463 * np.array([.33, .56, .04, .02]), 831 * np.array([.34, .55, .03, .01]), 600 * np.array([.29, .57, .05, .03])], dtype=int),\n",
        "    'Colorado': np.array([1150 * np.array([.45, .44, .05, .04]), 500 * np.array([.44, .38, .07, .02]), 550 * np.array([.39, .39, .05, .04]), 750 * np.array([.44, .41, .08, .04]), 685 * np.array([.45, .37, .10, .03]), 400 * np.array([.49, .38, .07, .03]), 602 * np.array([.44, .33, .10, .03]), 694 * np.array([.46, .40, .06, .02]), 784 * np.array([.41, .42, .13, .03]), 991 * np.array([.40, .39, .07, .02]), 644 * np.array([.44, .42, .10, .02]), 540 * np.array([.41, .34, .12, .03]), 600 * np.array([.38, .42, .13, .02]), 704 * np.array([.48, .43, .04, .02]), 605 * np.array([.43, .38, .07, .02]), 997 * np.array([.42, .39, .07, .02])], dtype=int),\n",
        "}\n",
        "\n",
        "states = sorted(survey_results.keys())\n",
        "print('Modeling', len(states), 'states with', sum(electoral_votes[s] for s in states), 'electoral college votes')"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Modeling 5 states with 38 electoral college votes\n"
          ],
          "name": "stdout"
        }
      ]
    },
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      "source": [
        "## Generative model\n",
        "\n",
        "1. For each state we generate an $\\vec{\\alpha}$ vector, which defines a Dirichlet distribution over the proportion of votes that go to each of the 4 candidates whenever we do a survey — including the final survey, namely the election itself which we want to predict. The prior over each component of $\\vec{\\alpha}$ is taken as a Cauchy distribution with location 0 and scale 1. Since the components of $\\vec{\\alpha}$ are positive, we actually use the positive half-Cauchy distribution.\n",
        "\n",
        "2. For each survey in a state we generate a probability vector $\\vec{p_i} \\sim \\text{Dirichlet}(\\vec{\\alpha})$ for the probability that a voter selects each of the 4 candidates.\n",
        "\n",
        "3. For each survey, we then generate the number of votes going to each candidate as $\\vec{k_i} \\sim \\text{Multinomial}(\\vec{p_i})$.\n",
        "\n",
        "### Tasks\n",
        "\n",
        "* Use Stan to sample from the posterior distribution over $\\alpha$ and visualize your results. There are 10 states, so you will have 10 posteriors.\n",
        "* The posteriors over $\\alpha$ show a lot of variation between different states. Explain the results you get in terms of the model and the data."
      ]
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        "outputId": "c85433ca-6dd8-42bb-fcee-14ef3b83f025"
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      "source": [
        "stan_code = '''\n",
        "data {\n",
        "\n",
        "  int<lower=0> num_surveys; // the number of surveys for each state\n",
        "  int<lower=1> num_candidates; // the number of candidates in the electoral round - in our case there are 4\n",
        "  int results[num_surveys, num_candidates]; // survey results for each candidate \n",
        "  \n",
        "}\n",
        "\n",
        "parameters {\n",
        "\n",
        "  simplex[num_candidates] theta[num_surveys];  // the probability that a voter selects each of the 4 candidates; here, use a simplex because we know that a vote has to select one of the 4 candidates, and therefore the probabilty must sum up to 1\n",
        "  vector[num_candidates] alpha; // the parameter of our alpha prior\n",
        "}\n",
        "\n",
        "model {\n",
        "\n",
        "  alpha ~ cauchy(0, 1); // we are using a cauchy prior for our alpha because of its broad distribution\n",
        "  for (i in 1:num_surveys) {\n",
        "    theta[i] ~ dirichlet(alpha); // we are modeling the probability vector with a dirichlet distribution of alpha\n",
        "    results[i] ~ multinomial(theta[i]); // multinomial distribution because there are 4 sets of outcomes\n",
        "  } \n",
        "}\n",
        "'''\n",
        "\n",
        "stan_model = pystan.StanModel(model_code=stan_code)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_3752f25ed6c551d42a2fb805f5e48a1c NOW.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6mYMenk5_SrH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 89
        },
        "outputId": "4976fb81-7ef6-4a45-d778-19cabe451eae"
      },
      "source": [
        "# Now, we have to fit the Stan model to our survey data to get the posteriors\n",
        "# but since there are 4 different states, we will have to parse them separately\n",
        "\n",
        "def fit_model(state_results):\n",
        "  dataset = {\n",
        "      'num_surveys': len(state_results),\n",
        "      'num_candidates': 4,\n",
        "      'results': state_results\n",
        "  }\n",
        "  posterior = stan_model.sampling(data=dataset)\n",
        "  return posterior\n",
        "\n",
        "posterior_alaska = fit_model(survey_results['Alaska'])\n",
        "posterior_arizona = fit_model(survey_results['Arizona'])\n",
        "posterior_arkansas = fit_model(survey_results['Arkansas'])\n",
        "posterior_colorado = fit_model(survey_results['Colorado'])"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING:pystan:291 of 4000 iterations ended with a divergence (7.28 %).\n",
            "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
            "WARNING:pystan:998 of 4000 iterations ended with a divergence (24.9 %).\n",
            "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZH5UtYWtNdLQ",
        "colab_type": "code",
        "colab": {}
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      "source": [
        "def plot_alpha(posterior_distribution, state):\n",
        "    samples = posterior_distribution.extract()\n",
        "    plt.figure(figsize=(18, 9))\n",
        "    for i in range(4):\n",
        "        plt.plot(sts.uniform.rvs(loc=i+1-0.1, scale=0.2, size=samples['alpha'].shape[0]), samples['alpha'][:,i], ',', alpha=0.5)\n",
        "    plt.title(f'Graph of the posterior distribution for the 4 candidates in {state}')\n",
        "    plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d7hA9kg0NgmZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 805
        },
        "outputId": "d0747104-8d5a-4e8d-b041-011bf48e50b0"
      },
      "source": [
        "print(posterior_alaska.stansummary(pars='alpha',probs=(0.025, 0.975)))\n",
        "plot_alpha(posterior_alaska, 'Alaska')"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Inference for Stan model: anon_model_3752f25ed6c551d42a2fb805f5e48a1c.\n",
            "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
            "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
            "\n",
            "           mean se_mean     sd   2.5%  97.5%  n_eff   Rhat\n",
            "alpha[1]  12.83     0.3   8.09   3.03  33.97    731    1.0\n",
            "alpha[2]  13.41     0.3   8.48   3.15  34.92    775    1.0\n",
            "alpha[3]   3.61    0.08   2.25   0.89   9.51    805    1.0\n",
            "alpha[4]   1.47    0.03   0.82   0.42   3.54    844    1.0\n",
            "\n",
            "Samples were drawn using NUTS at Thu Oct 24 10:59:06 2019.\n",
            "For each parameter, n_eff is a crude measure of effective sample size,\n",
            "and Rhat is the potential scale reduction factor on split chains (at \n",
            "convergence, Rhat=1).\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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7AADgSJobREgpfV5E/ErO+bGd3CCl9MqU0qMppUeffvrpnQwBwJA6G0BmAAAA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\nIiKKhEEEIiIiIiIiIork/wPkJ4uY4Ob4TwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1296x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QB8QEDDgbkme",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 805
        },
        "outputId": "ed319deb-4bd4-471c-98ec-62aa2c9c2779"
      },
      "source": [
        "print(posterior_arizona.stansummary(pars='alpha',probs=(0.025, 0.975)))\n",
        "plot_alpha(posterior_arizona, 'Arizona')"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Inference for Stan model: anon_model_3752f25ed6c551d42a2fb805f5e48a1c.\n",
            "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
            "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
            "\n",
            "           mean se_mean     sd   2.5%  97.5%  n_eff   Rhat\n",
            "alpha[1]  89.06    0.81   25.5  49.92 148.64    997   1.01\n",
            "alpha[2]  92.62    0.83  26.46  52.03 154.97   1016   1.01\n",
            "alpha[3]   12.1    0.11   3.52   6.68  20.47   1016   1.01\n",
            "alpha[4]   3.52    0.03   1.01   1.94   5.88   1157   1.01\n",
            "\n",
            "Samples were drawn using NUTS at Thu Oct 24 10:59:24 2019.\n",
            "For each parameter, n_eff is a crude measure of effective sample size,\n",
            "and Rhat is the potential scale reduction factor on split chains (at \n",
            "convergence, Rhat=1).\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RRzs8Rr8serOeBjgW/TwANtAi/rW/TRBimusAAAAweNMGGF4r6ZmS7pD0QUk/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            "text/plain": [
              "<Figure size 1296x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3ZaGatHbbpL0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 805
        },
        "outputId": "d32ac6c7-5316-46ae-8b0d-86801ea07925"
      },
      "source": [
        "print(posterior_arkansas.stansummary(pars='alpha',probs=(0.025, 0.975)))\n",
        "plot_alpha(posterior_arkansas, 'Arkansas')"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Inference for Stan model: anon_model_3752f25ed6c551d42a2fb805f5e48a1c.\n",
            "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
            "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
            "\n",
            "           mean se_mean     sd   2.5%  97.5%  n_eff   Rhat\n",
            "alpha[1]  22.12    1.74  23.76   2.48  87.58    187   1.01\n",
            "alpha[2]  38.58    3.02  41.57   4.01 147.53    189   1.01\n",
            "alpha[3]   2.86    0.21   2.93    0.5  10.66    192   1.01\n",
            "alpha[4]   1.57     0.1   1.43   0.32   5.27    205   1.01\n",
            "\n",
            "Samples were drawn using NUTS at Thu Oct 24 10:59:29 2019.\n",
            "For each parameter, n_eff is a crude measure of effective sample size,\n",
            "and Rhat is the potential scale reduction factor on split chains (at \n",
            "convergence, Rhat=1).\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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DAKezSgUAANskYNhAR6+7ddlDAAAAYJ+ZGTBk5tmZeSwzP5iZH8jMH2i3f01m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\n",
            "text/plain": [
              "<Figure size 1296x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kBKbLhbmbsNQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 805
        },
        "outputId": "9da154e6-dda0-486a-e5bc-efd7cc5ad9bc"
      },
      "source": [
        "print(posterior_colorado.stansummary(pars='alpha',probs=(0.025, 0.975)))\n",
        "plot_alpha(posterior_colorado, 'Colorado')"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Inference for Stan model: anon_model_3752f25ed6c551d42a2fb805f5e48a1c.\n",
            "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
            "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
            "\n",
            "           mean se_mean     sd   2.5%  97.5%  n_eff   Rhat\n",
            "alpha[1]  90.84    0.81   27.8  48.36 155.05   1188    1.0\n",
            "alpha[2]  82.64    0.74  25.38  43.82 142.61   1162    1.0\n",
            "alpha[3]  16.66    0.15   5.12   8.85  28.38   1194    1.0\n",
            "alpha[4]   5.74    0.05   1.76    3.0   9.71   1256    1.0\n",
            "\n",
            "Samples were drawn using NUTS at Thu Oct 24 10:59:45 2019.\n",
            "For each parameter, n_eff is a crude measure of effective sample size,\n",
            "and Rhat is the potential scale reduction factor on split chains (at \n",
            "convergence, Rhat=1).\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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IpqyCpvoNXYoz5teUAgS7FpayHOK8SuOxbQIAAGBuEWCYgtJWhzxQ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            "text/plain": [
              "<Figure size 1296x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lo0uRO_igkWT",
        "colab_type": "text"
      },
      "source": [
        "As seen from the 4 graphs above, my 95% confidence intervals are slightly different from the results given in the Pre-Class Work document, but close enough."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oy7Malvb_SrN",
        "colab_type": "text"
      },
      "source": [
        "## Simulation time\n",
        "\n",
        "Use the posterior samples to predict the outcome of the presidential elections.\n",
        "\n",
        "* Predict the probability that each candidate will win each state.\n",
        "   * Use the posterior $\\alpha$ samples to generate posterior predictive samples for $p$ — the proportion of votes each candidate would get in each state in an election.\n",
        "   * Use these $p$ samples to estimate the probability that each candidate will win each state.\n",
        "* Predict the probability that each candidate will win the presidential election.\n",
        "   * Use the posterior predictive probability that each candidate will win each state to generate samples over the total number Electoral College votes each candidate would get in an election.\n",
        "   * Use the total number of votes to generate samples over who would win the election."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "5oEQPRZa_SrS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def predicted_votes_proportion(posterior_distribution):\n",
        "  samples = posterior_distribution.extract()\n",
        "  # Make a new array with same dimensions as alpha\n",
        "  p_predicted = np.empty(samples['alpha'].shape)\n",
        "  # Generate one p sample for each alpha sample\n",
        "  for i in range(samples['alpha'].shape[0]):\n",
        "    p_predicted[i] = sts.dirichlet(samples['alpha'][i]).rvs()\n",
        "  return p_predicted\n",
        "\n",
        "alaska_prediction = predicted_votes_proportion(posterior_alaska)\n",
        "arizona_prediction = predicted_votes_proportion(posterior_arizona)\n",
        "arkansas_prediction = predicted_votes_proportion(posterior_arkansas)\n",
        "colorado_prediction = predicted_votes_proportion(posterior_colorado)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ga2vL4vwhxmd",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 503
        },
        "outputId": "0dda8426-3669-4d96-b65b-21fc0dbecb23"
      },
      "source": [
        "def p_results(p_predicted, state):\n",
        "  Clinton = \"%.2f\"%np.mean(p_predicted[:,0])\n",
        "  Trump = \"%.2f\"%np.mean(p_predicted[:,1])\n",
        "  Johnson = \"%.2f\"%np.mean(p_predicted[:,2])\n",
        "  Stein = \"%.2f\"%np.mean(p_predicted[:,3])\n",
        "  print(f'The posterior prediction the proportion of votes for each candidate in {state} is:')\n",
        "  print(f'Clinton({Clinton})')\n",
        "  print(f'Trump({Trump})')\n",
        "  print(f'Johnson({Johnson})')\n",
        "  print(f'Stein({Stein})')\n",
        "  def winner(Clinton, Trump, Johnson, Stein):\n",
        "    if max(Clinton, Trump, Johnson, Stein) == Clinton:\n",
        "      return('Clinton')\n",
        "    elif max(Clinton, Trump, Johnson, Stein) == Trump:\n",
        "      return('Trump')\n",
        "    elif max(Clinton, Trump, Johnson, Stein) == Johnson:\n",
        "      return('Johnson')\n",
        "    elif max(Clinton, Trump, Johnson, Stein) == Stein:\n",
        "      return('Stein')\n",
        "  print(f'The winner of this state is {winner(Clinton, Trump, Johnson, Stein)}.')\n",
        "  \n",
        "p_results(alaska_prediction, 'Alaska')\n",
        "print('')\n",
        "p_results(arizona_prediction, 'Arizona')\n",
        "print('')\n",
        "p_results(arkansas_prediction, 'Arkansas')\n",
        "print('')\n",
        "p_results(colorado_prediction, 'Colorado')"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The posterior prediction the proportion of votes for each candidate in Alaska is:\n",
            "Clinton(0.40)\n",
            "Trump(0.43)\n",
            "Johnson(0.12)\n",
            "Stein(0.05)\n",
            "The winner of this state is Trump.\n",
            "\n",
            "The posterior prediction the proportion of votes for each candidate in Arizona is:\n",
            "Clinton(0.45)\n",
            "Trump(0.47)\n",
            "Johnson(0.06)\n",
            "Stein(0.02)\n",
            "The winner of this state is Trump.\n",
            "\n",
            "The posterior prediction the proportion of votes for each candidate in Arkansas is:\n",
            "Clinton(0.34)\n",
            "Trump(0.58)\n",
            "Johnson(0.05)\n",
            "Stein(0.03)\n",
            "The winner of this state is Trump.\n",
            "\n",
            "The posterior prediction the proportion of votes for each candidate in Colorado is:\n",
            "Clinton(0.46)\n",
            "Trump(0.42)\n",
            "Johnson(0.09)\n",
            "Stein(0.03)\n",
            "The winner of this state is Clinton.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mTSJ8rzKmx8Y",
        "colab_type": "text"
      },
      "source": [
        "As seen above, Trump wins Alaska, Arizona and Arkansas, while Clinton wins Colorado.\n",
        "\n",
        "Given the electoral votes for these 4 states, Trump has won $3+11+6=20$ electoral votes, while Clinton has only won $9$ electoral votes."
      ]
    }
  ]
}