Election Outcome Simulation Analysis

Table of Contents

1. Introduction
2. Methodology
   • Data Sources
   • Simulation Process
3. Results
4. Discussion
5. Conclusion
6. Future Work
7. Code Snippets

Introduction

In this analysis, we simulate potential outcomes of a U.S. presidential election using statistical modeling techniques. The goal is to assess how different factors, such as state-level polling errors and correlated biases, could affect the electoral and popular vote distributions. By conducting 20,000 simulations, we aim to provide insights into the likelihood of various electoral scenarios.

Methodology

Data Sources

• 2016 Election Results: Data from the 2016 presidential election was used as a baseline. This includes total votes cast and electoral votes per state.
• State Polling Data: Historical polling data was analyzed to determine the mean and standard deviation of Trump’s vote share per state.
• Bias Term: A correlated bias term was introduced to simulate national-level polling errors or events that could influence multiple states simultaneously.

Simulation Process

The simulation process involves several key steps:

1. Initializing the Total Votes: Calculating the total number of votes cast based on the 2016 election data.
2. Setting Up Counters and State Data: Initializing counters for total electoral votes and popular votes for both candidates, and setting up data for each state.
3. Running the Simulation Loop: Running 20,000 simulations, adding a correlated bias in each run to simulate the impact of national-level polling errors or late-breaking news.

Results

The simulation results include the popular vote percentages for both candidates across all simulations. The difference between the popular vote percentages for Trump and the Democratic candidate is recorded for each simulation.

Discussion

• Impact of Correlated Bias: The introduction of a correlated bias provides a more realistic scenario compared to independent state polling errors. It shows how systematic polling errors or unexpected national events could significantly impact election outcomes.

• Election Forecasting: The results highlight the range of possible outcomes, indicating the uncertainty inherent in forecasting electoral results.

Conclusion

The election outcome simulation demonstrates the complexity of predicting electoral results, particularly in a polarized political environment. The results emphasize the importance of accounting for both local variations and broader, systemic factors that could influence voter behavior across multiple states.

Future Work

• Refine Bias Model: Future simulations could explore different bias distributions or incorporate additional real-world factors, such as economic indicators or major news events.
• Update Polling Data: As more current polling data becomes available, it can be incorporated into the model for more accurate predictions.
• Scenario Analysis: Additional simulations could include alternative scenarios, such as changes in voter turnout or the impact of third-party candidates.

Code Snippets

Initializing the Total Votes

total_votes = 0 
for state in results2016:
    total_votes += results2016[state]['vote_total']

print("Total votes in 2016 election:", total_votes)

Output

Total votes in 2016 election: 136582000

Step 2: Setting Up Counters and State Data

Step 3: Running the Simulation Loop

Visualizing the Results

import matplotlib.pyplot as plt

# Plot the histogram of results
plt.figure(figsize=(10, 7.5))
plt.hist([trump_final_countx, narrow_dem_win, dem_obama_zone, dem_blowout], 
         color=['red', '#00FFFF', 'blue', 'mediumblue'], 
         density=True, bins=100, edgecolor='black', stacked=True)
plt.legend(['Chance of Trump winning', 'Chance of narrow D win', 
            'Chance of D win in Obama zone', 'Chance of D blowout'])
plt.xlabel('Popular Vote Margin')
plt.ylabel('% of Simulations')
plt.grid()
plt.title(label="20,000 Simulations for 2020 Using Normal Symmetric Bias = 0.05")
plt.show()

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