1. (10 pts) After the initial vote counting stage of the 2020 presidential elections, there were many claims about the potential fraud problems. One of them is that violation of Benford’s law in many precincts. As statisticians, instead of absorbing the stories from others blindly, we should try to use our expertise and data to gure things out. In class, we have introduced the Benford’s law, which is a magic phenomenon in many real-world situations. And in this problem, you are asked to use visualization and analysis under this problem by yourselves.
In the CountyData 2000-2020.csv data set, you will nd the county voting counts in the US presidential election from 2000 to 2020. The variable meanings are clear by their names. We focus on Illinois, in which many counties are claimed to have clearly deviation of Benford’s law in the 2020 election. Though 2020 and Illinois would be our focus, notice that you can always use the other parts in the data set to help your analysis if necessary.
1. By visualization, show that whether the rst digits of votes in Illinois counties fol-low/violate Benfold’s law. Check this separately for Biden and Trump. (Convincing visualization and comments, 2.5 pts for each candidate)
2. Do what you observe in Part (a) indicate election fraud? Why or why not? Justify your answer by visualizations. (E ective visualizations 2.5 pts, convincing justi - cation 2.5 pts)
[Hint: make sure you understand the di erence between the two questions above. Crtical logics di erences exist. If you feel that Part (a) and (b) are essentially the same questions, perhaps you do not get the point. Our introduction of Benford law in the lecture might be helpful for you to nd some clues. Be creative, especially for (b), in designing a way to justify your statements based on all data you could use.]
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