Maybe you’ve seen the news. Congressional districts are redrawn every 10 years, but the president has asked a state that favors him to redraw their districts mid-decade to give him more seats (Politico, Aug 5).
https://youtube.com/shorts/pd2frUGueG8?si=cQYphF83SsiB9jL8
Representatives of the opposing party left the state in protest, preventing the Texas legislature from proceeding. Eventually they will convene again, and the governor of Democrat-majority California has sworn to retaliate if Republican-biased redistricting in Texas moves forward.
One of the goals of our course in probability and statistics is to gain the ability to watch interactions like these and critically assess claims that are being made. In the video above, the president says that because he won Texas by “the highest vote in history” (Did he?) he is “entitled” to more seats.
A good starting point is to ask, well, how many seats should Republicans have in Texas?
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In the 2024 presidential election, Donald Trump won 56.14% of the vote.
There are 38 congressional districts in Texas, so if Republicans won 22 districts, that would constitute 57.9% of districts.
In fact, Republicans won 27 districts in 2024. And the president is asking the state to redraw the maps so that he can win five more.
</aside>
Clearly, 27 is more than 22, but maybe things just worked out that way by chance?
Gerrymandering is the colloquial name given to the act of drawing congressional districts in such a way that they favor the party currently in power. We can use probabilistic and statistical thinking to assess whether it is possible that a real-life outcome falls within a reasonable range of natural variation, or if the real-life outcome is such a severe outlier that the process that generated it could not be fair.
A number of mathematicians, statisticians, political scientists, and economists have taken on the challenge of quantifying gerrymandering, i.e., trying to put a number on the degree of bias and develop the ability to definitively declare whether a process of drawing maps is unfair.
At its core, probabilistic thinking involves assessing a reasonable range of outcomes for a given situation and then deciding if the “real-world” outcome falls within that range, or is a concerning outlier. Throughout the course we will learn some commonly used probability models, but there is a universal approach if you have enough people and a little bit of curiosity.