 Dear Fellow Scholars, this is two-minute papers with Karo Ejone Fahir. Let's talk about the mathematical intricacies of the elections. Here you can see the shape of the 12th congressional district in North Carolina in the 90s. This is not a naturally shaped electoral district, is it? One might say this is more of an abomination. If you try to understand why it has this peculiar shape, we shall find a remarkable mathematical mischief. Have a look at this example of 50 electoral precincts. The distribution is 60% blue and 40% red. So this means that the blue party should win the elections and gain seeds with the ratio of 60 to 40. Right? Well, this is not exactly how it works. There's a majority decision, district by district, regardless of the vote ratios. If the electoral districts are shaped like this, then the blue party wins 5 to 0. However, if they are shaped like this, the red party wins 3 to 2, which is kind of mind-blowing because the votes are the very same, and this is known as the wasted vote effect. This term doesn't refer to someone who enters the voting booth intoxicated. This means that one can think of pretty much every vote beyond 50% plus 1 to a party in a district to be irrelevant. It doesn't matter if the district is won by 99% of the votes or just 50% plus 1 vote. So the counting plan is now laid out. What if instead we could regroup all of these extra votes to win in a different district where we were losing? And now we have ceremoniously arrived to the definition of gerrymandering, which is the process of manipulating electoral district boundaries to turn the tide of an election. The term originates from one of the elections in the USA in the 1800s, where Governor Albridge Gerry signed a bill to reshape the districts of Massachusetts in order to favor his party. And at that time, understandably, all the papers and comic artists were up in arms about this bill. So how does one perform gerrymandering? Gerrymandering is actually a mathematical problem of the purest form where we are trying to maximize the number of seats that we can win by manipulating the district boundaries appropriately. It is important to note that the entire process relies on a relatively faithful prediction of the vote distributions per region, which in many countries is not really changing all that much in time. This is a problem that we can solve via standard optimization techniques. Now hold on to your papers and get this. For instance, we can use metropolis sampling to solve this problem, which is absolutely stunning. So far, in an earlier episode, we have used metropolis sampling to develop a super-efficient light simulation program to create beautiful images of virtual scenes, and the very same technique can also be used to steal an election. In fact, metropolis sampling was developed and used during the Manhattan Project, where the first atomic bomb was created in Los Alamos. I think it is completely understandable that the power of mathematics and research still give many of us sleepless nights, sometimes delightful, sometimes perilous. It is also important to note that in order to retain the fairness of elections in a district-based system, it is of utmost importance that these district boundaries are drawn by independent organizations and that the process is as transparent as possible. I decided not to cite a concrete paper in this episode. If you would like to read up on this topic, I recommend searching for keywords like redistricting and gerrymandering on Google's scholar. Please feel free to post the more interesting findings of yours in the comments section, we always have excellent discussions therein. Thanks for watching and for your generous support, and I'll see you next time.