Given the massive political polarization across the United States, there isn’t much that Americans can agree on these days. However, there is one thing that we can come to a consensus on the American election system favors politicians, not the people. Arguably the most well-known way this happens is by gerrymandering. But the question arises, what exactly is gerrymandering? Keep on reading!
Expectation: Jackpot
It isn’t exactly a secret that casino games are rigged against the player and in favor of the casino. Of course, casinos would not be massive cash cows bringing money to the tune of billions without an edge. But nevertheless, the ways casinos manipulate probability and math can show just how rigged they are. Keep on reading!
RLAs: A Defense of Election Security
Finally, a topic near and dear to my hear, risk-limiting election audits (RLAs)! RLAs are an important part of verifying election results and protecting democratic integrity. In essence, an RLA is a statistical test that verifies election results. The primary goal of election audits is to build public trust in the electoral process by providing accountability. Risk-limiting election audits are a specific type of election audit that focuses on minimizing the risk of certifying incorrect election outcomes. Unlike traditional audits, which have fixed sample sizes, RLAs use statistics(a heck of a lot of math!)to determine the appropriate sample size based on the margin of victory and other factors. Keep on reading!
X Marks the Pitfalls of Democracy
The pirate game is one of the most well-known mathematical puzzles. In the game, five entirely rational pirates, A, B, C, D, and E, find a treasure of 100 coins. The hierarchy of the pirates is determined by their names in alphabetical order, so A is the most senior pirate while E is at the bottom of the chain. Given that their newfound loot needs to be spread, the pirates devise a mechanism to allocate the coins. Keep on reading!
The Madness of Monty Hall
Imagine you are a contestant on a game show, and you are faced with three closed doors. Behind one of these doors lies a valuable prize, such as a brand-new car, while the other two doors conceal lesser prizes, perhaps goats. Your goal is to select the door that hides the car and walk away with the grand prize.
Here’s where the dilemma arises. After you’ve made your initial selection, the host, Monty Hall, who knows what’s behind each door, decides to add an unexpected twist. Monty, with his mischievous grin, opens one of the remaining doors to reveal a goat. Now, there are two doors left: the one you originally picked and one other. Monty then gives you a choice: stick with your initial selection or switch to the other unopened door. The question is, what should you do to maximize your chances of winning the car? Keep on reading!
The Boarding Pass Problem: A Scramble for Seats
A previous post in this blog tackles the Birthday Paradox, showing how our minds fail to grasp the probability of real-world events. The missing boarding pass problem embodies a similar concept in a very different way. The problem is most often asked in the form of a riddle: You’re standing in a queue, waiting to board your flight. The first passenger has lost their boarding pass; because of this, they take a random seat. The line consists of 100 passengers, and each subsequent passenger will sit in their assigned seat if it’s available or choose randomly if it’s occupied. What is the probability that you, the last passenger in line, will be able to sit in your assigned seat? Keep on reading!
Statistical Illusions: Simpson’s Paradox
In the world of statistics and data analysis, there exists a phenomenon that can turn seemingly clear conclusions upside down: Simpson’s Paradox. Named after the British statistician Edward Simpson, who described it in 1951, this paradox challenges our intuitive understanding of aggregated data and statistical relationships. Keep on reading!
Birthday for Two
Imagine yourself in a room, surrounded by 22 other people. You might have nothing in common with these 22 people, not a single piece of similar background. What might surprise you is that there is a 50 percent chance that at least two people in the room share a birthday. Up the room to 50 people, and that same probability becomes 97 percent. Keep on reading!
St. Petersburg Paradox
In the world of probability and decision theory, few paradoxes are as perplexing and thought-provoking as the St. Petersburg Paradox. Named after the Russian city where it was first introduced by Swiss mathematician Daniel Bernoulli in 1738, this paradox challenges our intuitive understanding of rational decision-making and the value we place on uncertain outcomes. In this blog post, we will explore the St. Petersburg Paradox, its implications, and the proposed solutions that have arisen over the centuries. Keep on reading!
Welcome!
Hello and welcome to my blog! I hope to write about some cool tidbits of knowledge and facts whenever I can about society + math and how they intersect. Hopefully, this goes well! ~R