The Weight of a Vote

For Kaylynn Reyna, a senior mathematics major at Hardin-Simmons University from Abilene, Texas, her final year has been a journey into the surprising world of strategy, problem-solving, and real-world impact — all through the lens of game theory.

“I had no idea what game theory was at the beginning of the year,” Kaylynn admitted. “I knew I wanted Dr. Potter to be my advisor for my senior project, and he suggested it because that’s what his dissertation was about. Once he explained it to me, it just caught my eye. It was really cool to learn about.”

Initially, Kaylynn’s project was set to solve a specific question related to weighted voting and coalition probabilities. But as the year progressed, the

Kaylynn Reyna, Six White Horses

research pivoted.

“At first, we had a question we were trying to answer, but it wasn’t really leading anywhere,” she said. “So, in the end, it just turned into trying to learn more about game theory, understanding it, learning how to program it, and seeing how it applies to the real world.”

And apply it does — from simple board games to the strategies behind international politics.

“Game theory analyzes strategies between players and games to find the best outcomes,” Kaylynn explained. “It can be used for small things like chess or poker, but also for huge things like auctions, the stock market, politics, and even international deals.”

Throughout her project, Kaylynn created multiple Python programs to calculate different power indices like the Banzhaf Power Index, Shapley Value, and Shapley-Shubik Power Index — mathematical measures of influence in weighted voting systems like the U.S. Electoral College.

Kaylynn is also a member of the HSU Dance Team, the Spurs.

“Programming wasn’t something I was expecting, but it was so cool because it helped me really understand the concepts deeply,” she said.

Working under the mentorship of Dr. Andrew Potter, Kaylynn also uncovered the breadth of real-world applications.

“Even if you’re not physically doing the math behind game theory, just the thinking like ‘how do I maximize my profit?’ or ‘how do I oppose another strategy to get a better outcome?’ shows up everywhere, from auctions to business negotiations,” she said.

Her time at HSU and the supportive relationships she built made a significant impact.

Kaylynn Reyna accepts the prestigious Burnam Mathematics Award for Outstanding Mathematic Graduate of 2025

“I love our math department. Most times when I’d meet with Dr. Potter, we’d end up talking about so much more than just math,” she shared. “Being at a faith-based university gave me the opportunity to have real conversations about life and faith and that made my college experience even more meaningful.”

As she prepares to graduate, Kaylynn is setting her sights on a master’s at Texas A&M University and eventually a Ph.D. Her ultimate goal?

“I want to be a college math professor,” she said with a smile.

Dr. Potter shares that optimism, noting Kaylynn’s excellence and leadership. She was recently awarded the prestigious Burnam Mathematics Award for Outstanding Mathematic Graduate of 2025— the highest honor in HSU’s mathematics department — and an award given sparingly. Since its establishment in 1968, Kaylynn has become the 40^th recipient of the award.