Math Improves Campus Social Life…No, Really

Davidson's four eating houses were abuzz with excitement Feb. 6, as they welcomed 180 new members and hosted open parties to celebrate. A campus tradition decades running, "Self-Selection Night" is so named because of the system by which women gain membership – by choice.

But it isn't as simple as signing up for a specific house; each house has a limited number of membership spots available, so women interested in joining an eating house rank the houses in order of preference and hope to get one of their top choices.

While chance does play a small role in house placement, the women's fates are not written in the stars; rather they are written in computer code. Thanks to Professor of Mathematics Laurie Heyer and a small group of students from her 2001 Mathematical Modeling course, women are assigned to eating houses using a sophisticated algorithm designed to maximize overall satisfaction with the results.

This is a shift from years past, when the school used a lottery system to assign women to houses. With the lottery system, often women were placed into their last-choice houses, which led to decreased morale and volatile membership, according to school records. In 2001, one house received 28 new members for whom it was their last choice, Heyer said.

"At that time, it was not uncommon to hear students say, ‘I got into such-and-such house, and I was one of the few who actually wanted it,'" Heyer said.

Student satisfaction is key for house morale, and member retention is important for the houses financially, Patterson Court Advisor Sarah Pankratz said. Each member pays membership dues that cover meals, social events and service activities, and if a house sees a lot of member attrition, it could be in danger of closing.

With so many women placed in their last-choice houses, it was clear the old lottery system for placement wasn't working. That's where math came in.

Students in Heyer's Mathematical Modeling course study how to solve real-world operational problems using mathematics, such as optimizing customer satisfaction, maximizing profits, etc. One day, while discussing the mathematical "Transportation Problem" for delivery of goods, a student said, "This is the eating house problem!" Heyer remembers.

And just like that, the class had a new, real-world problem to solve.

A small group of students chose to take on the task that spring of 2001, and worked with Heyer over the next few months to develop a Transportation Problem-based algorithm they could use for placing women into the eating houses according to their preferences. In the self-selection scenario, each woman or cluster of women is a "source," and each house a "destination," with "demand" being the total number of women a house can accept, and the "costs" reflecting the women's preference for each house.

They applied the mathematical method to self-selection data from 2001, and it significantly reduced the number of women getting their last choice of house. With proof that the algorithm worked, Heyer met with Craig Rinker, the Patterson Court Advisor at the time, to better understand the existing self-selection problem, and see if staff would be open to a new suggestion.

Heyer met with multiple people over the course of the next year, all the while working on the algorithm. She presented the math group's work to the Patterson Court Council, and later, in spring 2003 a task force focused on Patterson Court issues recommended that the Patterson Court Advisor implement the algorithm for self-selection placement and that Heyer remain as a consultant to the advisor.

The method was first applied in 2004, and that year no woman was placed into her fourth-choice house. In fact, over the last decade, only three times have women been placed into their fourth-choice houses, and the numbers placed were minimal.

Here are some of the most recent results:

• This year, 136 got their first choice, 41 got their second, two got their third, and just one got her fourth choice.
• Last year, 145 women got their first choice, 33 got their second, and just 12 got their third.
• In 2012, 154 got their first choice, 16 got their second, and no one got their third.

On average, about 63 percent of Davidson women participate in eating houses, according to school records.

"It's a very unique, interesting process," Pankratz said, "and many women take pride in participating in this unique, Davidson tradition."

One reason participation is so high is that the self-selection system is "less overwhelming" than a traditional sorority system, in which women must be offered bids to join the houses, Pankratz said.

"Everything is open and inclusive, and every woman who wants to participate is guaranteed to get placed in a house," she said.

Various factors affect the outcomes of placement, including whether or not women choose to participate as a cluster (a group of up to four women, guaranteed to get into the same house) or as individuals, and how many women list certain houses as their top choices. But overall, higher satisfaction with placement in recent years has lead to less-volatile eating house membership and improved morale, Pankratz said. And the improvements are the direct result of the algorithm.

"We would never be able to hand-place students as effectively as the algorithm does," Pankratz said. It's a truly unique system."