Mathematical modeling explores the statistical mysteries of successful meeting planning

In a world where organizing a simple meeting can feel like herding cats, new research from Case Western Reserve University reveals how difficult it becomes to find an appropriate meeting time as the number of participants increases.

The study, published in the European Journal of Physics Bdelves into the mathematical complexities of this common task, offering new insights into why planning often seems so impossible.

“If you like to think the worst about people, this study might interest you,” joked Harsh Mathur, a researcher and professor of physics in CWRU’s College of Arts and Sciences. “But it’s not just about Doodle polls. We started out wanting to answer this question about polls, but it turns out there’s more to the story.”

The researchers used mathematical modeling to calculate the probability of successfully scheduling a meeting based on several factors: the number of participants (m), the number of possible meeting times (τ), and the number of times each participant is unavailable (r).

They found that as the number of participants increases, the probability of holding a successful meeting decreases sharply.

Specifically, the probability decreases significantly when more than five people are involved, especially if the availability of participants remains constant.

“We wanted to know the probabilities,” Mathur said. “The science of probability started with people studying games of chance, but it applies just as well to things like meeting planning. Our research shows that as the number of participants increases, the number of potential meeting times to survey increases exponentially.”

“The project started half as a joke, but this exponential behavior caught our attention. It showed that meeting scheduling is a difficult problem, comparable to some of the great problems in computer science.”

Interestingly, the researchers drew a parallel between scheduling difficulties and physical phenomena. They observed that as the probability of a participant rejecting a meeting proposal increases, there is a critical point where the probability of successfully scheduling the meeting drops dramatically.

It’s a phenomenon similar to what are called “phase transitions” in physics, Mathur explained, such as ice melting into water.

“Understanding phase transitions mathematically is a triumph of physics,” he said. “It’s fascinating to see how something as mundane as planning can reflect the complexity of phase transitions.”

Mathur also highlighted the broader implications of the study, ranging from informal scenarios like sharing appetizers at a restaurant to more complex contexts like writing climate policy reports, where agreement among many is required.

“It’s hard to come to a consensus,” Mathur said. “Like phase transitions, it’s complex. But that’s also the beauty of mathematics: It gives us tools to understand and quantify these challenges.”

Mathur said the study sheds light on the complexities of group coordination and decision-making, with potential applications in diverse fields.