The ubiquitous method of scheduling meetings nowadays is polling all the participants to find a time when everyone is available. Case Western Reserve research explores the statistical mysteries of everyday tasks. The study reveals that finding a suitable meeting time becomes challenging with a growing number of participants.
Scientists used a mathematical model to calculate the probability of successfully scheduling a meeting based on several factors: the number of participants (m), the number of possible meeting times (Ï„), and the number of times each participant is unavailable (r).
The results reveal that the probability of scheduling a successful meeting decreases sharply as the number of participants grows. More specifically, this probability drops when more than five people are involved, especially if participant availability remains consistent.
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Dr. Harsh Mathur said, “We wanted to know the odds. “The science of probability started with people studying gambling, but it applies just as well to scheduling meetings. Our research shows that as the number of participants grows, the number of potential meeting times that need to be polled increases exponentially.”
“The project had started half in jest but this exponential behavior got our attention. It showed that scheduling meetings is a difficult problem, on par with some of the great problems in computer science.”
Interestingly, there was a parallel between scheduling difficulties and physical phenomena. They found that as the chance of someone rejecting a meeting time increases, there’s a crucial point where scheduling the meeting becomes much more complicated. This is similar to “phase transitions” in physics, like ice turning into water.
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Mathur said, “It’s fascinating how something as mundane as scheduling can mirror the complexity of phase transitions.”
“The study’s broader implications range from casual scenarios like sharing appetizers at a restaurant to more complex settings like drafting climate policy reports, where agreement among many is needed.”
“Consensus-building is hard. Like phase transitions, it’s complex. But that’s also where the beauty of mathematics lies—it gives us tools to understand and quantify these challenges.”
“The study contributes insights into the complexities of group coordination and decision-making, with potential applications across various fields.”
Journal Reference:
- Brown, K., Mathur, H. & Narayan, O. Scheduling meetings: are the odds in your favor? Eur. Phys. J. B 97:120 (2024). DOI: 10.1140/epjb/s10051-024-00742-z
