Using Probability to Reduce the Size of a Voting Body

Abstract

Suppose a large group of people, such as a university faculty, traditionally makes decisions by meeting together and voting. Because of the COVID-19 pandemic, however, large group meetings have become impractical. Having a relatively small subset of the group meet and take votes would be safer and easier to organize. The purpose of this research is to use probability theory to choose a size for this subset which guarantees that the subset has a high probability of voting the same way as the entire group. Our research involves the study of the hypergeometric probability distribution and leads to a computer algorithm for determining the subset size.