ON A PROBLEM FROM THE ELECTION MATHEMATICS

• Main Authors: Ivan Georgiev, Jechka Dimitrova
• Format: Article
• Language: English
• Published: Union of Scientists - Stara Zagora 2018-03-01
• Series: Science & Research
• Subjects: election mathematics; simple and classified majority voting; pigeonhole principle
• Online Access: http://www.sandtr.org/download.php?id=12

The aim of this paper is to study a mathematical problem, related to a general voting scenario, in which a group of voters elects a committee from a pool of possible candidates. Every voter can vote positively or negatively for every candidate. The problem is to calculate the minimum number of positive votes, that each voter must make in order to elect at least a certain predefined lower bound of committee members. The authors have studied this problem in a previous paper, in which the committee members are elected by simple majority. The present paper generalises the result to other types of majorities, such as qualified majorities or more general parameter-based majorities. In the case when the group of voters is larger than the pool of candidates, a very good approximation of the answer is obtained, which does not depend on the total number of voters. The authors also analyze the error of this approximation, which happens to be at most one vote in absolute value.