Community College of City University

MATH 4998

Acknowledgements
This thesis was cooperatively done by Dr.To Kai Ming, my supervisor and myself.
All profiles and tables shown in this project were my own job. I would like to express
my deeply appreciation to Dr.To and i am so grateful to have an opportunity to
be a student of him. This project cannot be finished without his patient guidance.
I learned a lots of knowledges under voting systems and it was a very interesting
topic as well.
Ho Ka Lai, Karen
Department of Mathematics
Hong Kong Baptist University
VOTING SYSTEMS AND RELATED MATHEMATICS
HO KA LAI, KAREN
Abstract. This paper mainly focused on studying voting rules, particularly
scoring rules and the Borda rule. After reviewing the basics of social choice
theory, we characterized the Borda rule by identifying a condition under which
a scoring rule is equivalent to the Borda rule. We also identified the 8 distinct
(3, 3)-scoring rules and studied their manipulability.
Contents
1. Introduction 3
2. Basics of Social Choice Theory 4
2.1. Voting Rules: Definitions, Examples and Properties 4
2.2. Social Welfare Functions and Arrow’s Impossibility Theorem 7
2.3. Manipulability and Gibbard-Sather