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Table of Contents:

Chapter 1: Introduction
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Objectives of the Study
1.4 Research Questions
1.5 Limitations of the Study
1.6 Scope of the Study

Chapter 2: Literature Review
2.1 Theoretical Framework
2.2 Historical Overview of Voting Systems
2.3 Mathematical Models of Voting
2.4 Social Choice Theory
2.5 Criticisms of Existing Voting Systems

Chapter 3: Research Methodology
3.1 Research Design
3.2 Sampling Techniques
3.3 Data Collection Methods
3.4 Data Analysis Techniques
3.5 Ethical Considerations

Chapter 4: Discussion of Findings
4.1 Analysis of Voting Systems
4.2 Comparison of Voting Systems
4.3 Evaluation of Social Choice Theory
4.4 Implications of Findings
4.5 Recommendations for Future Research

Chapter 5: Conclusion and Summary
5.1 Summary of Findings
5.2 Conclusion
5.3 Contributions to the Field
5.4 Recommendations for Practitioners
5.5 Future Directions for Research

Overview:

The thesis “The Mathematics of Voting and Social Choice” explores the intersection of mathematics, voting systems, and social choice theory. The study aims to examine various voting systems and their mathematical properties, as well as to analyze the implications of social choice theory on decision-making processes.

Chapter one introduces the background of the study, defines the objectives, research questions, limitations, and scope of the study. Chapter two delves into the literature review, providing a theoretical framework, historical overview of voting systems, mathematical models of voting, and criticisms of existing systems. Chapter three outlines the research methodology, including research design, sampling techniques, data collection methods, data analysis techniques, and ethical considerations.

Chapter four presents the discussion of findings, analyzing different voting systems, comparing their properties, evaluating social choice theory, and providing recommendations for future research. Finally, chapter five concludes the thesis by summarizing the findings, drawing conclusions, discussing the contributions to the field, providing recommendations for practitioners, and suggesting future research directions.

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