The aim of this paper is to investigate to what extent different systems of voting can affect the results and the distribution of votes in single-winner elections. Moreover, during elections, there are always politicians who hold extreme beliefs and are either loved or hated by people and those who hold tempered beliefs but are tolerable by society. Consequently, the research also examines which of the two mentioned characteristics a candidate should have to increase the chances of winning by applying basic statistical measures such as mean or standard deviation.
The subject is relevant because it allows us to get a mathematical insight into single-winner electoral systems and can show whether a particular system of voting is only a tool, or directly contributes to the results. The paper analyses 4 different methods of voting that are or were used in the world to elect a President or other representatives for single-member posts: Supplementary Vote (SV), Instant-runoff voting (IRV), Bucklin Voting, and Coombs’ method.
It is worth adding that these systems are ranked-choice systems, that is voters rank their candidates from the most favorable one to the one that in their opinion is completely not suitable to accede to a particular office. Ranked-choice systems were chosen because this paper does not investigate only who wins the election but also how the situation of candidates in other positions changes.
Table of Contents
1. Introduction
2. Procedure
3. Analysis of voting systems
3.1 First past the post (Plurality voting)
3.2 Supplementary vote
3.3 Instant-runoff voting (IRV or Plurality with elimination)
3.4 Bucklin voting (Grand Junction system)
3.5 Coombs’ method
4. Is it better to be a stable candidate and have a similar number of votes on several places or to be an unstable one and have a different number of votes on all places?
5. Investigating how the votes are distributed in different systems of voting.
6. Evaluation
6.1 Conclusion
6.2 Strengths, limitations, and suggestions for improvement.
Objectives and Research Themes
The primary aim of this research is to investigate how various single-winner voting systems influence election outcomes and the distribution of votes. By analyzing specific ranked-choice methods using statistical measures like the mean and standard deviation, the study seeks to determine how candidate stability and voter preference patterns affect electoral success.
- Comparison of four distinct ranked-choice voting systems: Supplementary Vote, Instant-runoff voting, Bucklin Voting, and Coombs’ method.
- Application of statistical analysis to evaluate candidate performance and voting system fairness.
- Investigation into the relationship between candidate stability (standard deviation) and winning potential.
- Assessment of the susceptibility of different voting mechanisms to tactical manipulation.
Excerpt from the Book
3. Analysis of voting systems
Although this system does not belong to ranked voting systems and is not mathematically complicated, it is an excellent introduction to the systems described in the later part of this paper. The first past the post (FPTP) system, defined also as a plurality voting, functions as a way to elect a president in over 20 countries, for example in Honduras, Iceland, or Singapore. FPTP is a simple and logical method based on two main rules by which every citizen casts only one vote and the candidate who obtained the most votes wins.
Firstly, in the tables from section 2 the candidate with most first-choice votes can be found. This candidate is the winner of these elections (Candidate B-16 votes). The rest of the candidates have been ranked according to this criterion.
Summary of Chapters
1. Introduction: The author introduces the motivation for the study, stemming from the recent presidential elections in Poland, and establishes the research goal of analyzing how different voting systems impact results.
2. Procedure: This section details the methodology, explaining the use of anonymous polling and voluntary sampling among 54 participants to gather ranked preference data for six candidates.
3. Analysis of voting systems: This chapter provides a comparative study of the First Past the Post system and four specific ranked-choice voting methods, applying each to the gathered survey data to determine potential winners.
4. Is it better to be a stable candidate and have a similar number of votes on several places or to be an unstable one and have a different number of votes on all places?: The author applies statistical tools, specifically mean and standard deviation, to determine if candidate stability correlates with a higher probability of election success.
5. Investigating how the votes are distributed in different systems of voting.: This chapter utilizes box and whisker plots to visualize and analyze the distribution, median, and interquartile range of votes across the different voting systems.
6. Evaluation: The final section synthesizes the findings, confirming that voting mechanisms significantly alter outcomes, and reflects on the strengths and limitations of the research design.
Key Words
Ranked-choice voting, single-winner election, voting systems, statistics, mean, standard deviation, election results, electoral reform, plurality voting, instant-runoff voting, Bucklin voting, Coombs' method, candidate stability, ballot analysis, voter preferences.
Frequently Asked Questions
What is the core focus of this research paper?
The paper focuses on the mathematics behind various single-winner voting systems and investigates how changing the voting method can alter the outcome of an election.
Which specific voting systems are analyzed in the document?
The study examines First Past the Post (Plurality voting), the Supplementary Vote (SV), Instant-runoff voting (IRV), Bucklin Voting, and the Coombs’ method.
What is the main objective of the research?
The goal is to determine to what extent different voting systems affect election results and to identify what candidate characteristics, specifically stability, influence the likelihood of winning.
Which mathematical methods were employed for the analysis?
The author uses descriptive statistics, including the mean and standard deviation, as well as Spearman’s rank and Pearson’s product-moment correlation coefficients to analyze candidate performance and system fairness.
What is covered in the main body of the text?
The main body includes a data-gathering procedure, a detailed application of different voting algorithms to survey results, a statistical analysis of candidate stability, and a comparative evaluation using box plots.
Which keywords best describe this study?
Key terms include ranked-choice voting, electoral systems, statistical analysis, candidate stability, and election manipulation.
How does the author define a "stable" candidate?
A stable candidate is defined by having a lower standard deviation in their placement across the ranks, meaning their support is consistent rather than polarized.
What unique observation does the author make about Candidate E?
The author notes that despite receiving very few first-place votes, Candidate E performed surprisingly well in the third position when the Coombs’ method was applied.
Why does the author consider the Coombs’ method the "fairest" system?
The author identifies it as the most fair because the resulting candidate order closely aligns with the statistical ideal of having the lowest mean and standard deviation.
- Quote paper
- Maciej Nodzyński (Author), 2021, The Mathematics of Ranked-Choice Single-Winner Voting Systems. Can Different Systems of Voting Affect the Results?, Munich, GRIN Verlag, https://www.grin.com/document/1059528
