The Mathematics of Voting

Summary

This video explores the role of Mathematics in Political Science, specifically in voting systems. It begins by discussing the historical contributions of Marquis de Condorcet during the French Revolution. The video explains different voting methods, such as the plurality method, plurality with elimination, and instant runoff voting. Through practical examples, it illustrates how these methods work and their potential flaws, like the monotonicity criterion. The video highlights how ranked-choice voting can resolve some of these issues, offering a fairer approach to elections, similar to the method used in determining the Oscars' Best Picture.

Takeaways

• 😀 Mathematics plays a significant role in various fields like Biology, Chemistry, Medicine, Business, Computer Science, and even Political Science.
• 😀 The concept of the mathematics of voting dates back to the French Revolution, with contributions from political philosopher and mathematician Marquis de Condorcet.
• 😀 The main goal of voting systems is to reach a consensus, or general agreement, about the winner of a contest.
• 😀 The video explores five voting methods: Plurality Method, Plurality with Elimination, Instant Runoff Voting, Borda Count Method, and Pairwise Comparison Method.
• 😀 The Plurality Method is simple, where the candidate with the most first-choice votes wins, but it doesn’t guarantee majority support.
• 😀 An example illustrates the flaws of the Plurality Method, where a candidate can win even without the majority of votes, as seen with candidate B winning with 590 votes in the example.
• 😀 Plurality with Elimination addresses the issue of the Plurality Method by eliminating the candidate with the fewest votes and holding additional elections to ensure the winner has a majority.
• 😀 A problem with Plurality with Elimination is that it may violate the monotonicity criterion, where a candidate who should have won loses because of voting dynamics after elimination.
• 😀 The video demonstrates a scenario where Arampulo won using the Plurality Method but lost after Camiguin was eliminated, and Boracay emerged as the winner in the subsequent round.
• 😀 To avoid the drawbacks of both methods, the Instant Runoff Voting (Ranked-choice method) could be a better solution, as it allows voters to rank candidates, ensuring a more accurate representation of majority preferences.

Q & A

What is the main topic of the video?

The main topic of the video is the role of mathematics in political science, specifically focusing on the mathematics of voting systems.

How does mathematics contribute to political science?

Mathematics contributes to political science by providing methods to analyze and improve voting systems, aiming to find fair and representative ways of determining outcomes in elections.

Who is credited with the early contribution of mathematics to voting systems?

Mary Jean Antoine Nicolas de Caritat, also known as the Marquis de Condorcet, is credited with the early contribution of mathematics to voting systems during the French Revolution.

What is the goal of voting in any contest?

The goal of voting in any contest, such as a talent search or beauty contest, is to achieve a general agreement, known as consensus, on the winner.

What are the five different voting methods discussed in the video?

The five voting methods discussed in the video are: Plurality Method, Plurality with Elimination, Instant Runoff Voting, Borda Count Method, and Pairwise Comparison Method.

How does the Plurality Method work in elections?

In the Plurality Method, voters select their first-choice candidate, and the candidate with the most first-choice votes wins the election.

What is the main problem with the Plurality Method?

The main problem with the Plurality Method is that it can result in a winner who does not have the support of the majority of voters.

How does the Plurality with Elimination method address the issues of the Plurality Method?

The Plurality with Elimination method eliminates the candidate with the fewest votes and conducts another round of voting to ensure the winner has a majority.

What is the monotonicity criterion, and how does it relate to the Plurality with Elimination method?

The monotonicity criterion states that if a voter’s preference changes to favor the winning candidate, that candidate should not lose. The Plurality with Elimination method may violate this criterion if a candidate loses due to the preferences of voters who previously supported the eliminated candidate.

What is the Instant Runoff Voting method, and how does it differ from the Plurality Method?

Instant Runoff Voting (IRV), also known as Ranked-choice voting, asks voters to rank candidates in order of preference. If no candidate wins a majority, the candidate with the fewest votes is eliminated, and their votes are redistributed based on second-choice preferences. This process continues until a majority winner is found.