Voting Theory: Apply It 1

  • Determine the winner and assess the fairness of an election using preference ballots
  • Determine the winner and assess the fairness of an election using the Instant Runoff method
  • Determine the winner and assess the fairness of an election using a Borda count
  • Determine the winner and assess the fairness of an election using Copeland’s method
  • Determine the winner and assess the fairness of an election using the Approval Voting method
  • Apply Arrow’s Impossibility Theorem

Analyzing Voting Systems and Fairness

Welcome to a journey through the intricate world of voting systems. In this ‘Apply It’ section, we will explore various methods of determining election outcomes, each with its unique approach to capturing the will of the voters. From preference ballots in student council elections to the complexity of community surveys using Approval Voting, you will analyze how different voting methods can shape the results and the perceived fairness of elections. This exploration will provide insights into the strengths and limitations of each method and their implications in real-world decision-making.

Scenario 1: Student Council Elections – Preference Ballots

A school is holding elections for the student council president. Students are asked to rank candidates in order of preference. The voting data is given below.

Voting Data:

  • [latex]40[/latex] ballots: Mia > Hadi > Jin
  • [latex]35[/latex] ballots: Jin > Mia > Hadi
  • [latex]25[/latex] ballots: Hadi > Jin > Mia

Having examined the preference ballot system in a school setting, where students’ ranked choices directly impact the outcome, we now shift our focus to the Instant Runoff method used by a community organization. This transition allows us to compare how a different approach manages majority support and addresses the challenges of electing a leader in a more diverse voting group.

Scenario 2: Community Organization Elections – Instant Runoff Method

A local community organization is electing its new leader using the Instant Runoff method. The voting data is given below.

Voting Data:

  • [latex]30[/latex] ballots: Omar > Sofia > Lakshmi
  • [latex]25[/latex] ballots: Sofia > Lakshmi > Omar
  • [latex]20[/latex] ballots: Lakshmi > Omar > Sofia
  • [latex]15[/latex] ballots: Lakshmi > Sofia > Omar

Moving from the dynamic Instant Runoff method, where elimination rounds help distill majority preference, we enter the realm of the Borda count in a club leadership election. This scenario presents an opportunity to evaluate how a point-based system interprets voter preferences and whether it offers a fair representation of the club members’ choices.

Scenario 3: Club Leadership Election – Borda Count

The photography club is electing its new chairperson and decides to use the Borda count method. The voting data is given below.

Voting Data:

  • [latex]4[/latex] ballots: Yara > Andre > Kemi
  • [latex]3[/latex] ballots: Andre > Kemi > Yara
  • [latex]2[/latex] ballots: Kemi > Andre> Yara