Analyzing Voting Systems and Fairness Cont.

As we depart from the point allocation strategy of the Borda count, we approach Copeland’s method in a neighborhood committee setting. This method introduces us to the concept of pairwise comparison and its effectiveness in capturing the collective preference of a group, presenting a unique perspective on consensus-building in elections.

Scenario 4: Neighborhood Committee Election – Copeland’s Method

A neighborhood committee uses Copeland’s method to select its new chair. The voting data is given below.

Pairwise Voting Data:

• Aisha vs. Juan: Aisha wins [latex]60-40[/latex]
• Aisha vs. Nia: Nia wins [latex]55-45[/latex]
• Juan vs. Nia: Tie of [latex]50-50[/latex] 

Leaving behind the pairwise confrontations of Copeland’s method, we now examine the Approval Voting method employed in a community survey. This scenario will demonstrate how this method enables voters to express their preferences in a broader context and the implications it has for gauging public opinion on multiple options

Scenario 5: Community Survey – Approval Voting Method

A community conducts a survey to choose a new public project, using the Approval Voting method. The voting data is given below.

Voting Data (Number of Approvals):

• Park Renovation: [latex]120[/latex] approvals
• Community Center: [latex]150[/latex] approvals
• Public Library: [latex]110[/latex] approvals
• Sports Complex: [latex]130[/latex] approvals

After exploring the Approval Voting method in the community survey, where the simplicity of choosing multiple options comes into play, we now delve into the theoretical realm with Arrow’s Impossibility Theorem. This transition from practical voting methods to theoretical analysis invites us to consider the broader principles and potential limitations of voting systems as a whole. Arrow’s theorem challenges us to critically think about the possibility of achieving a perfect voting system that is fair, rational, and devoid of paradoxes, bringing a new dimension to our understanding of electoral fairness.

Scenario 6: Theoretical Analysis – Arrow’s Impossibility Theorem

In a theoretical discussion about voting systems, Arrow’s Impossibility Theorem is brought up.

As we conclude our exploration of various voting methods, consider the intricate balance between accurately representing voter preferences and maintaining fairness in election outcomes. Each method, from preference ballots to Approval Voting, offers unique insights into how we make collective decisions. Arrow’s Impossibility Theorem further reminds us of the inherent challenges in creating a perfect voting system, highlighting the complexity of achieving both fairness and rationality in the voting process. Excellent work today!