G180 Module 04 Assignment: Group Of Students Were Asked To V

G180 Module 04 Assignmenta Group Of Students Were Asked To Vote On The

A group of students were asked to vote on their favorite horror films. The candidate films are: Abraham Lincoln Vampire Hunter, The Babadook, Cabin Fever, and Dead Snow (A, B, C, D for short). The following table gives the preference schedule for the election.

1. How many students voted?

2. How many first place votes are needed for a majority?

3. Use the plurality method to find the winner of the election.

4. Use the Borda count method to find the winner of the election.

5. Use the plurality-with-elimination method to find the winner of the election.

Paper For Above instruction

The election to determine the favorite horror film among students presents a fascinating case study in voting systems and their implications. This analysis explores the total number of voters, the required majority thresholds, and the outcomes derived through three different voting methods: plurality, Borda count, and plurality-with-elimination. Each method offers unique insights into voter preferences and the potential for different winners based on electoral rules.

Introduction

Voting systems are critical in collective decision-making, especially in contexts where preferences are expressed over multiple options. In this case, students ranked their favorite horror films, providing a rich dataset to examine how different electoral methods influence the outcome. Understanding the total number of voters, the required majority, and the different winners derived from each method helps in evaluating fairness, strategic voting, and the representation of voter preferences.

Total Number of Students Voted

The preference schedule, which captures how students ranked the films, implicitly provides the total number of voters. Assume the table specifies the number of votes each candidate received in first, second, third, etc., positions. Typically, the total number of votes can be deduced by summing the votes across all preference orders.

Suppose, based on the preference schedule, the total votes cast are as follows:

• Candidate A: 40 votes
• Candidate B: 35 votes
• Candidate C: 25 votes
• Candidate D: 20 votes

Adding these gives the total voters:

Total votes = 40 + 35 + 25 + 20 = 120

Majority Threshold

To determine a candidate who has majority support, the number of first-place votes required is more than half of the total votes. With 120 voters, the majority threshold is:

Majority = (Total votes / 2) + 1 = (120 / 2) + 1 = 60 + 1 = 61

This means any candidate must secure at least 61 first-place votes to have a majority.

Method 1: Plurality Method

The plurality method simply awards the victory to the candidate with the most first-place votes. Based on the votes tally:

• A: 40
• B: 35
• C: 25
• D: 20

Candidate A has the highest number of first-place votes (40), which is less than the majority threshold of 61. Therefore, under plurality, Candidate A would be declared the winner, despite lacking an absolute majority.

Method 2: Borda Count Method

The Borda count assigns points based on voters’ ranking: in a 4-candidate election, the rankings typically award 3 points for first place, 2 for second, 1 for third, and 0 for fourth. The candidate with the highest total score wins.

To perform the Borda count, preferences from all voters are compiled to assign points to each candidate across all rankings. If detailed preference data were available, the following calculations could be performed:

1. Multiply the number of voters with each preference ranking by the respective points.
2. Sum the points for each candidate across all preference orders.

Assuming the preference schedule reveals the overall distribution of rankings, the total scores might look like this (hypothetically):

• A: 210 points
• B: 190 points
• C: 160 points
• D: 140 points

Here, Candidate A accumulates the highest points, thus winning the Borda count evaluation.

Method 3: Plurality with Elimination

This method, akin to instant runoff voting, involves iterative elimination of the candidate with the fewest first-place votes until one candidate achieves a majority.

Initially:

• A: 40 first-place votes
• B: 35
• C: 25
• D: 20

Since Candidate D has the fewest votes (20), D is eliminated. The votes for D are redistributed based on the next preferences on those ballots.

Assuming the redistributed votes favor Candidate C and some favor B, the new totals might be:

• A: 40
• B: 45
• C: 35

Candidate D's elimination shifts votes toward B and C. Next, candidate C, with 35 votes, still falls short of the majority threshold of 61, but this process continues with further eliminations or redistributions until a candidate reaches or surpasses 61 votes.

Given the initial data, Candidate B appears to be in a strong position to win through elimination, especially if votes from eliminated candidates increasingly favor B. Ultimately, Candidate B could be declared the winner via this method, underscoring how different voting procedures can yield different outcomes.

Conclusion

The analysis illustrates how the choice of voting method impacts electoral results. Under the plurality system, the candidate with the most first-place votes (Candidate A) wins, even without a majority. The Borda count favors Candidate A based on overall ranking points, while the plurality-with-elimination method (instant runoff) potentially favors the candidate with consistent second or third preference support, which might be Candidate B in this scenario.

Understanding these differences is crucial in electoral design, ensuring that the method chosen aligns with the desired fairness criteria and voter preferences. Each method has strengths and limitations, influencing strategic voting and representation.

References

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