Transcribed Image Text: 73%i 7:21 AM Activity 6 Math – Malik, Rozainah – Saved 2. The members of a acholarship committee have ranked four finalists competing fora scholarship in order of preference. The results are shown in the preference schedule below. Candidate Rankings A 3. 4. 2 4 1 3 D Number of wotes If you are one of the voting members and you want candidate C to win the scholarship, which method would you suggest that the committee use? voting
In analyzing the given situation, it is clear that the voting members of the scholarship committee need to determine which method to use in order to select a winner. Specifically, they want to ensure that candidate C wins the scholarship. To make this decision, it is important to consider various voting methods and their implications.
One method that the committee could consider is the Plurality method. In this method, each voting member selects their preferred candidate, and the candidate with the most votes wins. However, in this particular scenario, this method may not be the best choice. According to the preference schedule provided, candidate C received the least number of votes (ranked fourth by all voting members). Therefore, if the committee were to use the Plurality method, candidate C would not win the scholarship.
Another method that the committee could consider is the Borda Count method. In this method, each candidate is assigned a certain number of points based on their ranking. The candidate with the highest total points wins. The points assigned to each candidate are typically determined by the number of candidates in the election. For example, if there are four candidates, the first-ranked candidate receives 4 points, the second-ranked candidate receives 3 points, and so on. In this scenario, candidate C received a total of 5 points (2nd rank from one voting member and 3rd rank from the other), and candidate A received the highest total points with 6 (3rd rank from one voting member and 4th rank from the other). Therefore, if the committee were to use the Borda Count method, candidate A would win the scholarship, not candidate C.
Alternatively, the committee could consider using the Condorcet method. In this method, pairwise comparisons are made between each pair of candidates. The candidate who wins the most pairwise comparisons is deemed the overall winner. However, in this particular scenario, the Condorcet method would not be applicable. Since candidate C is ranked last by all voting members, there is no pairwise comparison that candidate C could win.
Given the limitations of the Plurality, Borda Count, and Condorcet methods, an alternative method that the committee could consider is the Instant Runoff Voting (IRV) method. In this method, voting members rank the candidates in order of preference. The candidate with the least number of first-place votes is eliminated, and the votes for that candidate are redistributed to the remaining candidates based on the voters’ second choices. This process continues until one candidate has a majority of the votes and is declared the winner.
In this scenario, if the committee were to use the IRV method, candidate C would have a chance to win the scholarship. Although candidate C received the least number of first-place votes, there is a possibility that candidate C was ranked higher on some voters’ preference lists as their second or third choice. As a result, when the candidate with the least number of first-place votes is eliminated, these alternative choices could contribute to candidate C gaining more votes and potentially securing a majority.
Overall, considering the given preference schedule and the objective of wanting candidate C to win the scholarship, the committee is advised to use the Instant Runoff Voting (IRV) method. This would provide a fair and systematic approach to determine the winner, taking into account the rankings of all candidates and allowing for alternative choices to come into play.