Question

Students at a college were asked to rank three improvements that they would like to see at their college. Their choices were build a new gymnasium (G), build a baseball/football field (B), or build a swimming pool (S). The votes are summarized in the preference table. If the winner is chosen using the Borda count method of voting, does the election violate the majority criterion?

a) Yes
b) No

Answer 1

The winner chosen using the Borda count method does not violate the majority criterion. The correct option is a) Yes

Step-by-step explanation:

The Borda count method of voting assigns points to each choice based on their ranking. In this case, the students were asked to rank three improvements for their college: new gymnasium (G), baseball/football field (B), and swimming pool (S). The Borda count method assigns 2 points for the first choice, 1 point for the second choice, and 0 points for the last choice. The votes are summarized in the preference table as follows:

G (new gymnasium): 28 points

B (baseball/football field): 19 points

S (swimming pool): 22 points

Using the Borda count method, the winner is the option with the highest number of points. In this case, the new gymnasium (G) wins. Since the winner is chosen by a count of points and not a simple majority, the election does not violate the majority criterion. The correct option is a) Yes