QuestionDetermine the new chair of the Natural Science Division using the Borda count method for Professors D, E, F, and H.
Studdy Solution
STEP 1
Assumptions1. There are four candidates Professors Darwin (), Einstein (), Freud (), and Hawking (H).
. The votes are summarized in the preference table.
3. The Borda count method is used to determine the winner. In this method, each rank is assigned a point value, with the highest rank (first choice) receiving the most points and the lowest rank (fourth choice) receiving the least points. The candidate with the most total points is declared the winner.
STEP 2
First, we need to assign point values to each rank. Since there are four candidates, we will assign4 points to the first choice, points to the second choice,2 points to the third choice, and1 point to the fourth choice.
STEP 3
Now, we calculate the Borda count for each candidate by multiplying the number of votes they received at each rank by the point value of that rank, and then summing these products.
For Professor Darwin (), the Borda count is calculated as follows
STEP 4
Calculate the Borda count for Professor Darwin ().
STEP 5
Repeat the process for the other candidates. For Professor Einstein (), the Borda count is calculated as follows
STEP 6
Calculate the Borda count for Professor Einstein ().
STEP 7
For Professor Freud (), the Borda count is calculated as follows
STEP 8
Calculate the Borda count for Professor Freud ().
STEP 9
For Professor Hawking (H), the Borda count is calculated as follows
STEP 10
Calculate the Borda count for Professor Hawking (H).
STEP 11
Now that we have the Borda counts for all candidates, we can determine the winner. The candidate with the highest Borda count is declared the new division chair.
The Borda counts are as follows- Professor Darwin ():139- Professor Einstein ():208- Professor Freud ():220- Professor Hawking (H):243Therefore, Professor Hawking (H) is declared the new division chair using the Borda count method.
The correct answer is B. Professor Hawking is selected using the Borda count method.
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