PROBLEM
66 voters ranked cereals A,B,C, and D. Use the Borda count method to find the winner.
STEP 1
Assumptions1. The number of voters is66.
. The voters are asked to rank four brands of cereal A,B,C, and $$.
3. The votes are summarized in the given preference table.
4. We are using the Borda count method to determine the winner.
STEP 2
The Borda count method assigns points to each choice based on its rank. In this case, with four choices, the first choice gets points, the second choice gets2 points, the third choice gets1 point, and the fourth choice gets0 points. We can write this asFirst Choice= pointsSecond Choice=2 pointsThird Choice=1 pointFourth Choice=0 points
STEP 3
Now, we calculate the total points for each cereal brand. For each brand, we multiply the number of votes it got in each position by the points for that position, and then add up these products.
For brand A, we haveTotal points for A=(23×3)+(34×2)+(5×1)+(×0)
STEP 4
Calculate the total points for brand A.
Total points for A=(23×3)+(34×2)+(×1)+(4×0)=69+68++0=142
STEP 5
Repeat the process for brands B,C, and $$.
For brand B, we haveTotal points for B=(5×3)+(23×2)+(34×1)+(4×0)
STEP 6
Calculate the total points for brand B.
Total points for B=(5×3)+(23×2)+(34×1)+(4×0)=15+46+34+0=95
STEP 7
For brand C, we haveTotal points for C=(4×3)+(5×2)+(23×1)+(34×0)
STEP 8
Calculate the total points for brand C.
Total points for C=(4×3)+(5×2)+(23×1)+(34×0)=12+10+23+0=45
STEP 9
For brand ,wehave\text{Total points for D} = (34 \times3) + (4 \times2) + (5 \times) + (23 \times)$$
STEP 10
Calculate the total points for brand $$.
Total points for D=(34×3)+(4×2)+(5×)+(23×0)=102+8+5+0=115
SOLUTION
Now, compare the total points for each brand. The brand with the highest total points is the winner.
A142 pointsB95 pointsC45 points115 pointsBrand A has the highest total points, so it is the winner.
The winner is brand A.
Start understanding anything
Get started now for free.