QuestionGiven a preference table, find the winner using Borda count, and check if majority and head-to-head criteria are met.
Studdy Solution
STEP 1
Assumptions1. The preference table is given as above.
. We are using the Borda count method to determine the winner.
3. The Borda count method assigns points to each candidate based on their rank in each voter's preference. The candidate with the highest total points is the winner.
4. The points are assigned as follows1st choice gets5 points,nd choice gets4 points,3rd choice gets3 points,4th choice gets points, and5th choice gets1 point.
5. The number of votes for each preference order is multiplied by the points for each rank to get the total points for each candidate.
STEP 2
Calculate the Borda count for each candidate.For candidate
STEP 3
Calculate the Borda count for candidate A
STEP 4
Calculate the Borda count for candidate B
STEP 5
Calculate the Borda count for candidate C
STEP 6
Calculate the Borda count for candidate D
STEP 7
Find the candidate with the highest Borda count. This candidate is the winner according to the Borda count method.
STEP 8
Assumptions for part B and C1. The majority criterion is satisfied if the candidate who has the most first-place votes wins.
2. The head-to-head criterion is satisfied if, when comparing every pair of candidates, the candidate who wins in a head-to-head comparison with every other candidate is the winner.
STEP 9
Check if the majority criterion is satisfied. This is done by seeing if the candidate who received the most first-place votes is the same as the candidate who won according to the Borda count method.
STEP 10
Check if the head-to-head criterion is satisfied. This is done by comparing each pair of candidates and seeing if the candidate who won according to the Borda count method also wins in a head-to-head comparison with every other candidate.
Was this helpful?
