1.6 Rankings
• Sometimes, we are not just interested in the first place winner of the election, but also want to know who comes in second, third …
• There are 2 methods which we can use to rank candidates:– Extended Method– Recursive Method
Extended Plurality Method
• Since A gets 10 votes, B gets 11 votes, C gets 4 votes, and D gets 2 votes so the order will be.
1st place winner: B
2nd place winner: A
3rd place winner: C
4th place winner: D
10 6 5 4 2
1st A B B C D
2nd C D C A C
3rd B C A D B
4th D A D B A
Extended Borda Count
A1A4A8A:10D:144th choice
B2C8B16D:20C:283rd choice
D3D12C:24B:30B:422nd choice
C4B16D:32C:40A:561st choice
1481014Number of voters
1point
2points3points
4points
A gets 79 points, B gets 106 points, C gets 104 points, and D gets 81 points. Therefore the order will be:
1st place winner: B
2nd place winner: C
3rd place winner: D
4th place winner: A
Extended Pairwise Comparisons
Number of voters
14 10 8 4 1
1st choice A C D B C
2nd choice B B C D D
3rd choice C D B C B
4th choice D A A A A
C gets 3 points, B gets 2 points, D gets 1 point, and A gets 0 point, so the order will be:
1st place winner: C
2nd place winner: B
3rd place winner: D
4th place winner: A
Extended Plurality with Elimination Method
Number of voters
14 10 8 4 1
1st choice A C D B C
2nd choice B B C D D
3rd choice C D B C B
4th choice D A A A A
Number of voters
14 10 8 4 1
1st choice A D D D D
2nd choice D A A A A
Number of voters
14 10 8 4 1
1st choice A C D D C
2nd choice C D C C D
3rd choice D A A A A
4th choice
B gets eliminated first, C gets eliminated on the 2nd round and then A. Therefore the order will be:
1st place: D
2nd place: A
3rd place: C
4th place: B37 votes, need 19 for a majority vote
Recursive Plurality Method
10 6 5 4 2
1st C D C C D
2nd D C D D C
10 6 5 4 2
1st A B B C D
2nd C D C A C
3rd B C A D B
4th D A D B A
B is the 1st place winner.
Now remove B and apply the same method again
A is 2nd place winner
Now remove A
10 6 5 4 2
1st A D C C D
2nd C C A A C
3rd D A D D A
C is the 3rd place winner
And D is the 4th place winner
Recursive Borda Count
A1A4A8A:10D:144th choice
B2C8B16D:20C:283rd choice
D3D12C:24B:30B:422nd choice
C4B16D:32C:40A:561st choice
1481014Number of voters
1point
2points
3points
4points
A gets 79 points, B gets 106 points, C gets 104 points, and D gets 81 points. Therefore the order will be:
1st place winner: B
Now remove B and create a new table to find the 2nd place winner
Work together on the board
Recursive Plurality with Elimination Method
Number of voters
14 10 8 4 1
1st choice A C D B C
2nd choice B B C D D
3rd choice C D B C B
4th choice D A A A A
Number of voters
14 10 8 4 1
1st choice A D D D D
2nd choice D A A A A
Number of voters
14 10 8 4 1
1st choice A C D D C
2nd choice C D C C D
3rd choice D A A A A
4th choice
D is the 1st place winner. Now remove D and do the whole process all over again.
Work together on the board