1. 1.6 Rankings

2. 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

3. 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. 1 st place winner: B 2 nd place winner: A 3 rd place winner: C 4 th place winner: D 106542 1 st ABBCD 2 nd CDCAC 3 rd BCADB 4 th DADBA

4. Extended Borda Count A1A4A8A:10D:144 th choice B2C8B16D:20C:283 rd choice D3D12C:24B:30B:422 nd choice C4B16D:32C:40A:561 st 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: 1 st place winner: B 2 nd place winner: C 3 rd place winner: D 4 th place winner: A

5. Extended Pairwise Comparisons Number of voters 1410841 1 st choiceACDBC 2 nd choiceBBCDD 3 rd choiceCDBCB 4 th choiceDAAAA C gets 3 points, B gets 2 points, D gets 1 point, and A gets 0 point, so the order will be: 1 st place winner: C 2 nd place winner: B 3 rd place winner: D 4 th place winner: A

6. Extended Plurality with Elimination Method Number of voters 1410841 1 st choiceACDBC 2 nd choiceBBCDD 3 rd choiceCDBCB 4 th choiceDAAAA Number of voters 1410841 1 st choiceADDDD 2 nd choiceDAAAA Number of voters 1410841 1 st choiceACDDC 2 nd choiceCDCCD 3 rd choiceDAAAA 4 th choice B gets eliminated first, C gets eliminated on the 2 nd round and then A. Therefore the order will be: 1 st place: D 2 nd place: A 3 rd place: C 4 th place: B 37 votes, need 19 for a majority vote

7. Recursive Plurality Method 106542 1 st CDCCD 2 nd DCDDC 106542 1 st ABBCD 2 nd CDCAC 3 rd BCADB 4 th DADBA B is the 1 st place winner. Now remove B and apply the same method again A is 2 nd place winner Now remove A 106542 1 st ADCCD 2 nd CCAAC 3 rd DADDA C is the 3 rd place winner And D is the 4 th place winner

8. Recursive Borda Count A1A4A8A:10D:144 th choice B2C8B16D:20C:283 rd choice D3D12C:24B:30B:422 nd choice C4B16D:32C:40A:561 st 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: 1 st place winner: B Now remove B and create a new table to find the 2 nd place winner Work together on the board

9. Recursive Plurality with Elimination Method Number of voters 1410841 1 st choiceACDBC 2 nd choiceBBCDD 3 rd choiceCDBCB 4 th choiceDAAAA Number of voters 1410841 1 st choiceADDDD 2 nd choiceDAAAA Number of voters 1410841 1 st choiceACDDC 2 nd choiceCDCCD 3 rd choiceDAAAA 4 th choice D is the 1 st place winner. Now remove D and do the whole process all over again. Work together on the board