Name Date I. Consider the preference schedule in an election with 5 candidates.
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1 Name Date I. Consider the preference schedule in an election with 5 candidates. 1. How many voters voted in this election? 2. How many votes are needed for a majority (more than 50% of the vote)? 3. How many first place votes does candidate A have? 4. How many first place votes does candidate B have? 5. How many first place votes does candidate C have? 6. How many first place votes does candidate D have? 7. How many first place votes does candidate E have? 8. Who is the winner of the election by the Plurality Method? II. Consider the preference schedule in an election with 5 candidates above. 1. Who is the first candidate to be eliminated in the Plurality with Elimination (Hare) method? 2. When the candidate in #1 gets eliminated, which candidate gets those votes in the second round? 3. In the Plurality with Elimination (Hare) method, who gets eliminated in the second round? 4. In the Plurality with Elimination (Hare) method, who wins? 5. How many votes does the winner have in the last round of the Plurality with Elimination (Hare) method? 6. In the Plurality with Run-off method, who are the top two candidates who get to be in the run-off? A. A and B B. A and C C. B and D D. C and E 7. Which candidate wins in the Plurality with Run-off method?
2 III. Consider the following preference schedule in an election with 3 candidates. 1. In the Borda Count method, how many points does each candidate get for a first place vote? 2. In the Borda Count method, how many points does each candidate get for a 2nd place vote? 3. What is candidate A s Borda score? 4. What is candidate B s Borda score? 5. What is candidate C s Borda score? 6. Who is the winner by the Borda Count method? IV. Consider the following preference schedule in an election with 3 candidates above. 1. In the method of Pairwise Comparisons, who wins in the A v B? 2. In the method of Pairwise Comparisons, who wins in the A v C? 3. In the method of Pairwise Comparisons, who wins in the B v C? 4. Who is the winner in the method of Pairwise Comparisons? V. Consider the preference schedule in an election with 5 candidates. 1. In the method of sequential pairwise voting with the agenda of A,B,C,D,E, who wins in AvB? 2. In the method of sequential pairwise voting with the agenda of A,B,C,D,E, who will the winner of AvB be paired with in the second match-up? 3. In the method of sequential pairwise voting with the agenda of A,B,C,D,E, who wins round 2? 4. In the method of sequential pairwise voting with the agenda of A,B,C,D,E, who wins round 3? 5. In the method of sequential pairwise voting with the agenda of A,B,C,D,E, who wins the election?
3 VI. 1. Consider the following preference schedule in an election with 5 candidates. 2. How many voters voted in this election? 3. Which candidate will be elected using the plurality method? 4. Which candidate will be elected using the Borda Count method? 5. Which candidate will be elected in Plurality with Elimination (Hare) method? 6. Which candidate will be elected using the sequential pairwise agenda A,B,C,D,E? 7. Which candidate will be elected using the sequential pairwise agenda A,C,B,D,E? VII. Consider the preference schedule for an election with 4 candidates. 1. Which candidate will be elected using the plurality method? 2. Which candidate will be elected using the Borda Count method? 3. Which candidate will be elected in Plurality with Elimination (Hare) method? 4. Which candidate will be elected using the sequential pairwise agenda A,B,C,D? 5. How many votes are required for a majority in this election?
4 VIII. Consider the preference schedule for an election with 3 candidates. 1. How many voters voted in this election? B 2. Which candidate will be elected using the plurality method? 3. Which candidate will be elected using the Borda Count method? 4. Which candidate will be elected in Plurality with Elimination (Hare) method? 5. Which candidate will be elected using the sequential pairwise agenda A,B,C? 6. How many votes are required for a majority in this election? IX. Consider the preference schedule for an election with 4 candidates. 1. Which candidate will be elected using the plurality method? 2. Which candidate will be elected using the Borda Count method? 3. Which candidate will be elected in Plurality with Elimination (Hare) method? 4. How many votes are required for a majority in this election?
5 X. Consider the following approval voting results: Candidate VOTER 1 VOTER 2 VOTER 3 VOTER 4 VOTER 5 VOTER 6 VOTER 7 A X X X X B X X X X X C X X X X D X X X F X X 1. Which candidate is chosen if only one of them is to be selected? 2. Which candidate(s) is (are) chosen if a 50% approval rating is required and at most 3 are elected? 3. Which candidate(s) is (are) chosen if a 60% approval rating is required and at most 3 are elected? 4. Which candidate(s) is (are) chosen if a 70% approval rating is required and at most 3 are elected? 5. Which candidate(s) is (are) chosen if an 80% approval rating is required and at most 3 are elected?
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