Question 1 1 pts Arrow's Impossibility Theorem implies O that there is a voting method that satisfies all of the fairness criteria. O that it is impossible to have a voting method that satisfies all of the fairness criteria. O none of these O that in every election, each of the voting methods must produce a different winner Question 2 1 pts An election is held among four candidates (A, B, C, and D). Using a voting method we will call X, the winner of the election is candidate A. Due to an irregularity in the original vote count, a recount is required. Before the recount takes place, candidate B drops out of the race. In the recount, still using voting method X, candidate D wins the election. Based on this information, we can say that voting method X violates the independence of irrelevant alternatives criterion. O monotonicity criterion. O majority criterion. O Condorcet criterion. Question 3 1 pts An election is held among four candidates (A, B, C, and D). Using a voting method we will call X, the winner of the election is candidate A. However, candidate D beats each other candidate in a head to head, pairwise comparison. Based on this information, we can say that voting method X violates the O Condorcet criterion. O independence of irrelevant alternatives criterion. O monotonicity criterion. O majority criterion.For an election with four candidates (A, B, C. D) we have the following the following preference table NUMBER OF 5 18 VOTER 15 Choice D A C and Choice 4 A and Choice 4 B D th Choice C C D Using the plurality method, which candidate wins the election? OC OA OD OB Question 5 1 pts For an election with four candidates (A, B, C, D) consider the following preference table: NUMBER OF 5 8 VOTER st Choice D A C and Choice B A A and Choice 4 D 1th Choice C D Using the Borda count method, which candidate wins the election? OC O B OD O AFor an election with four candidates (A, B, C. D) consider the following preference table: NUMBER OF 5 8 VOTERS 1" Choice A C 2nd Choice 4 A 3rd Choice 4th Choice C C D B Using the majority method, which candidate wins the election? DB OA OD O) No winner Question 7 1 pts If there is a majority winner in an election let say candidate X, then candidate X will also be the plurality method winner. then candidate X will also be the pairwise sequential winner. O then candidate X will also be the Condorcet method winner. O all the the statements are true.Question 8 1 pts Given the following preference table, the plurality method winner is RANKING 15 12 8 11 9 1st Q T R S Q 2nd S Q S T 3rd R R Q T S 4th T S T Q R OT OS OR Question 9 1 pts Given the following preference table, the Condorcet winner is _ RANKING |15 12 8 11 9 1st Q T R S O 2nd S Q S R T 3rd R R T S 4th T S T Q R OR OS OTQuestion 10 1 pts Given the following preference table, the Borda score of Candidate S is RANKING 15 12 8 11 9 1st Q T R S Q 2nd S O S T 3rd R R Q T S 4th T S T Q R O 100 Q 88 143 Q 104 Question 11 1 pts Given the following preference table, the winner using the Hare method is RANKING |15 12 8 11 9 1st Q T R S Q 2nd S S R T 3rd R R Q S 4th T S T Q R OT OS ORQuestion 12 1 pts The winner using the Sequential Pairwise voting with agenda TSQR is RANKING 15 12 8 11 9 1st Q T R S 2nd S Q S R T 3rd R R O T S 4th T S T Q R OS OT OQ OR Question 13 1 pts An election is held among four candidates (A, B, C, and D). Using a voting method we will call X, the winner of the election is candidate A. However, candidate D beats each other candidate in a head to head, pairwise comparison. Based on this information, we can say that voting method X violates the O Monotonicity criterion Majority criterion ) Condorcet criterion O Independence of irrelevant alternatives criterionQuestion 14 1 pts Given the graph 2 IC 6 Which of the following is TRUE? O The given graph contains multiple edges. O The given graph is a multigraph. O Vertices C and H are adjacent. O The given graph is disconnected. Question 15 1 pts Given the graph 2 Which of the following is a walk of length 6? O (H.E.D.A.F.G.E) O (A,B.C.B.E,D) O (A.B.A.B.A.B.A) O (A,B,C.H.E.G)