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5. (10 points) Assume that a student committee with five members is using an especial voting system to choose its new representative between three candidates. vi for i E {1, 2, ... ,5} shows a voter and cj for j E {1, 2, 3} shows a candidate. The voting system works as follows: . In the first round, each vi announces her ranking over the three can- didates: U1 V2 V3 V4 V5 C1 C2 C3 C2 C3 C2 C1 C1 C1 C1 C3 C3 C2 C3 C2 . Then the candidate who is the first choice of the lowest number of the voters is eliminated. . The procedure repeats between the remaining candidates and the candidate who is the first choice of the highest number of the voters is chosen as the new representative. (a) Can the Condorcet winner be the chosen representative under this voting system? Explain. (5 pts) (b) How strategic voting can change the outcome? Explain. (5 pts)