(20 points) Assume the local government wants to build a new park in the area. Five locations, a, b, c, d and e have been chosen as potential locations for this park. The park will be built on the location that is chosen by the majority of the residents. The voting system works as follows: local population is divided into 5 small groups. Each group sends a representative to the voting meeting. These representative, let's call them agent 1, agent 2, agent 3 agent 4 and agent 5, report their preferences over the locations and then the winner location will be announce. The preference rankings over ve locations are: agentl agentZ agentS agent4 agent5 c b a e e b a c d d a c d c b d e b a a e d e b c (a) Order the options alphabetically from left to right and draw the preferences. (4 pts) (b) Which agent has single-peaked preferences and who has not? (4 pts) (c) If the majority voting is used then which location is chosen? If none is selected, explain why. Show the voting steps. (5 pts) (d) If the Plurality voting is used to choose the location. Which location is the winner? Now let us assume it has been decided that if the plurality voting leads to a tie then the majority voting chooses the winner between the ones with the same scores. Does any agent have an incentive to vote strategically? If yes who can get a better results by strategically voting and how?(7 pts)