3. Median Voter Theorem (8 points) Consider the following the model of an election. A society has 99 people, and each person's political views can be summarized by a single number detailing how liberal/conservative they are. In particular, person 1 is the most liberal and person 99 is the most conservative. and they must decide how liberal/conservative to be. They play a "game" in which each of them chooses a number between 1 and 99 , placing themselves on the political spectrum. Each voter will choose the candidate who is closest to her preferred ideology. For example, if Candidate A picks the number " 10 " and Candidate B chooses the number " 60 ", Person 15 will choose candidate A, because the distance from 15 to 10(5) is smaller than the distance from 15 to 60(45) (Hint: You could model this as a 9999 game matrix, but that is not necessary - try to think it through logically.) 3. Median Voter Theorem (8 points) Consider the following the model of an election. A society has 99 people, and each person's political views can be summarized by a single number detailing how liberal/conservative they are. In particular, person 1 is the most liberal and person 99 is the most conservative. and they must decide how liberal/conservative to be. They play a "game" in which each of them chooses a number between 1 and 99 , placing themselves on the political spectrum. Each voter will choose the candidate who is closest to her preferred ideology. For example, if Candidate A picks the number " 10 " and Candidate B chooses the number " 60 ", Person 15 will choose candidate A, because the distance from 15 to 10(5) is smaller than the distance from 15 to 60(45) (Hint: You could model this as a 9999 game matrix, but that is not necessary - try to think it through logically.)