(moderately difficult) A public facility needs to be located on a street , which I denote by the interval [0, 1]. In the city there are 11 voters. Each voter i has an ideal location pi , 0 pi 1, where she wants the facility to be located. If the facility is located at l, 0 l 1, then the utility of voter i is (pi l) 2 The following voting game is played to decide on the location. Every citizen/ voter i votes for a location xi , where 0 xi 1. Given the voted location profile, x = (x1, , x11) the facility is chosen at location W(x) where W(x) is a rule that picks a location for every voted location profile x. We call W(x) a voting rule. The specific W(x) that the city uses, is the following: W(x) = W(x1, , x11) = median{x1, , x11}. 1 Dipjyoti Majumdar That is the voting rule arranges the numbers x1, , x11 from lowest to highest and pics the one that is in the middle. For example, if there are 5 voters and the voted location profile is x1, x2, x3, x4, x5 with x1 < x2 < x3 < x4 < x5, the voting rule selects x3 as the location. (a) Define the game in normal form. (5 points) (b) (15 points) Is it the case that, it is a weakly dominant strategy for each agent to vote for her ideal location, given the voting rule described above. Explain why, or why not.