An odd number n of agents are located along the line interval [0,1] and must decide where to build a sports centre in that interval. The preferences of agent i (i=1,2,...,n) are represented by the utility function

U(x) = 1 - x - xil,

where x = [0,1] denotes the location of the sports centre and x/ [0,1] is the location

of agent i's home. The collective decision is made by minimizing the sum of the distances between the centre and the agents' homes.

a) Draw the utility function of a representative agent.

b) Is the chosen location a Condorcet winner? Explain your answer.