(30 points) Let the set of alternatives be X = {x, y, z} and the set of individuals be N = {1, 2}. Suppose that both individuals hold strict preference rankings over X. Define as ( 1 , 2 ) the profile given by x 1 y 1 z, y 2 x 2 z. Consider the following preference aggregation function F: F( 1 , 2 ) = 1 F(1, 2) =2 for any (1, 2) = ( 1 , 2 ). In other words, individual 1 decides the social ranking when the individual preference profile is ( 1 , 2 ), but individual 2 decides the social ranking in all other preference profiles. (i) Does F satisfy the Pareto property? Why or why not? (ii) Does F satisfy IIA? Why or why not