2. (30 points) Let the set of alternatives be X = {r, y, z} and the set of individuals be N = {1, 2}. Suppose that both individuals hold strict preference rankings over X. Define as (>1, >?) the profile given by Consider the following preference aggregation function F: F(>1,>2) =>1 F(>1,>2) =>2 for any (>1, >2) # (x1.>2). In other words, individual 1 decides the social ranking when the individual preference profile is (>1, >;), 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