B. There are four candidates for mayor of Blissville, persons A, B, C, and D. The three members of the city councilGrace, Rafaela, and Tomhave to choose the mayor. Their preferences over the candidates are as follows: m Grace FlafaeIa To_ 1 D C B 2 C B A 3 B D D 4 A A C (1) a. Show that the social preferences resulting from majority voting are intransitive in this case. b. By switching two candidates in one member's list, these preferences can be made such that it can be shown that under the assumption of transitivity in majority voting, D is preferred to A; yet A is preferred to D. Perform the switch and demonstrate that this happens. (2) Using the original rankings from (t) a., the council decides to use rankorder voting to choose the mayor. a. Is there a clear winner for mayor, and if so, who? b. Candidate B dies, so the council votes again. Is there a clear winner for mayor, and if so, who? (3) Compare the outcomes in (2) to those found using rank-order voting on the rankings in (1) b. (4) Can you devise a voting scheme under which C would always win