The following electoral method is used to choose the mayor of Whoville: Every resident ranks the candidates from most preferred to least preferred, and places this ranked list in a ballot box.
Each candidate receives a number of points equal to the number of residents who prefer him to all the other candidates. The candidate who thus amasses the greatest number of points wins the election.
If two or more candidates are tied for first place in the number of points, the winner of the election is the candidate among them whose social security number is smallest. Assume there are at least three candidates.
(a) Show by example that this electoral method is not monotonic.
(b) Show by example that this electoral method is not manipulable.