Three politician are holding a vote to see which policy they should prompt in their next joint campaign. Here are their preferences: John Mary Will 1st choice Education Job creation Healthcare 2nd choice Job creation Healthcare Security 3rd choice Healthcare Security Education 4th choice Security Education Job creation (a) The politicians vote by majority rule. If the vote is Education vs Job creation, which policy will win? Education vs Healthcare? Education vs Security? Job creation vs Healthcare? Job creation vs Security? Healthcare vs Security? (b) Define or explain transitive preferences. In the current example, is the aggre- gation of preferences by pairwise voting (majority rule in each case) transitive? Explain. (c) They decide to vote in a single-elimination rule: two options are voted on and the winner of the first round proceeds on to a second round where they are voted against one of the two options that hasn't been considered yet, then the winner of the second round proceeds on to the third (final) round. Now, suppose Will is in charge of deciding which order to hold the votes. He wants to make sure that his favorite policy is selected. How should Will stack the order of voting? (d) Consider John as a non sincere voter while the other politicians are; that is, John votes strategically while the others vote in their most preferable choice. Would the result in (e) change? Explain.