Three members of a city council are about to hold a vote on whatmunicipal project to devote funds to. The councilors' preferences (which ideally represent their constituents' preferences, but one never knows...) are as follows:

Alice prefers a playground, to a bike path, to a community center. Bob prefers a bike path, to a community center, to a playground. Carol prefers a community center, to a playground, to a bike path. It is decided that they will hold a two-round pairwise vote, and that one councilor, chosen by drawing straws, will set the agenda (the order of the votes, e.g. playground vs. bike path, then winner vs. community center).

A) Suppose that Alice sets the voting agenda, and that she believes Bob and Carol will vote truthfully. What voting agenda should Alice set, in order to ensure as favorable an outcome as possible? (Hint: There are three possible voting agendas. Given Bob and Carol's true prelerences, find the best outcome that Alice can obtain in each one.) B) Now suppose that Alice instead believes that Bob and Carol will vote strategically. What voting agenda should Alice set, in order to ensure as favorable an outcome as possible? C) Based on your answers to A and B, does this voting system violate axiom 4 of the Arrow Impossibility Theorem? Does it violate axiom 5