Three members of a city council are about to hold a vote on what municipal project to devote funds to. The councilors preferences (which ideally represent their constituents preferences, but one never knows...) are as follows: Pat prefers a playground, to a bike path to a community center. Quentin prefers a bike path, to a community center, to a playground. Ruby prefers a community center, to a playground, to a bike path. It is decided that they will hold a runoff, 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). Suppose that Ruby draws the short straw and gets to set the voting agenda: a) Ruby intends to vote truthfully, and believes Pat and Quentin will do the same. What voting agenda should Ruby set, in order to ensure as favorable an outcome as possible? Briefly explain why. b) Now suppose that Ruby instead plans to vote strategically, and believes Pat and Quentin will do the same. What voting agenda should Ruby set now, and why? c) Finally, suppose that Ruby plans to vote strategically, and believes that Pat will do the same but that Quentin will vote truthfully. What voting agenda should Ruby set now, and why?