Assume that there is a society with three individuals (Marie, Pablo and Stefanie) trying to decide how much money to spend on library. There are three options for spending: L (Low), M (Medium) and H (High). These three individuals rank these three options as follows: Stefanie H Rank 1 2 3 Marie M L H Pablo L M H N M L a) Plot the preference mapping of each individual and propose an alternative voting mechanism. Did the mechanism that you proposed lead to a stable outcome on spending on library. Would giving one person the ability to set the agenda affect the outcome? Explain. b) Now suppose Stefanie's preference ordering changed to this order: First choice=L, second choice=H and third choice=M. Would your proposed rule in (b) lead to a stable outcome. Explain with the reasons. c) Explain the Median Voter Theorem and how one may use the Median Voter Theorem to derive a result (Not just Theorem, also apply to the question!)