pls be with all the steps and in a clean write

1. (30 pts) 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: Rank 1 2 3 Marie M L H Pablo I M Stefanie H M L a) Could majority voting be applied to make a decision on how much to spend on library? Explain b) 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 c) 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. d) 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!)