Consider a society with three people (John, Eleanor, and Abigail) who use majority rule to decide how much money to spend on schools. There are three options for spending on a public park: \(H\) (high), \(M\) (medium), and \(L\) (low). These individuals rank the three options in the following way:

a. Consider all possible pairwise elections: \(\mathrm{M}\) versus \(H, H\) versus \(L\), and \(L\) versus \(M\). What is the outcome of each election? Does it appear, in this case, that majority rule would lead to a stable outcome on spending on the public park? If so, what is that choice? Would giving one person the ability to set the agenda affect the outcome? Explain.

b. Now suppose that Eleanor's preference ordering changed to the following: first choice \(=\mathrm{L}\), second choice \(=\mathrm{H}\), and third choice \(=\mathrm{M}\). Would majority rule lead to a stable outcome? If so, what is that choice? Would giving one person the ability to set the agenda affect the outcome? Explain.

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Rank John Eleanor Abigall 1 M L H 23 2 L M M H H L