1. Consider a society with 3 people (John, Eleanor and Abigail) who use the majo
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Question
1. Consider a society with 3 people (John, Eleanor and Abigail) who use the majority voting rule to decide how much to spend on a public park. There are 3 options, high (H), medium (M) and low (L) spending and the individuals rank the options in the following way:
Rank John Eleanor Abigail
1 M L H
2 L M M
3 H H L
Who is the median voter? Why?
Show the outcome of every possible pairwise election.
Will majority voting lead to a consistent choice? If so, what is that choice?
Suppose that Eleanor’s preference ordering changed to the following: First choice L, second choice H, and third choice M. Are Eleanor’s preferences in this case single or multiple peaked? Explain.
Using Eleanor’s preferences from part d, how could Eleanor, if she were in charge of the agenda, arrange the pairwise voting to guarantee that her first choice wins?
Explanation / Answer
As John and Eleanor prefers M over H, the outcome of the first election (M vs. H) is M. As John and Eleanor prefers L over H, the outcome of the second election (H vs. L) is L. As John and Abigail prefers M over L, the outcome of the third election (L vs. M) is M. Majority rule leads to a stable outcome since M defeats both H and L.
The median voter theorem states that "a majority rule voting system will select the outcome most preferred by the median voter". As , M was the first option of John, John is the median voter.
Show the outcome of every possible pairwise election. - Already stated in the first paragraph.
Will majority voting lead to a consistent choice? If so, what is that choice? Majority rule leads to a stable outcome , M since M defeats both H and L.
Suppose that Eleanor’s preference ordering changed to the following: First choice L, second choice H, and third choice M. Are Eleanor’s preferences in this case single or multiple peaked? Explain.
With the change in Eleanor’s preference ordering, majority rule no longer generates a stable outcome. In a vote between M and H, the outcome is H. In a vote between H and L, the outcome is L. In a vote between L and M, the outcome is M. So, giving one person the ability to set the agenda affects the outcome. For example, Abigail prefers H, so she might pit L against M first in order to eliminate L and avoid having L defeat H.
Using Eleanor’s preferences from part d, how could Eleanor, if she were in charge of the agenda, arrange the pairwise voting to guarantee that her first choice wins?
Eleanor prefers L, so she might pit M against H first in order to eliminate M and avoid having M defeat L. So, the arrangement of pairwise voting would be (M,H) and then (H,L)
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