1. Majority voting (5 points) Suppose there are three voters: Michael, Bugs, and
ID: 348836 • Letter: 1
Question
1. Majority voting (5 points) Suppose there are three voters: Michael, Bugs, and Lola. They need to decide whether to have low (L), medium (M), or high (H) levels of spending on public art installations. Suppose that their preferences orderings are as follows: Rank M Iola L M Which level of public art spending wins if the election is H vs. L? Which level of public art spending wins if the election is L vs. M? Which level of public art spending wins if the election is M vs. Ht the social preference ordering. Does pairwise majority voting lead to a stable collective decision-making rule in this case?Explanation / Answer
1. If election is H vs. L then low level of public art spending wins because 1 out of 3 voters has given rank 1 and 1 out of 3 voters has given rank 2 to low spending whereas 2 out of 3 voters have given rank 3 to high spending.
2. If election is M vs. L then medium level of public art spending wins because 2 out of 3 voters have given rank 2 to medium spending whereas 1 out of 3 voters has given rank 2 to low spending. 1 out of 3 voters has given rank 1 to both medium and low spending so it gets cancelled out.
3. If election is H vs. M then medium level of public art spending wins because 2 out of 3 voters have given rank 2 to medium spending whereas 2 out of 3 voters have given rank 3 to high spending.
4. Social preference ordering is as below:
a. Medium spending
b. Low spending
c. High spending
This is because Rank 1 is equally distributed among L, M and H so it gets cancelled out. 2 out of 3 voters have given rank 2 to medium spending and 1 out of 3 voters has given rank 2 to low spending. 2 out of 3 voters have given rank 3 to high spending.
5. Yes, in this case pairwise majority voting leads to a stable collective decision-making because it yields accurate result in this case.
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