The existence of a majority voting equilibrium is possible when preferences are single peaked. I am currently living in a small-sized society with four other members: A, B, C and D. We, as a society, would want to come to a conclusion regarding our preferred level of expenditure on pure public goods such as streetlights. We agreed on a majority voting equilibrium as our preferred level of expenditure on public goods.
a) Fill in the following tables showing the preferred level of public expenditure of each individual. My preferred expenditure level as a median voter is given to you all. (4 marks)
| A | B | Me | C | D |
| $10,000 |
b) What is your conclusion based on the above findings? Explain. (1 mark)
Here is the table showing the preferred level of public expenditure on pure public goods for each individual in your small-sized society:
A: $5,000
B: $7,000
Me: $8,000 (Median Voter)
C: $9,000
D: $10,000
In this table, we have listed the preferred expenditure levels of each member of your society for streetlights, which are considered a pure public good. As the median voter, your preferred expenditure level is $8,000. This means that when arranging the preferences in ascending order, your preference is right in the middle, with two individuals preferring a lower expenditure and two preferring a higher expenditure.
b) Based on the preferences of the members of your society for public expenditure on streetlights, it is evident that there exists a majority voting equilibrium. Here’s why:
In a society with an odd number of members, like yours with five individuals, a majority voting equilibrium can be achieved when the median voter’s preference aligns with the chosen level of expenditure. In this case, your preferred expenditure level of $8,000 is the median preference, which is positioned between the preferences of A, B, C, and D.
Since three members (A, B, and C) prefer lower expenditure levels, and only one member (D) prefers a higher expenditure level than you, the majority of the society prefers an expenditure level equal to or lower than $8,000. Thus, it is reasonable to conclude that the majority voting equilibrium for your society’s preferred level of expenditure on streetlights is $8,000, which aligns with your preference as the median voter.
In essence, this means that your society has successfully reached a decision on the level of expenditure for pure public goods like streetlights through a majority vote, where the preference of the median voter, you, holds the most weight due to its position in the middle of the preference distribution. This outcome demonstrates the power and practicality of majority voting in small-sized societies when preferences are single-peaked, as it helps in making collective decisions that are reflective of the preferences of the majority.
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