For each description in the following table, identify the property of a desirable voting system it portrays. Independence of Irrelevant Alternatives No Description Unanimity Transitivity Dictators If everyone prefers B to A, then B beats A. There is no person who always gets what he wants, despite everyone else's preferences If B beats A, and A beats C, then B beats C. The ranking between C and A does not depend on whether B is also available. Consider the following voting system:
For each description in the following table, identify the property of a desirable voting system it portrays. Independence of Irrelevant Alternatives No Description Unanimity Transitivity Dictators If everyone prefers B to A, then B beats A. There is no person who always gets what he wants, despite everyone else's preferences If B beats A, and A beats C, then B beats C. The ranking between C and A does not depend on whether B is also available. Consider the following voting system:
Principles of Microeconomics
7th Edition
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Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter22: Frontiers Of Microeconomics
Section: Chapter Questions
Problem 7PA
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Question
Arrow's impossibility theorem states that under certain assumptions about preferences, no voting system exists that satisfies all of the following properties:
• | Unanimity |
• | Transitivity |
• | Independence of irrelevant alternatives |
• | No dictators |
![Assume individuals in a society have preferences regarding the following possible outcomes: A, B, and C.
For each description in the following table, identify the property of a desirable voting system it portrays.
Independence of Irrelevant
Alternatives
No
Dictators
Description
Unanimity
Transitivity
If everyone prefers B to A, then B beats A.
There is no person who always gets what he wants, despite
everyone else's preferences
If B beats A, and A beats C, then B beats C.
The ranking between C and A does not depend on whether B is also
available.
Consider the following voting system:
In a pairwise voting system, voters first choose between two outcomes, then the winner of that vote gets paired against the remaining
outcome to determine the voters' choice. Suppose someone suggests choosing first between A and B and then comparing the winner to
C. This results in the voters choosing C. However, if the voters choose first between B and C and then compare the winner to A, the
voters end up with B instead.
Which property does this voting method violate, according to Arrow's impossibility theorem?
O Independence of irrelevant alternatives
O Transitivity
O No dictators](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda8c5e25-0a1b-41c4-bd54-1504c508d2e8%2F96c28afe-8a45-4e15-9ff2-2ffc3e97fbda%2F6mne1l9_processed.png&w=3840&q=75)
Transcribed Image Text:Assume individuals in a society have preferences regarding the following possible outcomes: A, B, and C.
For each description in the following table, identify the property of a desirable voting system it portrays.
Independence of Irrelevant
Alternatives
No
Dictators
Description
Unanimity
Transitivity
If everyone prefers B to A, then B beats A.
There is no person who always gets what he wants, despite
everyone else's preferences
If B beats A, and A beats C, then B beats C.
The ranking between C and A does not depend on whether B is also
available.
Consider the following voting system:
In a pairwise voting system, voters first choose between two outcomes, then the winner of that vote gets paired against the remaining
outcome to determine the voters' choice. Suppose someone suggests choosing first between A and B and then comparing the winner to
C. This results in the voters choosing C. However, if the voters choose first between B and C and then compare the winner to A, the
voters end up with B instead.
Which property does this voting method violate, according to Arrow's impossibility theorem?
O Independence of irrelevant alternatives
O Transitivity
O No dictators
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