7. Understanding Arrow\'s impossibility theorem Arrow\'s impossibility theorem s
ID: 1225140 • Letter: 7
Question
7. Understanding Arrow's impossibility theorem Arrow's impossibility theorem states that under certain assumptions about preferences, no voting system exists which satisfies a 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 No Description Unanimity Transitivity Alternatives Dictators The ranking between Cand A does not depend on whether Bis also available There is no person who always gets what he wants, despite everyone else's preferences If C beats A, and A beats B, then C beats B If everyone prefers C to A, then C beats A. Consider the following voting system:Explanation / Answer
Arrows impossibility theorem states that under certain assumptions about preferences, no voting system exist which satisfies all of the following properties:
Ans:- Transitivity
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.
Description
Unanimity
Transitivity
Independence of Irrelevant Alternatives
No Dictators
The ranking between C and A does not depend on whether B is also Available
?
There is no person who always gets what he wants , despite everyone else’s preferences
?
If C beats A, and A beats B, then C beats B.
?
If everyone prefers C to A, then C beats A.
?
Which property does this voting method violate according to Arrow’s impossibility theorem?
Ans:- No Dictators
Description
Unanimity
Transitivity
Independence of Irrelevant Alternatives
No Dictators
The ranking between C and A does not depend on whether B is also Available
?
There is no person who always gets what he wants , despite everyone else’s preferences
?
If C beats A, and A beats B, then C beats B.
?
If everyone prefers C to A, then C beats A.
?
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