Question: 11. Understanding Arrow's impossibility theorem Arrow's impossibility theorem states that under certain assumptions about preferences, no voting system exists which satisfies all of the following




11. Understanding Arrow's impossibility theorem Arrow's impossibility theorem states that under certain assumptions about preferences, no voting system exists which 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. ndependence of Irrelevant Noy the property of a desirable voting system it portrays. Independence of Irrelevant No Description Unanimity Transitivity Alternatives Dictators There is no person who always gets what he wants, despite O O O O everyone else's preferences If everyone prefers C to A, then C beats A. O O O If A beats C, and C beats B, then A beats B. O O O O The ranking between A and C does not depend on whether B is also O O O O available. Consider the following voting system: In the Borda count voting system, each voter ranks the possible outcomes, giving 1 point to the last-place outcome, 2 points to second to last, etc. The outcome that receives the most total points wins. Suppose when outcomes A, B, and C are available, outcome B is the winner according to a Borda count voting system. However, when outcome C is no longer possible, outcome A is the winner according to a Borda count voting system.Which property does this voting method violate according to Arrow's impossibility theorem? O No dictators O Unanimity O Transitivity Independence of irrelevant alternatives
Step by Step Solution
There are 3 Steps involved in it
Get step-by-step solutions from verified subject matter experts
