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



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 No Description Unanimity Transitivity Alternatives Dictators The ranking between C and A does not depend on whether B is also O O O O available. There is no person who always gets what he wants, despite O O O O everyone else's preferences If everyone prefers B to A, then B beats A. O O O O If A beats C, and C beats B, then A beats B. O O O OConsider 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 Unanimity Independence of irrelevant alternatives Transitivity O No dictators
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