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Math 171

# Math 171 - Math 17 Arrow's Impossibility Theorem So what is...

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Math 17 Arrow’s Impossibility Theorem So what is the problem? Why are there so many methods? Is one method better than another? In the late 1940s, Kenneth Arrow discovered this idea: In an election involving three or more candidates, there is no consistently fair democratic method for choosing the winner. He called this idea Arrow’s Impossibility Theorem . In 1972 Kenneth Arrow was awarded the Nobel Prize in Economics for his work. Arrow’s Impossibility Theorem All voting methods violate at least one of the four fairness criteria. Majority Criterion If a choice receives a majority of first-place votes in an election, then that choice should be the winner of the election. Condorcet Criterion If there is a choice that in a head-to-head comparison is preferred by the voters over each of the other choices, then that choice should be the winner of the election. Monotonicity Criterion If choice X is a winner of an election and, in a reelection, the only changes in the ballots are changes that only favor X, then X should remain a winner of the election.

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