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 firstplace votes in an election, then that choice should be the
winner of the election.
Condorcet Criterion
If there is a choice that in a headtohead 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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 Spring '08
 Karstens
 Math, Voting system, Kenneth Arrow, choice 4th choice

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