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Although elections form the backbone of democratic governments around the world, there is no consensus (academic or otherwise) on the best way to combine votes into a collective decision. First we define and analyze three of the most popular voting methods: plurality voting, instant-runoff voting, and the Borda count. After observing some non-intuitive behavior from these methods, we state the Gibbard-Satterthwaite theorem, which shows that a broad class of voting methods can be manipulated by voters. We then examine some more methods in light of this theorem: random ballot, approval voting, and range voting.

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