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A pure democracy is a form of government where everyone has a vote. Each person of each state gets a vote, and they all vote for what they feel is best and then all the votes come together to make the decision. Madison felt it was not the best choice because of the factions that would or could form and would result in people voting on what the faction feels and not their individual selves opinions. One example of where a pure democracy could be the best type of government is when it is just a state vote on something since there are much fewer votes to count than an entire country's population. Another example when a pure democracy could be the best choice is when a company is trying to make a decision on something, so they hold a vote for what people feel is best, that way the decision will be made based off the most popular answer or choice.
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