The time period after the war of 1812 which saw only one political party was called the Era of Good Feelings.
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The Great Compromise solved the issue of representation by putting the ideas of large(Virginia) states and small( New Jersey) states together. This compromise started off by keeping a two house Congress which were the House of Representatives and the Senate. The House of Representatives came from the large states plan, and the Senate came from the small states plan. The first house represented the people, and it involved a number of representatives based on population of the state. The second house represented the states, and each of the states will have two senators that were elected by their legislature which constructed equal representation.
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