Jackson introduced policies about universal male suffrage which increased the number of voters. Before those policies, only those who belonged to certain religions or those who were property owners were allowed to vote. After those policies, all men of age were allowed to vote regardless of their religion or their ownership status.
In the elections of 1800, Thomas Jefferson was elected by the House of Representatives over Aaron Burr.
In 1800 the presidential elections were held, these being the fourth presidential elections of the United States. In this election, John Adams (Federalist Party) and Thomas Jefferson (Democratic-Republican Party) faced each other.
The result of this election was Jefferson's victory over Adams. However, in the election, the Electoral College in charge of electing the president and vice president resulted in a voting tie between Jefferson and Aaron Burr for which the House of Representatives had to choose and the result of this election was Thomas Jefferson.
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When Jeffersonian Americans sought "cultural independence" they meant that they wanted the freedom and "space" to live life the way they wished, without having to conform to the norms and customs of immigrant and other groups.