Two ways that the representative democracy of the Roman Republic is similar to American democracy are:
The Roman Republic had a legislative which comprised of the Senate and an Assembly and they also had an executive branch that was headed by consuls. This is similar to the United States which has Congress and the executive which is headed by the President.
Congress in the United States is bicameral which means it comprises of two houses which are the House of Representatives and the Senate. This was the same as the Roman Republic which had an Assembly of Representatives and a Senate.
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