The electoral system broke down in the election of 1800 because of the

Answer: lack of distinction between President ballots and Vice-President ballots.

Explanation:

Before the 12th amendment, the electoral system granted the position of vice president to the second most voted candidate, though no distinction was made in case two candidates got the same amount of votes. With the 12th amendment, candidates now ran either for President or Vice President, ensuring that no one candidate was elegible for multiple positions.