The election of 1800 influenced American democracy primarily in the following way:
It set a precedent for a peaceful transfer of power between two presidents of different political parties.
This election marked a critical moment in U.S. history as it demonstrated that power could change hands without violence or upheaval, reinforcing the democratic principle of electoral transitions and solidifying the legitimacy of the electoral process. The other options listed do not accurately reflect the significance of the 1800 election.