Final answer:
The dominant party between 1788 and 1800 was the Federalist Party, though they only won one of the three elections during that time, with the Democratic-Republicans winning the critical election of 1800.
Step-by-step explanation:
Between 1788 and 1800, the dominant party in the United States was the Federalist Party.
However, they won just one of the three presidential elections held during that period. The Federalists won the election of 1796 when John Adams was elected president.
Yet, the subsequent election of 1800 marked a pivotal point in U.S. political history. Thomas Jefferson, representing the Democratic-Republicans, won against the Federalist incumbent, John Adams.
This election, determined by the House of Representatives because of an electoral vote tie, highlighted the growing strength of the Democratic-Republican Party and paved the way for its dominance in the early 19th century.
The 1800 election, often referred to as the Revolution of 1800, represented a peaceful transfer of power from one party to the other, an event that reinforced the stability and resilience of the young nation's political system.
This marked a shift away from Federalist policies towards the Democratic-Republican vision, emphasizing a smaller federal government and an agrarian republic, as evidenced by the Louisiana Purchase under Jefferson's administration.