The correct answer is A) spoiled the election for one of the two major parties.
One role that third parties have played within the American political party system is "spoiled the election for one of the two major parties."
The United States has a bipartition political system dominated by the Republican Party and the Democratic Party. When a third political party has been part of one election, it gives the US citizens another option to choose from. Third parties had played an important role in breaking up the dominance of these two major parties. They draw votes away from Republicans and Democrats, helping people to have a new perspective of the US affairs and conditions.
The other options of the question were A) overthrown the government and instituted a new regime. C) prevented new major parties from adopting the ideas of their supporters. D) campaigned and won for two presidential elections in the 20th century.