Final answer:
The biggest example of the winner-take-all style in American elections is the Electoral College used in presidential elections, where a candidate wins all of a state's electoral votes by securing the plurality of votes, contributing to the prevalence of the two-party system.
Step-by-step explanation:
The biggest example of the winner-take-all style of American elections is the Electoral College system used in presidential elections. This system requires that all of a state's electoral votes go to the candidate who wins the plurality of the popular vote in that state, except in Maine and Nebraska which divide their electoral votes.
The winner-take-all system leads to a two-party system because voters often cast strategic votes for candidates they believe will win, rather than those who they prefer but may not be viewed as viable. Consequently, this discourages the formation and success of third-party candidates.
One of the clearest examples of this system at work was when Abraham Lincoln won the presidency in 1860 with only 40 percent of the popular vote due to a split among four different parties, securing a majority in the Electoral College.