Two-party system
A two-party system is a party system where two major political parties dominate the government. One of the two parties typically holds a majority in the legislature and is usually referred to as the "majority" or "governing party" while the other is the "minority" or "opposition party". Around the world, the term has different senses. For example, in the United States, Jamaica, and Malta, the sense of "two-party system" describes an arrangement in which all or nearly all elected officials belong to one of the only two major parties, and third parties rarely win any seats in the legislature. In such arrangements, two-party systems are thought to result from various factors like winner-takes-all election rules. In such systems, while chances for third-party candidates winning election to major national office are remote, it is possible for groups within the larger parties, or in opposition to one or both of them, to exert influence on the two major parties. In contrast, in the United Kingdom and Australia and in other parliamentary systems and elsewhere, the term "two-party system" is sometimes used to indicate an arrangement in which two major parties dominate elections but in which there are viable third parties which do win seats in the legislature, and in which the two major parties exert proportionately greater influence than their percentage of votes would suggest.
United States presidential primary
There is no provision for the role of political parties in the United States Constitution, since the Founding Fathers did not originally intend for American politics to be partisan. In Federalist Papers No. 9 and No. 10, Alexander Hamilton and James Madison, respectively, wrote specifically about the dangers of domestic political factions. Thus in the first two presidential elections, the Electoral College handled the nominations and elections in 1789 and 1792 that selected George Washington. The beginnings of the American two-party system then emerged from Washington's immediate circle of advisors. Hamilton and Madison, who wrote the aforementioned Federalist Papers against political factions, ended up being the core leaders in this partisanship: Hamilton became the leader of Federalist Party while Madison co-helmed the Democratic-Republican Party with Thomas Jefferson.