What type of primary is held if no candidate receives a majority of the vote?

A run-off primary is held when no candidate achieves a majority of the votes in the initial primary election. This situation often arises in elections with multiple candidates competing for a single nomination. In a run-off, the top candidates, usually the top two, face off in a subsequent election to determine who will secure the party's nomination. This process ensures that the selected candidate is one who has garnered enough support to achieve a simple majority, which is essential for party unity heading into the general election.

Caucuses, closed primaries, and open primaries do not specifically address the scenario where no candidate receives a majority of the vote. Caucuses are gatherings where party members discuss and select candidates, while closed and open primaries refer to who can vote in those elections based on party affiliation. Thus, neither of those formats necessitates a run-off based solely on majority voting outcomes.