How might the presence of two dominant political parties have eliminated some of the confusion in the election of 1824?

declicans and replicans

The democratic party and the national republican party

In a two-party system such as that in the United States, this is referred to as a "third party".

The two new parties that formed after the election are The wig partie (repulicans) and the freadom choads (democrats)

republicans and democrates