Minor political parties have most often contributed to us politics by

They do this by providing more candidates from which a voter can choose.

Explanation:

There are several minor political parties in the United States. The main two that is heard about more often is the Democrats and Republicans. Other parties are Libertarian and Independent. There is also an option for voters to write in a candidate on any ballot in an official election.  

By having numerous choices in an election, this balances out the main group and lets the voters have discussions about issues that are concerning to them. Many of the third party choices do support the wealthiest candidate if they drop out of the race.