What impact do third parties and their candidates have on U. S. politics?

Negligible most of the time, or being able to flip a major party's success at best.

Explanation:

The United States is known to be using a mostly 2 party system ever since the nation was created. The current two major parties are the Republican Party and the Democratic Party, and currently are the only two that actually win presidential elections. At best, the the largest third party (Independents) have seats within Congress, but never have they actually have a representative elected as president.

However, note what I stated at the end of the answer. Third party representatives within the US government is essential to be won over especially when trying to pass controversial party-aligned bills that may not garner support from the opposition. In cases like these, the major parties would try to appease the third parties in order to flip the majority vote to their side. In this case, they play an important role in influencing the US politics, but in any other cases, they are merely representative at best.

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it increased the power of the king of england.

i believe the correct answer is b.