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

Answer 1

Political scientists often use the term "minor party" to describe parties other than the dominant two, since there are dozens of small parties at any given time. Third parties in the USA have, at best, been 'spoilers' Their influence is at most to shed light on a specialized problem or issue. This in turn can and has made the two primary political parties more responsive. Few examples exist of third parties becoming a major party with any clout or permanance. Most third parties have been focused on a single issue, and can sometimes put that issue in the national spotlight. The Know-Nothing/American Party was anti-immigrant and anti-Catholic, the Free-Soil Party was abolitionist, and the Dixiecrat Party was pro-segregation.

The only third party which gained prominence at the national level was the Republican Party in the 1850s; The Whig Party was falling apart at the time, while the Democratic Party was weakened by sectionalism (the Democrats ran two Presdential candidates in 1860, a Northern and a Southern one). The weakness of the major parties allowed the Republican Party to sweep into power in 1860, at which point the Whigs all but disappeared, and the Republicans became a major party. Most other minor parties have not had success at the national level; the Know-Nothings of the 1850s were highly successful in state elections in New York and New England, but could not break through to the national level, and disappeared almost as quickly as they came, when the Republican Party rook over many of their positions (and voters).

There are a few factors limiting the influence of minor parties in the US:
The federal election system: Because of the US election system, which awards office to the first place winner in most elections (even if they don't have a majority(, minor parties stand little chance of winning. In contrast, many Parliamentary democracies have proportional voting systems, where a party passing a certain threshold (often 5% of the vote) will receive a percentage of seats equal to their percentage of the vote. Additionally, many parliamentary systems use some form of runoff voting, where if one candidate or party does not get a majority, a second round of voting begins between the top two or three finishers. In runoff elections, a minor party candidate can perform better, as some voters' first choice may have been eliminated, and voters switch to their second choice. The single-round voting in the US means that elections are almost always between a Democrat and a Republican.
The "Big Tent" parties: Both the Democratic and Republican Parties are broad coalitions, at least compared to parties in some other countries. The parties have a wide appeal, and even house factions which are opposed to each other; the Democratic Party holds both environmentalists and mining or logging unions, while the Republican Party has both libertarians and social conservatives. These broad coalitions mean that national parties are often more like groups of more specialized parties, and the primaries can be seen as the equivalent to a first round of a runoff election.
Narrow focus of minor parties: As mentioned above, minor parties tend to be focused on a single issue, while the major parties have a platform that deals with a wide range of issues. On a similar note, minor parties tend to be more ideologically extreme (farther to the left or the right) than the major parties, which are successful when they can appeal to moderate and swing voters.
Strategic voting: All of these factors add up to an environment where it is very hard for a minor party to win. Public opinion polling tends to show minor parties doing better than their eventually share of the vote on Election Day. This is probably because some voters like the ideas of a minor party candidate, but they do not want to feel like they have wasted their vote, so they end up pulling the lever for a major-party candidate. This becomes something of a self-fulfilling prophecy in some cases.
The "spoiler" effect: minor parties can attract the anger of members of the major party if they are perceived as costing the party an election. Democrats often blame Al Gore's loss in Florida in 2000 on the Green Party, which drew liberal votes away from the Democratic ticket, while Republicans blamed the Dixiecrat Party for Harry Truman's surprise win in 1948.

Answer 2

Third parties split the vote, which can change the outcome of an election.