Not so. Third parties make policy happen. To get more votes, the major two parties have to start adopting third party policies. If they want less people to vote for third parties, they need to take on third parties' beloved policies. Here are a few examples of how this works:
Women's Right to Vote
Both the Prohibition and Socialist Parties promoted women's suffrage during the late 1800's. By 1916, both Republicans and Democrats supported it and by 1920, the 19th Amendment giving women the right to vote had been ratified.
Child Labor Laws
The Socialist Party first advocated laws establishing minimum ages and limiting hours of work for American children in 1904. The Keating-Owen Act established such laws in 1916.
Immigration Restrictions
The Immigration Act of 1924 came about as a result of support by the Populist Party starting as early as the early 1890's.
Reduction of Working Hours
You can thank the Populist and Socialist Parties for the 40-hour work week. Their support for reduced working hours during the 1890's led to the Fair Labor Standards Act of 1938.
Income Tax
In the 1890's, the Populist and Socialist Parties supported a "progressive" tax system that would base a person's tax liability on their amount of income. The idea led to ratification of the 16th Amendment in 1913.
Social Security
The Socialist Party also supported a fund to provide temporary compensation for the unemployed in the late 1920's. The idea led to the creation of laws establishing unemployment insurance and the Social Security Act of 1935.
"Tough on Crime"
In 1968, the American Independent Party and its presidential candidate George Wallace advocated "getting tough on crime." The Republican Party adopted the idea in its platform and the Omnibus Crime Control and Safe Streets Act of 1968 was the result. (George Wallace won 46 electoral votes in the 1968 election. This was the highest number of electoral votes collected by a third party candidate since Teddy Roosevelt, running for the Progressive Party in 1912, won 88 votes.)
