Voter fraud has not decided one single election. This is a red herring.
In 1948, Johnson again ran for the Senate and won. This election was highly controversial: a three-way Democratic Party primary saw Johnson facing a well-known former governor, Coke Stevenson, and a third candidate. Johnson drew crowds to fairgrounds with his rented helicopter dubbed "The Flying Windmill". He raised money to flood the state with campaign circulars, and won over conservatives by voting for the Taft-Hartley act curbing unions and by criticizing unions on the stump. Stevenson came in first, but lacked a majority, so a runoff was held. Johnson campaigned even harder, while Stevenson's efforts were poor. The runoff count took a week as the two candidates see-sawed for the lead. The Democratic State Central Committee handled the count (not the state, because it was a party primary), and it finally announced Johnson won by eighty-seven votes. The committee voted 29-28 to certify Johnson's nomination, with the last vote cast on Johnson's behalf by the Temple publisher Frank W. Mayborn, who rushed back to Texas from a business trip in Nashville, Tennessee. There were many allegations of fraud on both sides. Thus one writer alleges that Johnson's campaign manager, John B. Connally, was connected with 202 ballots in Precinct 13 in Jim Wells County that had curiously been cast in alphabetical order and all just at the close of polling. Robert Caro argued in his 1989 book that Johnson had rigged the election in Jim Wells County, and other counties in South Texas, as well as rigging 10,000 ballots in Bexar County alone.[16]
The state Democratic convention upheld Johnson. Stevenson went to court, but ? with timely help from his friend Abe Fortas ? Johnson prevailed. Johnson was elected senator in November, and went to Washington, D.C. tagged with the ironic label "Landslide Lyndon," which he often used deprecatingly to refer to himself.
http://en.wikipedia.org/wiki/Lyndon_B._Johnson#1948_contested_electionand then there is this:
Nixon advisors believed that Kennedy benefited from vote fraud, especially in Texas and Illinois, and that Nixon actually won the national popular vote despite the fact that Republicans tried and failed to overturn the results in both these states at the time--as well as in nine other states. These two states are important because if Nixon had carried both, he would have won the election in the electoral college.
Kennedy won Illinois by less than 9,000 votes out of 4.75 million cast, even though Nixon carried 92 of the state's 101 counties. Kennedy's victory in Illinois came from the city of Chicago, where Mayor Richard J. Daley held back much of Chicago's vote until the late morning hours of November 9. The efforts of Daley and the powerful Chicago Democratic organization gave Kennedy an extraordinary Cook County victory margin of 450,000 votes --- more than 10% of Chicago's 1960 population of 3.55 million[12] -- thus (barely) overcoming the heavy Republican vote in the rest of Illinois. Earl Mazo, a reporter for the pro-Nixon New York Herald Tribune, investigated the voting in Chicago and claimed to have discovered sufficient evidence of vote fraud to prove that the state was stolen for Kennedy.
http://en.wikipedia.org/wiki/U.S._presidential_election,_1960#Controversies