Read this: From 1952 to 1964, most voters were registered Democrats, but the state voted for the Republican presidential candidate in every election except for 1964. The following year, Congress passed and President Lyndon B. Johnson signed the Voting Rights Act of 1965, providing for oversight of state practices and enforcement of constitutional voting rights for African Americans and other minorities in order to prevent the discrimination and disenfranchisement that had excluded most of them for decades from the political process.

Voter demographics of florida in the 1950's 
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1952 to 1964, most voters were registered Democrats, but the state voted for the Republican presidential candidate in every election except for 1964