I would place very heavy odds that Carter voted for LBJ in '64 and I really doubt he voted for Nixon in '72; he opposed McGovern at the convention, but also
lobbied for the veep slot after McGovern was chosen. It's likely his "stop McGovern" efforts was a show for conservative voters back home, and I suspect the same of his claim to have supported Wallace in '68 (elsewhere, he intimated he had backed RFK for the Dem. nomination). Speaking of RFK, I seem to recall reading somewhere that he had voted for Eisenhower over Stevenson in either '52 or '56; it wouldn't completely surprise me if his older brother or LBJ did as well.