The Last Time Incumbent President Lost Without Third Party Hurting Him was Jimmy Carter in Reelection Defeat

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Bill Clinton beat George H. W. Bush in 1992 only because Ross Perot gained 20% of the vote as a third party candidate (most of them who would have voted for Bush), thus woeful Jimmy Carter in 1980 was the last incumbent president to have lost reelection in a one-on-one match-up.