The 1839 Michigan gubernatorial election was held from November 4, 1839, to November 5, 1839. Whig nominee William Woodbridge defeated Democratic nominee Elon Farnsworth with 51.56% of the vote.
This was the most recent election in which neither a Republican or Democrat won.
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Text from the Wikipedia article “1839 Michigan gubernatorial election”, available under CC BY-SA 4.0.