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Sometimes things are not what they seem. In 1912, Teddy Roosevelt ran as a third party candidate, expecting to draw off both dissatisfied Republicans and progressive Democrats. Instead, the Democrats mainly stayed with their candidate, Woodrow Wilson, while Republicans split their vote. Wilson won.
This year, if the Republicans nominate a grotesque gargoil, as seems likely, Bloomberg would give their voters a place to flee. If Democrats mainly stick with their candidate, he or she would win as Wilson did, and as an extra treat, it could badly damage the Republican brand.