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The 1932 Kansas gubernatorial election was a three way battle: Incumbent Democrat Harry H. Woodring faced liberal Republican and state chairman Alf Landon, but also faced an independent candidacy by the disbarred "doctor" (and now well-known quack) John R. Brinkley. All three men polled above 30 percent, and Landon only won by 5,637 votes (.7%) over Woodring, with Brinkley not that far behind either of them:
Alf Landon (R) – 278,581 (34.82%) Harry Woodring (D) – 272,944 (34.12%) John Brinkley (I) – 244,607 (30.58%)
Now, regardless whether Woodring or Brinkley win, the main effect would be that Landon wouldn't be Governor, and wouldn't have the clout to win the 1936 Presidential nomination. The main questions I have are: Who would be the 1936 Republican nominee? What direction would the party take after their likely loss in it?
One the state level, assuming the quack doctor wins, what would a Brinkley administration look like? Having a disbarred quack running a state during the Great Depression would be interesting if nothing else.