Edwin Edwards defeated Duke 61-39 in 1991. While Edwards was white, he was also known to be corrupt even then and would have easily lost to a non-Klansman opponent. Also, presumably LA was more racist 23 years ago. So Obama.
It matters how this scenario came to pass, though (and is it for the Presidency? It wasn't specified). How did David Duke become the Republican nominee? Either he's managed to completely redeem himself (did he singlehandedly save the world or something?) or it was some kind of nefarious trick. In the former scenario, he wins LA because he's done something big to overcome his obvious issues. In the latter, there's a good chance that he ends up being a de facto third party nominee with the "true" Republican candidate being a third party or write-in candidate, in which case he comes third.
Why would David Duke need to redeem himself to win a Republican primary? Most Republican primary voters are mini David Dukes.
Considering David Duke ran for the Republican nomination for President in 1992 and got a grand total of 0.94% of the vote (and no delegates), and the country has gotten significantly less racist since then, that seems pretty suspect.
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