) T. Roosevelt
It was by pure charisma that he could emerge second--as a 3rd party nominee--in the 1912 election.
2) JFK
His charisma was such, that the entire country, more or less, mourned his death. His charisma outshined his Catholicism in a time, when there was some fear among voters that he would be taking order from the Pope. It was his charisma that made him wins his party's primary election despite th fact that he was still young and inexperienced.
3) Reagan
His optimism and TV persona pulled even Democrats into a more optimistic view of America. None of the Republican's today, who claim to be following Reagan, emulate this optimism, or even Reagan's eagerness to compromise with the other party to get things done. He was able to be above his scandals, as well, through this personality.
4) Andrew Jackson
He is harder to estimate, since he lived in a time before radio, TV, internet, etc. Yet, Jackson's populism and charisma carried him to victory despite the piles and piles of criticism, controversy and insults. In a way, he was the first Donald Trump, except with some experience. Despite his personal wealth, he was able to be a surrogate for the common man, and the common struggles against the elites. As an embodies will of the people, he was virtually unstoppable. Any Democrat wishing to get ahead, had to be Jacksonian. Had Jackson lived 100 years later, he might even be higher on this list. I admit his charisma, but I personally think he was a terrible president
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5) Bill Clinton
He was able to defeat a rather popular president, after emerging from sex scandals and having blown his key note speech in 1988. Despite mounting criticism and controversy, Clinton's personality, and perhaps competency, has somehow made him forgivable
6) Barack Obama (especially 2008-2009 Obama)
One would have to have charisma to defeat Hillary Clinton in the primaries, and John McCain in the general election as an African-American with the name Barack Hussein Obama during the War on Terror. I'd argue his charisma went from a "5" for 2008 to a "4" for 2012, mostly through disappointment, since expectations were so high. He is placed 6th, because he couldn't maintain the high charisma, I think. I think it could return in his post-presidency as a surrogate, however
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7) FDR (especially 1932, 1936, and 1940)
FDR was helped a lot by the Great Depression and WWII. He was able to project the optimism of being America in a much more trying time than Reagan; although, arguably not any more dangerous, being that Reagan operated in a nuclear age. The fire-side chats were turned on in about every household that had a radio. I have him ranking 7th, primarily because it's hard to estimate his true charisma. He faced no real threat in any of his primaries, or in the general election. Hoover had not a chance, and the challengers to FDR were regional figures. The GOP was too disorganized to field a legitimate candidate until 1944. FDR's amazing competency and political skill carried him more than his personal magnetism as great as it was. I can see the argument of placing him at #5. He could be the most charismatic, but his competition for his office was too weak to accurately judge the personal magnetism--Herbert Hoover, Alf Landon, Wendell Wilkie, Thomas Dewey, while competent, smart men, had the charisma of a Romney or HClinton at best.
8) Donald Trump
I admit, it was personal charisma that would have allowed Trump to win, despite his well-known notorious behavior during the campaign--both primary and general. There is not a single politician that could have pulled this off in 2016. Whereas Clinton could use the word "deplorable," and have it weigh her down throughout the general. Trump could say anything, and it would rub off in a week or less. He does not rank as high as the others, since a large minority probably believes he is the total opposite of charisma, since his language, looks, etc., repel rather than attract. In my book, as much as I dislike him, he's a 4 in charisma. But to me, he could have been a 2, if the election had not gone his way. One could argue that a lack of charisma is the reason why Clinton (mostly universally uncharismatic) is likely to defeat Trump by 3 million votes. For this reason, Trump is 8th. Could Trump have beaten Cory Booker or another young, charismatic, energetic Democrat?