Arthur Winters
Arthur Coleman Winters was the President of the United States circa spring 2008. After "Harold Saxon" announced the existence of the Toclafane to the world, Winters served as designated United Nations ambassador to the Toclafane.
After Winters angered Saxon, who in actuality was the Master, Saxon ordered one of the Toclafane to kill Winters. His death signalled the start of the Toclafane occupation of Earth. (TV: The Sound of Drums)
The destruction of the paradox machine only rolled back time to a few moments after Winters' death, meaning that it still happened. (TV: Last of the Time Lords)
Personality
Pompous, arrogant, cynical and extremely narcissistic, President Winters saw himself as the rightful Earth representative. He was antagonistic towards the British and displayed what he saw as perfect patriotism, but was in fact textbook arrogance.
Behind the scenes
"President-Elect"
When meeting the Toclafane, Winters referred to himself as "President-Elect", suggesting that he had recently won an election but had not yet been sworn in. However, during The Sound of Drums, he was referred to as "President" numerous times and by different characters. Moreover, his plane was designated as Air Force One, which would not be true were he merely the President-elect.
Unless American law differs in the Whoniverse, it is impossible for an individual to be called the "President-elect" in the spring. The term applied to the winner of the US presidential election during the brief period from Election Day in November to Inauguration Day on the following 20 January — well before the events of The Sound of Drums. Additionally, a President-elect has no official standing or duties until formally taking office and becoming President, so Winters being on his mission at all would be extraordinarily unlikely were he still only President-elect.
This reference to the "President-elect" was almost certainly a production error that can be jointly laid at the feet of the script editor, the writer and the continuity supervisor, since it only occurs once in the script.
The later introduction of Barack Obama to the Whoniverse opens the question as to whether in the fictional universe of Doctor Who, Obama was elected president in a standard election, or if he was initially elected as the vice-presidential running mate of Winters and succeeded to the office upon Winter's death (as per American law).
