Election
The Lord President of the High Council of Gallifrey might be chosen by election. (AUDIO: Mindbomb, etc.)
Jack Robertson planned to run in a American presidential election in 2020. (TV: Arachnids in the UK)
There were also other types of elections like a general election that Great Britain's parliament system used. Harriet Jones won a general election in a landslide majority to secure herself and her party a term in government. (TV: The Christmas Invasion) Later, the Saxon Master (posing as "Harold Saxon") won a general election. (TV: The Sound of Drums)
The Daleks held elections every Skaro year to appoint the Dalek Emperor and the Black Dalek as their rulers. However, the Daleks had little choice in the matter. When in one re-election, the Red Extra-Galactic Squadron spoke out and demanded a more effective leader, the Emperor had the Black Dalek obliterate them. (COMIC: The Secret of the Emperor)