Through leadership skills, military prowess, personal charisma, or other means. In their latest 10,000 Reader Poll, Charapedia asked fans which anime/manga character would make the ideal Prime Minister. 67 choices were suggested by a pool of respondents that was 54.3% female and 62.1% in their teens and 20s.
Source: http://www.charapedia.jp/research/0172/
20. Dragon Ball's Freeza - 102 votes
19. Haruhi Suzumiya - 106 votes
18. Death Note's Light Yagami - 120 votes
17. Arslan of The Heroic Legend fame - 127 votes
16. Psycho-Pass' Akane Tsunemori - 137 votes
15. One Piece's Monkey D. Luffy - 163 votes
14. Kuroko's Basketball's Seijūrō Akashi - 169 votes
13. Hozuki of Coldness fame - 184 votes
12. Doki Doki Precure's Mana Aida - 197 votes
11. My Hero Academia's All Might - 218 votes
10. Doraemon's Hidetoshi Dekisugi - 240 votes
9. Naruto - 310 votes
8. Assassination Classroom's Koro-sensei - 364 votes
7. Gintama's Gintoki Sakata - 395 votes
6. Kochikame's Kankichi Ryotsu - 479 votes
5. Case Closed's Shinichi Kudo - 523 votes
4. Prince of Tennis' Keigo Atobe - 569 votes
3. Division Chief Kosaku Shima - 614 votes
2. The Irregular at Magic High School's Tatsuya Shiba - 768 votes
1. Code Geass' Lelouch Lamperouge - 801 votes
Yes that's right even Freeza made the list.
(But deskpro2k3, what is a Prime Minister? Answer: A Prime Minister is the head of an elected government; the principal minister of a sovereign or state.)