Palpatine wants to become the Chancellor. But as we see in the movie, he is a cunning politician. He is also in control of both sides in the war between the Republic and the Separatists. His goal is to rule the galaxy. Now, did he cheat during the elections to become the Chancellor in order to gain power?
Palpatine, or Sheev as he is affectionately known, mostly blackmailed and used his powers as a Sith to 'motivate' other Senators into voting for him, after Chancellor Valorum's removal. What is also worth noting, is that during Episode 2-3, following Padme's frequent excursions away from the Senate, his increased pressure on Binks, resulting in emergency powers being given to him. It is not hard to imagine him pressuring key members of the Senate in this way.
So to conclude, yes, Palpatine did cheat, using blackmail and other forms of persuasion in order to gain power.