On the main screen, there's options to vote for the Senate and the World Council, which the game says will globally affect players. However, it doesn't specify how often you get to vote for a new initiative or president.
The descriptions are vague, saying that "frequent" votes take place for the Senate, and new presidents are appointed on a "regular" basis.
For example, this is the current Senate vote.
As you can see, some of the bonuses are quite good, but I'm wondering how long these bonuses will last before new ones are cycled in.