When someone gets enough votes then he/she becomes the new Senator.
Once in a while, you'll get a 'hint' message who is the current senator (if any).
The senator can be voted by people at the Voting station in La Trinité or the Town Hall next to Jail located south of Malden.
When you go to the Hydrant in front of the building you will get the action 'vote' in your action menu.
From the pulldown menu, you can select the person you want and press the 'vote' button.
When a senator is elected he/she gets an extra action called 'Change Taxes'.
This will open a menu where he/she can change taxes on vehicle, fuel and weapons prices in shops.
If the senator dies the taxes will go up and he/she will lose their place as senator.