It does not prevent favoritism. The Supervisor/Manager can say hey, I like you, so I'm not going to write you up. They can also say hey, I don't like you, so I'm going to nit pick you and find stupid stuff to write you up for that no one else gets written up for.
What you need to do is make your own record of instances where management demonstrates a double standard. Where I work, any verbal/written reprimands require two officers present to meet with the employee in private. The Battalion Chief also needs to approve the reprimand. So, that's three people that the write up needs to go through. If you feel that you're being singled out, you can always go to the Deputy Chief. The union will represent you from the start. Represent you, not make the charge go away. If you did wrong, you'll get the write up. The union is there to make sure that you're not being singled out, that you're treated the same as anyone else regarding SOP's.