Depends how close to policy-making you want to get, but Papers, Please seems pretty excellent. Certainly well-received. You play the border guard of immigration control of a fictional state that's very picky about who gets to pass by its fortified wall and who doesn't. You gotta look out for forged documents, but also talk to a lot of people in order to keep getting paid - do you slip up or try to let someone through unauthorized?
Otherwise I think (real-time) strategy might be your best bet perhaps? Tropico has you running a "banana republic" island and negotiating with various political groups to stay in power. There's also the Civilization series which is turn-based, but those are hella deep & daunting games that make you lead an empire through hundreds of years.