So in a recent edition of Improvised Radio Theatre with Dice, Roger and Michael suggested the need for a Random Political Shenanigans Table (roughly 36:00). I was intrigued by this idea, and I think you could actually probably do it.
There's probably two very broad categories of approaches to something like this.
Focused approach
In the first approach, you have a table of specific shenanigans that occur. I think for this one to work, you need to have things quite well pinned-down. That's to say, I think you could probably do something like this for Ankh-Morpork, or for The Eight Queendoms, or for the governments of the various Outer Stars, where you have a very specific setting and tone in mind.
You'd probably also need either a broad-minded approach to the events that happen, or quite a lot of interpretation to make them better fit the context.
Prodecural politics
The second approach, and the one I'm going to actually dabble in, is something more like (to borrow from Shamus Young) procedurally-generated politics. That is to say, rather than a table of specific events to roll on, this would be a set of rules for generating events.
The thing here is that you'd be tracking various variables of the situation, and then deriving shenanigans based on those variables.