BoingBoing.net posted a variation of Rock, Paper, Scissors (what I call the legislative Executive Session), one called Monkey-Pirate-Robot-Ninja-Zombie: Rock Paper Scissors 9.0
You will have to click the link to read what to yell when a given role wins, the diagram below shows who has the advantage.
In Washington State politics we have a top two primary. The major political parties have games the system, and carved up legislative districts to their advantage. The problem now is that political parties are struggling with making endorsements that lead to unified support for one person. Gone are the days where the tax payer was on the hook to fund this decision making through the partisan primary system.
At some point soon the local legislative districts will have to make a more meaningful effort to make decisions early enough to gain some benefit from political party support.
I suggest they try "How to Play Monkey-Pirate-Robot-Ninja-Zombie", and act on the results long before the primary.
My guess is that there would be plenty of infighting to decide who gets to be which character