What if there was a boxing ring added?
Located in the college district, the boxing ring requires an entry fee of $250, which is refunded upon winning a match. You send a liberal there on Fridays only, and he wins or loses a fight based on heart, injuries, strength, agility, and martial arts. If you win a fight, you choose in between making a little speech about an issue, or receiving a cash prize. The amount of money or political sway you get depends on how powerful the opponent was. If you go on a day that isn't Friday, you can pay $20 to train various boxing related skills and find out how hard the next fight will be. Win or lose, you'll probably come home from a match with some bruises.
At C+ gun laws, the boxing ring turns in to a dueling ring, where gunslingers try to shoot their opponent before they get shot, as determined by chance and pistol skill. Only fools would get themselves killed like that, so you may only enter a duel if you have wisdom below 5.
At L+ gun laws where boxing gloves are illegal, the boxing ring becomes a forum. You enter contests in the same manner, only you debate politics instead of boxing. Science, intelligence, and all those types of skills and stats affect your chance of winning. If you lose a debate, public opinion on that subject shifts conservative. if you win the debate, the public opinion becomes more liberal and you receive a prize based on the int of your opponent.
Think this idea could work?