A game mechanic

More specifically, a mechanic for capturing collective action problems.

You need at least three people to play, but ideally five. Odd numbers are best, no ties. That said, tie-breaking can be done with a coin or dice.

You have three teams. Everyone who is playing is assigned to one of the teams at random. If there’s no one on one of the teams, the least populous team donates one member. Everyone rolls a die and triples the result. This is taken as their initial score. Then, they vote. The vote can be to give one of the teams two points, or to give all teams one point, or to take one point from a team. After the vote the dice is rolled. 1-3 means one of the teams loses a point, 3-6 means one of the teams gains a point.

The first player to break fifty points wins, but if any player is under twenty-five points when the game finishes, everyone loses.

Obviously there are elaborations to be made to make this a palatable mechanic, and it might be possible to make the idea simpler, but I just wanted to benchmark where my thinking was at this point.