The US Congress is trying to resolve the national debt by getting hundreds of people to agree on a solution.  This is silly.  They should agree on the rules of a game to play that will result in a solution, and then play the game.

Here is an example game.  Suppose there are N representatives, all with an equal vote.  They need to reduce the budget by $D.

1. Order the representatives numerically, in some manner that interleaves Republicans and Democrats.
2. "1 full turn" will mean that representatives make one move in order 1..N, and then one move in order N..1.
3. Take at least two full turns to make a list of budget choices.  On each move, a representative will write down one budget item - an expense that may be cut, or something that may become a revenue source.  They may write down something that is a subset or superset of an existing item - for instance, one person might write, "Air Force budget", and another might write, "Reduce maintenance inspections of hanger J11 at Wright air force base from weekly to monthly".  They can get as specific as they want to.
4. If there are not $2D of options on the table, repeat.
5. Each representative is given 10 "cut" votes, worth D/(5N) each; and 5 "defend" votes, also worth D/(5N) each.  A "defend" vote cancels out a "cut" vote.
6. Each representative secretly assigns their "cut" and "defend" votes to the choices on the table.
7. Results are revealed and tallied up, and a budget will be drawn up accordingly.

What game-theoretic problems does this game have?  Can you think of a better game?  Is it politically better to call it a "decision process" than a game?

The main trouble area, to my mind, is order of play.  First I said that budget items would be listed by taking turns.  The 1..N, N..1 order is supposed to make neither first nor last position preferable.  But taking turns introduces complications, of not wanting to reveal your intentions early.

Then I said votes are placed secretly and revealed all at once.  This solves problems about game-theoretically trying to conceal information or bluff your opponent.  It introduces other problems, such as tragedy-of-the-commons scenarios, where every Republican spends their "defend" votes on some pork in their state instead of on preventing tax cuts, because they assume some other Republican will do that.

Is it better to play "cut" votes first, reveal them, and then play "defend" votes?

Is there a meta-game to use to build such games?