I wonder if there is some way we could use auction theory to reach a compromise for the debt ceiling -- or political decision-making in general. To motivate this, consider the following examples, where one might use auctions for making decisions
Examples of making choices with auctions
1. My roommate and I want to figure out who gets which room in our new apartment. On sealed bids, I say I'm willing to pay X1 and X2 for the rooms, respectively; and my roommate says he'll pay Y1 and Y2 for the rooms, respectively (the sealed-bids part is important, since it means we assign our true values to the rooms). It's then clear who gets which room -- but he gets the room for the roommate's bid on that room. Each person is happy because he got the room for less than he bid. As described so far, we're also incentivised to bid our true values (Technically, we'd probably need to adjust the room prices to make sure they sum to the total rent, which may remove the true value bit, but bear with me).
2. Four of us want to choose between three different movies. We each place some value on watching each of these movies and write our bids down on a piece of paper (secretly at first). Once these bids are made public, we choose the movie which maximizes overall utility using the VCG auction. In particular, the auction also stipulates that we redistribute total revenue from the auction in such a way that it maximizes overall utility. So if I end up having to watch a movie I really don't want to see, I get paid for watching it, so it's not so bad after all. Jonny, who got to see the movie he wanted, paid a bit more for it, but he's still happy with the outcome, since he paid less than he was willing to pay.
The benefit of the two auctions is that we're all incentivized to place our true values on these items. Further, the auction maximizes social utility.
A debt-ceiling compromise
Using this sort of an idea, a compromise might look like this: all possible spending cuts -- and even crazy amendments and such -- would receive secret "bids" by Democratic and Republican leadership. Cuts could be valued as either negative or positive. The appropriate algorithm would then proceed by selecting cuts with the most-socially-useful outcome until the $2T or $4T mark is met. Each time an outcome is selected, the parties would need to pay the VCG price.
For example, suppose policymakers are considering cutting Medicare by $1T and (independently) cutting defense by $2T. Republicans might place a party value of $2M and $-0.5M on these two, respectively. Democrats place values of $-3M and $.6M on these. The likely outcome of this case is that Medicare is not cut, and Democrats need to pay Republicans millions of dollars; and defense is cut, and Democrats pay millions of dollars to Republicans. This example might sound skewed, since Democrats paid out millions of dollars both times, but remember, these were their true values of these outcomes. If Republicans were to try to game the system by bidding a lot more so they get more payment from Democrats, they might end up winning the auction, in which case they need to pay a lot to the Democrats.
Arguments against auctions and why they're still mostly OK
This was a really simple example, and it ignores things like outcome interactions and rule by wealth. In the former problem, baskets of outcomes might have different values than the sum of their parts; combinatorial auctions with VCG mechanisms (on which there's plenty of literature) can address this. The latter problem -- where a wealthy party can achieve its ends no matter what -- isn't such a big deal in theory, because everyone is still incentivized to bid his true value, and the poor will end up getting paid quite a bit of money from their point of view -- enough to offset the damages they see. Again, if Republicans were bidding crazy amounts for their outcomes, they'd end up paying dearly for this, right into Democrats' pocketbooks.
Yet what is to prevent one party from introducing legislation which is awful for the other party and always bidding $1 for it and $0 against, just to earn money or win these votes? One solution is to penalize legislators post-facto with the hit to public utility from the status-quo position. This utility could be inferred from the VCG auction bids. Since the auction should maximize utility, overall utility is still increased.
Per-person or per-legislator auction credits
Finally, it's worth considering having individuals in society bid for these outcomes or even assigning "bid points" for legislators to use, where each legislator gets so 100 bid points per Congressional session and can only use bid points he has to bid on outcomes. This may end up giving bizarre behavior on legislation toward the end, but it's worth considering.
