Another thought experiment: Imagine that via a Constitutional amendment, the US legislative branch was cloned. Two senates, two houses of representatives. Each initially inherits the full US legal code, but can freely add or repeal laws afterwards.
Initially, states are chosen randomly and their representatives and senators assigned to one Congress or the other. However, the states will be allowed to switch from one Congress to the other, presumably via their own legislatures passing a law to do so. This is just the right of free association correctly applied to the situation.
The national dept would be split between the two congresses, divided up per-capita.
The two US congresses don't have to work together to fund any specific government program; they are free to disagree about things. Joint funding is possible and likely for many things.
OK, that's the scenario. I have altered today's system in one fairly simple way. What consequences flow from that, and are they good?
Well, first off we can see that there will be an initial flurry of states changing their affiliation. Just by random chance, the two congresses will get slightly different average political centers. One will be slightly more Republican; the other, slightly more Democratic. As a result, the two will pass different laws. This makes the consequences of belonging to the two congresses different, which creates an incentive for states to change their affiliation if they think that they would be better served in the other congress. A very Democratic state, perhaps Massachusetts (with 10 Democratic representatives and zero Republicans), finding itself in the slightly more Republican congress would move to the slightly more Democratic congress. Note, though, that in so doing, not only does the Democratic congress become more Democratic, the Republican congress gets more Republican. So both congresses will now be able to pass or repeal a few more laws than previously, and both legal codes will shift farther away from the average opinion of Americans as a whole, towards the average opinion of their respective party.
This process will continue, until all of the states have moved to the congress which best reflects the average politics of their citizens. Each party will end up easily controlling one congress. The representation in each congress will end up something like 15-20% from one party, and 80-85% from the other. (If all states had a definite leaning but were split 50-50, you would expect the split in the dual congress to end up 25-75.) With clear majorities in each respective congress, we can expect one thing in the short term: substantial legal change. The Republican congress would probably lower taxes some more, implement some forced private savings in lieu of some of social security, perhaps dabble in national voucher programs for education. The Democratic congress might implement national health care, give away more federal money to hire teachers, repeal welfare reform, raise social security taxes, etc.
So that's the short term, that is, two years or less. What happens when elections come? Well, new parties arise, or the existing parties split. The two party system always adjusts towards the middle; what is odd in this experiment is that there are two distinct middles. So in the long run the system might end up with up to four parties; in each congress the two would be ideologically close to that congress' midpoint. Three parties, I think, would also be stable: a "big tent" centrist party contesting elections in both congresses, and then a leftist party and a rightist party that would mostly limit themselves to one or the other congress.
Another effect that would happen in the longer term: people would physically relocate in order to get into one or the other legal regime. For instance I would probably leave Maryland (almost certain to be in the left leaning congress), for somewhere safely in the lower-tax right-leaning Congress. Over time, many Americans would do similarly; this would tend to reinforce the ideological polarization of the two congresses.
What sort of laws would be produced? Well, as I have suggested above, initially the system would produce both better law and worse law than exists currently. The "Republic" (the congress with the Republican majority) would lower taxes. The "Democracy" would raise them. Both can't be better.
But over time, a good thing would happen: the congress with the less libertarian laws would be forced to scale back its laws. Why? Well, consider as an example welfare. The Republic tightens it even further. The Democracy repeals it to its pre-Clinton state, or even makes welfare more generous. Initially this would cause no problems. But in the longer run, as I have described above, it would. The welfare-receiving poor would clearly have an incentive to move from the Republic to the Democracy. So welfare reform would work in the Republic, in part because they can dump their problems on the Democracy. The Democracy, unable to keep out those seeking its handouts, would gradually be forced to scale back its plan to close to that offered by the more stingy Republic. In fact, it is possible that some whole states, tired of freeloaders and their problems, would defect from the Democracy to the Republic over this issue.
Voting with one's feet is a very powerful way to get liberty. With two Americas, it is a much more viable option than with just one.
Let's take another issue: school reform. The Republic would set up a national voucher system. The Democracy would continue with tax and spend, paying even more for salaries and bureaucrats, but doing nothing for kids or the job quality of the teacher/guards. Over time, because the vouchers create competition, the Republic system would clearly beat the system in the Democracy. It would be cheaper, there would be fewer administrators, and kids would actually learn. The Democracy would eventually be forced by citizen pressure to adapt, as their system continued to fail.
The previous example shows another mechanism for libertarian change that doesn't happen in our current monopoly system: experimentation and copying of success. With only one system, there can be little experimentation, and there is therefore no way to learn new things to be copied. With two systems, a comparison can be made. Of course, it is possible, now, to experiment in small ways or small locales, with exceptional populations. But results from these sorts of experiments take a long time to amount to much, and even then are inherently difficult to apply to the political whole. (Consider the debate over the Cleveland program as an example.)
What about for stuff that the two congresses have to agree on? Consider national defense. Presumably the two congresses will cooperate on this one, each throwing in more or less half of the defense budget. Why half? Because otherwise people in the side throwing in more would feel cheated. Now consider the budget from the point of view of the two congresses. The Republic wants a big military, let's say $300b/year. The Democracy, a small one, say $100b/year. What happens? Well the Democracy has a trump card: they simply pass their budget allocating $50b this year to the military, then invite the Republic to do whatever it wants. A more libertarian budget gets passed. (At this point, I hope you are working out for yourself why Republic can't preempty the Democracy and pass its budget for $150b.)
Generally, in things that the two congresses do jointly, the one wishing to spend less always has the ability to pull the spending its way. Given that all government spending originates as taxes of some form, this is libertarian.
Seen generally, competition in the provision of law almost always moves the law in a libertarian direction. It is not immediately obvious why this is, but it is definitely the case; we have now examined three mechanisms for it: voting with the feet, experimentation, and the "race to the bottom". Of course, with only two law-providers, and the aggregation of the customers by state, the system is pretty crude. There will be a lot of Republicans ending up in Democratic states with nothing they can do about it. Choice here is increased over the real-world, but it's only increased somewhat.
So, now imagine there are 10 congresses, all with their own law. Or 100. And imagine that rather than aggregating by state, each individual American could choose the congress whose laws he or she wants to live under.