No, it doesn't seem to me like the right track.
To me, it sounds like a proposal to base medicine on a model of the human body that would start from the basic laws of chemistry. In other words, the phenomena you'd like to model and the systems you'd like to design are so complex and subject to such ill-understood forces and mechanisms that your model, given the realistic limitations you're working under, cannot even begin to capture reality.
That said, just like in medicine you can often figure out things by looking at some simpler aspects of what happens in the human body, you can model certain aspects of the existing political systems with some accuracy. Public choice theory is one such reasonably successful attempt. However, such models must start from a deep understanding of an existing system based on observation and experience that will tell you what peculiar simplifying assumptions can be made about it, which gives you a workable starting point. Beginning from the first principles will get you nowhere at all.
I second the endorsement of public choice theory. A good place to begin from when designing a new government.
Patrissimo argue that we should try to design good mechanisms for governance rather than try and use the current broken mechanisms.
I agree, however we don't have a theoretical framework that we can use to evaluate different systems that are proposed. Ideally we would be able to crunch some numbers and show that a Futarchy responds to the desires/needs of the populace better than "voting for politicians who then make decisions" or anything else we come up with.
So we need to be able to do things like quantifying how well the system responds to the people. Pretending that humans are agents which have a utility function would seem like an obvious simplification to make in the model. We also need to formalise "being in charge".
I tend to formalise who has authority in a system as a number of pairings of people and posts. Posts might be the seat in the senate or the presidency, although we will want to expand this notion of post to look at all bureacracy and how they are filled.
One way a proposed mechanism would work would be through controlling the pairings. Futarchy suggests that we might look at other ways to make the mechanism work. This would be quite hard to model, we would have to model the incentives of the people making the prosperity indexes and the incentives of the market participants.
So we want a system that selects the people/post pairing that maximises the groups utility function, while assuming that the people in control of the post will maximise their utility and everyone else will try to (ab)use the mechanism to maximise their own utility.
Does this seem like the right track?