Warning: This is really rather abstract. It is much less concrete than most of my other public writings. If you are uncomfortable with that or just find discussions of that nature uninteresting, do yourself a favor and keep it moving. I hope to apply what I've written here to some specific examples. In fact I have a few in mind.
Our politics is quite a complicated affair, or rather collection of affairs. But we are a republic. Perhaps less controversial is the statement that it was intended upon our foundation by a significant coalition that we should become and remain a republic. If you will permit me a bit of histrionics (as if you had a choice) we are The Republic. But how do we talk about being citizens of any republican form of government in a coherent way where we can assume a fairly robust intersection of mutual knowledge.
Let's assume that the later Wittgenstein is correct and that it is true that you have not fully articulated the meaning of a term until you have exhausted all possible uses of the word which have some appreciable semantic content. For most terms there exists an extraordinary number of instances in which the term could be used in recognizably meaningful ways. This is also subject to further proliferation. That makes describing what it means to be a republic very difficult. Simply put, republic could mean a number of very different things to different people, and many of those instantial meanings, the complete set of which we have assumed is both necessary and sufficient for describing the universal meaning of the term, may be incompatible in ways that are confounding.
One fact about our republic and perhaps republics in general is that the citizens of it seem to possess the ability to say and think what they wish, within reasonable limits, and as such are permitted to construe the meaning of very foundational concepts about our way of life however they wish. These constuals may be honest attempts to capture their apprehensions of the objective order of things or they may be entirely self-serving formulations and used for the purposes of manipulating others toward a rather provincial agenda. In other words we are tolerant, which is for most purposes a very good property for a society to hold. But we are so tolerant as to render any construal unaccountable to reasonable standards of concept formation, regardless of how rogue it may be (in fact I bet many Americans would be uncomfortable with labeling a construal "rogue").
Further complicating matters is the tendency of some individuals to use a variety of terms to describe our form of government; terms like "democracy," "representative democracy," democratic republic," "constitutional republic," &tc. Some of these terms may be redundant or even self-contradictory. But I will resist the urge to take up that issue here. I will say that there exists enough variety to make it clear that all these terms are not intended to describe precisely the same form of government. What that means is that people talking about American government are not even in agreement about exactly what form of government they are making reference to.
Hopefully after all this I have convinced you that figuring out what our politics and government are basically about confronts a sensitive analyst with some troublesome conundrums. The question may rest on false assumptions: it does not even look like our political system is about anything specific enough to register in our perception. If you are reasonably clever you are probably expecting me to try and evade all that mess and respond in elegant fashion with a solution to the question of what it is that our republican government is about. Right you are.
So let me borrow a bit from Popper and justify the fact that my arguments regarding what republicanism is about do not rest on indubitable foundations. According to Popper, it is not the case that there exists any such thing as indubitable foundations. There is always room for progress and I will leave myself some room for progress by leaving the open question of how I reconcile my answer to the questions with all the troublesome problems I talked about earlier in a manner such that I leave fewer questions than answers.
The state of being a republic is about being representative. Any meaningful talk of a republic is talk which makes appeal to at least the conceptual understanding of representation, if not explicitly referencing representation. What I would like to do is build a framework for talking about representation. But it may suffice to merely expose such a framework.
The logic of representation rests on the assumption that people can find a satisfying substitute for them on matters of public affairs. This substitute need not be identical to them in the relevant respects and so there may not be one-to-one mapping between a citizen's policy preferences and their representative's policy preferences. A person may vote for someone who is starkly different from them because they may believe that the person they are voting for is better qualified than they are to make decisions on the behalf of the citizenry and their confidence in this elite representative makes them willing to consent to the representative's program. On the other hand, a citizen may look for a substitute who is not particularly clever. The value of this unsophisticated substitute to a citizen is that the substitute is predictable and the citizen can plan their personal decisions around predictable policy outcomes. The matter of candidates' technical competence is but one category that may go into a voter's decision function. Surely there are countless others and many may be shared by most if not all citizens in most if not all elections. Some considerations may be unique and endemic to a particular citizen or class of citizens!
What we must remember is that these categories should be understood as a matter of tastes and preferences and these tastes and preferences can seem idiosyncratic or even erratic when compared to a model voter. I could build an elegant model of a rational voter with perfect information who operates in a frictionless decision environment with zero search costs and no agency costs of employing representatives and who makes decisions based on how the expected outcomes of candidates' policy positions will affect their optimization criteria and vote based on the solution to the optimization problem. However that will only partially explain election outcomes and probably do a poor job of so doing. If a citizen wishes to dispense with considerations of competence or even expected outcomes with respect to their own self-interest then that is their prerogative.
Ultimately, we must be careful to avoid being absolutist about representation. Just as citizens of The Republic are free to choose their representatives, so are they free to choose what they consider counts as an appealing category of representation. If what they value in representation are superficial qualities such as gender, race, or age, then who are we to tell them that they should not. For example, if black American voters want to vote for Barack Obama only because he is bi-racial and identifies himself as a black man, why should we believe they are making an error in judgment? They may know something we do not which makes it perfectly sensible for them to vote based on a single and seemingly superficial criterion. If what citizens value in a representative are personal similarities in terms of culture, religion, or economic philosophy then who are we to argue, even if it is true that the policies of those representatives are not in the best interests of the people who vote for them. For example, TEA party members may be putting themselves at a disadvantage when they argue for less government spending, even though they may be unemployed and government spending may be the only mechanism of moving the economy back to full employment in relatively short order. But that is their right.
These considerations are predicated on value judgments. Aren't value judgments fundamentally arbitrary (I mean with good cause we call them "value judgments" and not "value arguments")? In fact value judgments may indeed be capricious, in the sense that they are sometimes induced by mental states which are not mappable to models of rationality and thus have no rational justification. A government about representation does not permit a disinterested patrician reformer, no matter how enlightened or liberal, to take the view from nowhere and optimize social conditions with respect to immutable laws of nature. A republic is going to be politically messy. Representation is a messy business that reflects the messy nature of the human condition. But representation is the best business around. If you have a better idea I would like to hear it.