*We also (probably) have an army, but I will arbitrarily define "army" as the organization that uses violence outside the sovereign political unit (the police are inside), and I'm concerned here with the function of the state in a domestic context.
I also want to disambiguate republicanism from democracy. In a republic, the people choose their rulers; in a democracy, the people themselves rule. All modern "democracies" are republics, and almost all political science consists of how to make republics more efficient. There is good evidence in the Federalist papers that the framers of the U. S. Constitution created a republic intentionally to avoid democracy. In this task, they succeeded. I reject the concept of the republic; the republic is an essentially bourgeois institution; I do not believe there can be a stable and humanitarian socialist or communist republic. There is, I think, no channel in the republic between the Scylla of authoritarianism and the Charibdys of plutocracy. The only way out is true democracy.
Fundamental to a true democracy is that everyone has to become accustomed as individuals to the routine, daily exercise of political power as they are to the daily, routine management of money. I used to live in a condo complex with a homeowners' association. With fewer than a hundred households, there was no reason we couldn't have run the association with direct democracy, but the association was instead run with a republican model: we elected officers, who served for a fixed term, and the rest of the residents were occasionally invited to offer "feedback", which was usually ignored. Whoever managed to get elected had free reign to impose their personal hobbyhorses, and use the privilege of their office to maintain their power. Fundamental to a democratic state is that individuals must manage local, neighborhood resources by direct democracy. Without this feature, democracy will collapse to republicanism and ruling class oppression.
It's probably not feasible to have a direct democracy with more than a few hundred or a few thousand individuals. Aside from the purely technical problems of obtaining a reliable vote, the totality of issues facing the governance of a 300 million person country or a seven billion person world are too complex for any individual to grasp. Indeed, besides maintaining bourgeois privilege, this complexity is the principle argument for republicanism. But the republican, trustee model is not the only model possible. There is the delegate model and the franchise model.
In the delegate model, relatively small groups of individuals (no more than about a thousand) choose delegates, whom they can recall at any time. To address larger units of administration, delegates can themselves choose delegates to the next larger level. A delegate cannot act independently of her constituency using her term of office as a shield. It's also important to ensure that a delegate cannot routinely act officially in secret. Everything a delegate does must be transparent. A delegate can condense and summarize the complexity of her tasks to a well-defined constituency, and an independent press can provide alternative sides to the story.
In the franchise model, would-be representatives assemble a "floating" constituency. Each individual would therefore choose someone to represent him at each level of administration: I would have my city council member, my state representative, my federal legislator. Each of these representatives would vote in proportion to her constituency. If I didn't like what my representative was doing, I'd switch my choice to someone else, anytime I liked. A representative who lost too much support would be immediately ejected from the policy-making body.
Both models have advantages and disadvantages, but both models also share the fundamental issue that they are by design less stable than republicanism, and consequently both are potentially more problematic for individual rights. I'll address these issues in future posts.