This may be a dangerous post to write, but what the hell.
The old saying goes that you shouldn’t talk politics or religion on mixed company. Of course, lots of science-fiction deals with politics and religion, but most of the time, they are utopias or dystopias that extol the virtues or expose the dangers of whatever systems the author feels like dealing with. And so the political systems of the future are full of Empires, as in The Mote In God’s Eye, or Star Wars. For democratic socialists we have Star Trek‘s Federation, and for libertarians we have Michael Z. Williamson’s Freehold.
Historically, though, we see that “new” political systems tend to be 1) surprising and 2) not all that new. The two examples in recent history that have achieved success in spreading throughout the world may be worth looking at, here, which are the American-style constitutional republic and the Soviet-style one-party socialist state.
It’s worth remembering that in 1787, there were no functioning large republics or democracies in the world. It was widely believed that such a thing could not work. And yet not only did the American system thrive, its Enlightenment ideals spread through the European states, encouraging their liberalization over the next centuries into functioning republics themselves.
In 1917, the chaos of World War I led to the Soviets seizing control of the Russian Empire. While this system did not thrive in the same way, it certainly spread, and resentment against imperialism and colonialism and the inequalities found in capitalism ensures that it continues to have its supporters despite its disastrous legacy of approximately 100 million directly killed.
Of course, it’s quite possible to argue that neither of these things are precisely “new” forms of government (and that communism isn’t a government, but an economic system, which is both true and stupid, since it’s an economic system that necessitates and advocates a certain style of government), but if that’s the case we might as well go all the way and cite the Iron Law Of Oligarchy: All governments inevitably devolve into oligarchy. But that ends the discussion I’m interested in, which is this:
Is there any room for, and are we capable of imagining, a truly future system of government, one that has never been attempted, or has been attempted only on a very small scale? Honestly, there are only two examples I can think of, one of which has become cliche and the other that’s unclear. In the first, we have Government By Computer. This is almost always a dystopia, as the idea of being ruled by a hypercapable God-machine is rather frightening on its face. The other is Dan Simmons’s hyperdemocratic All Thing in his Hyperion novels, in which there is a fairly direct democracy mediated by the equivalent of the Web. However, this government does elect an Executive that runs humans space, so it’s not really as direct a democracy as all that.
Edited To Add: I can’t believe I forgot to include Ursula LeGuin’s excellent The Dispossessed, which is unique for me in that it a) imagines a form of anarcho-socialism that I actually find semi-plausible, and b) admits to flaws in such a society that significantly hurt the protagonist without being c) dystopian socialism.
I’d be interested in hearing people’s thoughts on this, as well as being directed to any works that explore this that I’m not conscious of.
G. Scott Huggins 
As with all things, we can turn to Heinlein. I feel like his ideas in The Moon Is A Harsh Mistress, while certainly libertarian, have some interesting implications (I think specifically about the trial conducted fairly early in the story, where whoever is nearby is essentially co-opted as judge and jury). Also, I know he had one story where the Supreme Court was literally crowdsourced (a random sample of citizens were video-conferenced together and decided the case).
I feel like he put far too much faith in humans in these examples, but they do seem fundamentally different than the democracy we practice today.
Indeed, and Starship Troopers’ veteran-limited franchise republic, though roundly denounced as “fascist” by those who hate and fear the military, provides yet another possibility.
What about a direct democracy with only the most limited executive imaginable, but where not every vote counts the same? How much your vote counts depends on a point system similar to the one China seems to be developing, measuring your positive or negative influence on society. So a high amount of taxes would increase your number of votes, as would community service, raising children, creative work etc.
Criminal acts, selfish behaviour etc. would decrease your influence.
Or L. Neill Smith’s semibdirect democracy, where each delegate to the Continental Congress is there to vote a sheaf of proxies? Government by shareholder meetings.
Neal Asher’s Polity throws up an interesting notion of a computer-controlled polyglot Imperial state (in all but name) … maybe like and idealized historical Ottoman Empire? … supporting and merged with social and individual Libertarianism. Although really you could say that the entire system boils down to an enlightened liberal despotism with an AI caste replacing the nobility.