Ancient Athens can testify that pure democracy doesn't work. It's a lovely concept: any citizen can propose a piece of legislation, and everybody votes on it, and if accepted the proposal becomes law. Since everybody gets a vote, democracy is simple and extremely fair. It would be the perfect system of government, if only humanity were perfect. Unfortunately, democracy has several fatal flaws. Nobody has the time and intellect to read, research, and vote on every piece of legislation that comes before the citizenry. This leads people to take shortcuts for the sake of expediency: they either make poor decisions on proposals they don't understand, they ignore proposals they don't understand, or they give their vote to somebody else who has the time and inclination to participate in the system.
This last one, delegation of authority, was the undoing of Athens (since the Athenians tended to elect popular demagogues), but has become the foundation of Western "democracy." Though we think of our governments as being democracies, of course they are not. Modern nation-states are simply too large and too complex to be directly governed by the citizens. If the relatively small city-state of Athens couldn't manage democracy, it's unlikely that any fully developed nation-state could. Instead, our political systems in the West typically rely on representation and more closely resemble republics than democracies. The citizens of a country vote on candidates to represent them in certain political roles, and those representatives then make all the decisions of government.
Representative democracy is a system that allows the citizenry to go about their daily business without devoting an inordinate amount of time to the making, interpreting, and enforcing of laws. Unfortunately, representative democracy dis-empowers the population, because our representatives are not directly answerable to us. Eventually they must stand for reelection, but by that time many have forgotten their mistakes and missteps and reelect them. Even those who remember their representatives' political foibles often find themselves without a viable competing candidate to vote for, and decide which way to cast their vote based on a "lesser of evils" approach.
As a result, bureaucracy becomes entrenched, special interests thrive, and the will of the people is diluted or even superseded. Additionally, voters find themselves forced to elect representatives whose political views do not completely align with their own. This is inefficient at best, and disillusioning at worst. A voter who believes in gun control may be 'forced' to vote for a candidate who does not, because the other electoral choices are even worse. Furthermore, elections tend to be winner-take-all events, where a very large minority can find themselves outvoted and effectively disenfranchised, since "their" representative will not actually be representing their viewpoints at the local, regional, or national level.
True democracy is the only system which can fully enfranchise the populace, but one must find a way to overcome the flaws of such a system. This has been impossible--until now. Consider a reddit-style system where one could log onto the internet once a day, or week, or month, and "upvote" the issues and legislative proposals that are of interest to them.
Theoretically, the best proposals would rise to the top, and upon meeting a certain threshold would either become law, or as an intermediate step, could be submitted to a legislature for debate and vote by elected representatives. Such a system would enable citizens to vote on issues they understand and regard as important, while allowing others to decide upon issues of less direct relevance. Furthermore, a voter could express the full range of his political convictions, rather than relying entirely on representatives whose ideals may not align with those of the voter.
Such a system would have considerable challenges to overcome. Sybil attacks would be the most serious danger, so a form of identity verification would be required. One idea would be for each nation to assign a "colored coin" to each voter based on his national ID number. This would ensure that each person could only cast one vote per issue or election. Universal adoption is another major barrier. The first step toward a distributed democracy would likely be in the form of "suggestions" or petitions (similar to change.org), where elected leaders are strongly encouraged to consider certain issues. As time goes by and the system is proven to be robust, and more people begin participating, certain distributed democracy votes could be made legally binding.
Distributed democracy is not something that can be created overnight. Those in power will be reluctant to relinquish it, and people who are not technically savvy will be loath to change their habits. The voting system would have to be 100% secure, or at least very close to it. Likewise, the system would have to be easy to use, in order for average people to make sense of it. Finally, highly complex, technical, or specialized issues/proposals would be difficult to decide due to the fact that not everybody will be able to grasp them. Any form of distributed democracy must therefore begin slowly, and gradually increase in universality and importance.
Despite these caveats, such a system would be game-changing. The world sorely needs better political systems than those which are currently available, and technologies which allow the creation of distributed organizations may eventually find themselves able to create distributed political system as well. If Ethereum succeeds in its goals, this is only one of the ways in which it could change the world.