I think democracy fails because those who represent the electorate are not directly accountable to them, and the electorate has no chance to discuss matters with them. It fails because the person elected is seeking approval and endorsement from thousands, if not millions of people they have never - can never - meet.
I have been considering an alternative for many years. It flies in the face of what people consider to be true democracy, but I believe it offers a more responsive and responsible form of governance.
First of all, every locality of 100* households elects a representative for themselves - who must be a resident in one of those households. 100 of these representatives form the local or borough council, representing 10,000 households.
The local council then elects from its membership a chairperson or speaker and a regional representative. 100 councils elect 100 regional representatives sit on the regional council, which is responsible for around 1 million households.
Then the region elects their own speaker and a national representative, who sits on the national parliament (100 million households) with the other regional electives.
Finally, all the national parliaments elect one of their own to sit on a world parliament, to replace the UN and adopt some state sovereignty in a manner similar to the EU (not the US, as the federal government has too much sovereignty over the states, and abuses it constantly). This world government would elect, from its membership, a world president.
Most importantly, any constituency may, at any time, convene a recall election that can replace their representative with another member of their group.
This means that the 100 households where the world president lives can, at any time, depose him. So might the 100 local representatives he is supposed to represent. So might the regional council, and so might his or her own national government.
At each level the representatives will be able to know all the names and concerns of his whole constituency. Every vote would count because you would not be voting for a name with a party affiliation, but for your neighbour, or the colleague you have been debating budgets with for three years.
While it is true that with this system, not everyone gets to vote for the people at the top, it is also true that the people at the top can never forget their original constituency, and they can never forget that the people at each level of the heirarchy have a similar vulnerability to a recall by ordinary people. It would lead to a fairly fluid make-up of each council, since representatives would stay in place until they are recalled, but they can be recalled at, perhaps, less than a week's notice.
This system also allows the party systems of most democracies to be abolished. They are inherently corrupt as representatives put loyalty to their party above that to their constituency. And as has been all too obvious lately, getting millions of people to vote for you is expensive and that means you can easily be bought off by corporate interests.
Getting elected by 100 people, on the other hand, is relatively cheap and can be a matter of simply talking to them over a meal a few at a time. Getting elected by other politicians, moreover, means that your currency is no longer currency, but the political motivations and bugbears of your electorate.
That is democracy.
* all values are approximate and can be adjusted to reflect local geography and existing political divisions.