A representative democracy is founded on the principle of elected individuals representing the people. Usually you elect a representative (individual or party) for a fixed term – if you change your mind during the term – you can’t do much about it. Also representatives usually stand for a whole package of political objectives. If you don’t find your own mix – you need to accept compromises.
On the other hand a pure (or direct) democracy may be less efficient, is believed to be impracticable on a large scale, and warnings of a mob rule go back as far as Plato. This being said many people, honorable or otherwise, hold up the dream of a pure democracy. New technology such as the Internet could place it within reach. Of course this is only the technical aspect. The remaining question is: will everybody be able to deal with every question or will people stop participating? Or will there be superficial decisions? – “sounds good – let’s vote for it”.
This is where Liquid Democracy comes in. The basic idea: a voter can delegate his vote to a trustee (technically a transitive proxy). The vote can be further delegated to the proxy’s proxy thus building a network of trust. All delegations can be done, altered and revoked by topic. I myself vote in environmental questions, Anne represents me in foreign affairs, Mike represents me in all other areas but I can change my mind at any time.
Anyone can select his own way ranging from pure democracy on the one hand to representative democracy on the other. Basically one participates in what one is interested in but for all other areas gives their vote to somebody acting in their interest. Obviously one may make a bad choice once in a while but they can change their mind at any time.