The "problems" with modern democracy are more to do with the electoral process than anything else. Most "democracies" with only two real main parties in power are based on a first-past-the-post (FPTP) system, which naturally tends towards a two party system. Alternatives such as AV (alternative vote) and proportional representation fix this problem, as long as the electoral boundaries are not corrupted (a process known as gerrymandering).
My personal favourite is a system of my own devising, where (thanks to modern technology) the government is in a constant state of election; each voter being able to change their vote at any time, meaning that (finally) governments are held accountable in real-time to the decisions they make. All voting would be done online (at home, or via a permanent public voting booth), with the vote counting system being cryptographically secure and distributed so that the potential for fraud is reduced to near zero.
My personal favourite is a system of my own devising, where (thanks to modern technology) the government is in a constant state of election; each voter being able to change their vote at any time, meaning that (finally) governments are held accountable in real-time to the decisions they make. All voting would be done online (at home, or via a permanent public voting booth), with the vote counting system being cryptographically secure and distributed so that the potential for fraud is reduced to near zero.