It's perhaps worth noting that the merit of liberal democracies is less their representative way of governance but their provision of a legal and structural framework in which even harsh and intricate disagreements can occur, be debated, and resolved.

While there may be representative democracies (not necessarily liberal once) with more efficient ways of conflict resolution and decision finding (e.g., the Haudenosaunee Confederacy or the Quakers), these are most often models designed for small populations. Liberal democracies on the other hand are currently the best way to accomodate differences in opinion without breaking apart the society of large populations.

The advantage of liberal democracies becomes even clearer when contrasted with non-liberal societies of large scale that generally tend to be authoritarian. Authoritarian or autocratic societies cannot deal with disagreements (esp. harsh once) except via force, oppression, and violence, which leads to silent populaces, complicit populations, or all out resistance movements.

So perhaps the benfit of liberal democracies should less be seen how well the "will of the people" is represented and applied, but by the way they allow for diagreements to occur and abide. They allow for the time necessary to sort things out without their societies breaking apart in the meantime.

#talkingtomyselflettingyoulisten