As far as I know, Islam does not provide a political system. It leaves it to the ppl(or leaders) to decide a system for them. This is evident from the way the first four pious caliphs were selected. all were selected differently. Instead, islam emphasises on the formulation of laws and their implementation.
So if a democratic country formulate laws through its parliament, and if these laws does not contradict islamic laws, then, i think, democracy and islam are always in harmoney. there is no problem.