have heard many Muslims say that democracy is not compatible with Islam.  For example, what if the majority of people decide that they want something that is un-Islamic (for example, banning hijab).  Then, this majority votes for the un-Islamic thing and wins (because that is how democracy works). 

Thanks Suleyman. I note this on democracy from the link you sent:

"Democracy in Islam

The above explanation of the term Khilafat also makes it abundantly clear that no individual or dynasty or class can be Khalifah, but that the authority of caliphate is bestowed on any community which accepts the principles of Tawhid and Risalat. In such a society, each individual shares the God given caliphate. This is the point where democracy begins in Islam.

Every person in an Islamic society enjoys the rights and powers of the caliphate of God and in this respect all individuals are equal. No one can deprive anyone of his rights and powers. The agency for running the affairs of the state will be established in accordance with the will of these individuals, and the authority of the state will only be an extension of the powers of the individuals delegated to it. Their opinion will be decisive in the formation of the Government, which will be run with their advice and in accordance with their wishes. Whoever gains their confidence will carry out the duties of the calilphate on their behalf; and when he loses this confidence he will have to relinquish his office. In this respect the political system in Islam as perfect a democracy as ever can be.

What distinguishes Islamic democracy from Western democracy is that while the latter is based on the concept of popular sovereignty the former rests on the principle of popular Khilafat. In Western democracy the people are sovereign, in Islam sovereignty is vested in God and the people are His caliphs or representatives. In the former the people make their own laws; in the latter they have to follow and obey the laws(Shari ‘ah) given by God through His Prophet. In one the Government undertakes to fulfil the will of the people; in the other the Government and the people alike have to do the will of God. Western democracy is a kind of absolute authority which exercises its powers in a free and uncontrolled manner, whereas Islamic democracy is a kind of absolute authority which exercises its powers in a free and uncontrolled manner, whereas Islamic democracy is sub-servient to the Divine Law and exercises its authority in accordance with the injunctions of God and within the limits prescribed by Him."

So democracy in a completely Islamic state should be EASIER to run than in an ordinary Western country. You follow God's laws, but encourage education, discussion and voting.

However, in the West we cannot just say "we follow God's laws". Which God? Which set of laws? Our countries are FILLED with people of different religions and creeds. WHOSE traditions and laws should we follow? Answer - we CAN'T. We have to decide between ourselves what is moral and just WITHOUT the help of having a God to decide it for us. 

Kim...