I think yes, Islam is compatible with democracy. It is also compatible with a lot of other methods of government. There's nothing mandating or prohibiting any particular form of rule in the source texts of Islam (Quran and Hadith).Quraishi, who teaches constitutional law and Islamic law here at the UW Law School, explained how, historically, Islamic law developed, with a "public lawmaking realm [that] was separated from the realm of those who derived law from from interpretation of divine texts." This traditional public lawmaking "could very easily translate to a democratic public legislative (even representative democracy, even federalism if you like that too) system."
The question then becomes what do you do with the law that is derived from divine texts (and this is law, by the way, that a lot of Muslims in the world like, and in fact demand their rights under - much the same way we demand our constitutional rights - and this includes women, often in a very empowering way, but that's another topic) - i.e. the doctrinal corpus of law created by private Muslim jurists (fiqh).I wish everyone could hear Asifa give this presentation. She's a terrific speaker, and she uses Powerpoint slides, which I normally hate, quite brilliantly. There's a point in the presentation where one circle moves to a different position and everyone feels a great sense of enlightenment.
What I was tackling in my presentation was the roadblock in this issue that I think is presented by the western tendency to think that the sovereign state should be the location of all law for all of society. Once we are able to re-think the location of legal authority in a society, that some can exist as valid and authoritative, yet outside the realm of public lawmaking mechanisms, then I think that we will have gotten much further to coming up with a system of government and lawmaking and adjudication for Muslim societies that can be (but doesn't have to be, frankly I don't care what it looks like, that's up to them) "democratic" but in a very different model than western nation-state democracies.
I don't have any specific proposal on how this would look, and how it would work (that's something for me to work on for the next several years). I'm just saying that the western model is not the only one, and then I try to push that point by showing how the merging of nation-state model with Islamic law pressures from the people and political movements has actually resulted in the worst of both worlds - i.e. theocratic-type authorities despite the fact that neither Islamic heritage, nor the western model would have chosen that on their own.
UPDATE: Welcome Instapundit readers. Feel free to continue into the comments, where some readers take issue with Quraishi, and I relay some of her responses and note that she likened muftis (whom I initially mistakenly call mullahs) to law professors.