Draft article by Patrick O'Donnell for the Encyclopedia of Islam:
Democracy, or “rule by the people” (typically, a majority thereof) is a term that has been used to
describe a number of different kinds of government: from ancient Greek city-states (e.g., Athens) to the contemporary (liberal, corporatist, and social democratic) welfare states of Europe and North America, to the myriad post-World War II democracies (particularly since the 1970s) around the globe, North and South, East and West. Today, democratic rule is usually connected to Liberal ideas and ideals of governance and government by popularly elected officials who legislate and enforce the laws in accordance with constitutionally ensconced notions of individual liberties and civil rights, hence “the people” rule indirectly through those elected to represent their considered preferences and interests as expressed in the voting booth. Historically, Islamic juridical and political thought has legitimated various kinds of governance: from the despotic to the benign. Indeed, the bountiful intellectual fruits of Islamic traditions—philosophical, theological, jurisprudential, mystical—are capable of justifying (through the provision of what philosophers, after Bernard Williams, term 'internal' reasons) a wide array of political models and forms of political behavior and rule, including models and forms of democratic governance and government (Hashemi, 2009 and March, 2009). We cannot here address a recent claim by Wael Hallaq that is clearly germane to our discussion, namely, that “[t]he 'Islamic state,' judged by any standard definition of what the modern state represents, is both an impossibility and a contradiction in terms.”
More here.