In an Islamic democracy Sovereignty over the country belongs of Allah and the power is to be exercised by the representatives elected by the people or those who take vote of allegiance of the people (Bai’at) as the pious Caliphs and the other Muslim rulers did in the later period of Islamic history. In the electing the caliphs such candidates were chosen who where pious, God fearing and righteous (however this system did not continue where the so called Caliphs of Umayyad and Abbasids dynasties made the designation of Caliph as henditary and virtually ruled like kings and they behaved as possessors of sovereignty.
Still some righteous Caliphs like Umer Bin Aziz of Ummayad dynasty formulated Shoora (the panel of advisers). However the present day King of Saudi Arabia, Morocco and the Sheikhs of Sheikhdom of UAE. Bahrain, Kuwait, do not observe this principle of sovereignty of Allah.
However Turkey, Pakistan and Iran observe western type of democracy in which only Pakistan claims that sovereignty belongs to Allah as laid down in Objective Resolution (1949) and the constitutions of 1965, 1962 and 1973. Pakistan however was ruled and is being ruled by Army Generals who openly abuses the basic conception of Islamic sovereignty of Allah under the influence of big powers.