There are two forms of democracy that are evident in Abrahamic religions, specifically Judaism and Islam. (I am less familiar with Christian-specific forms of democracy.)
One is Kritarchy, which is a particularly Jewish form of pseudodemocracy, seen in both the pre-monarchy rule by
shoftim and the post-exilic Sanhedrin / rabbinic structure of
beit din. In brief, political leaders generate popular support through their scholarship as as mediated through local (
beit din) and national (
Sanhedrin) courts of law, such that society functions in a decentralized manner with interpersonal conflicts being addressed through litigation, including suits by community scholars against individuals who are accused of committing sin (i.e. as opposed to formal agents of the State prosecuting criminals for violations of law). It is considered normative within Judaism that a proper Torah-observant monarch (including the Messiah) would not interfere with the kritarchy structure at either the local or national level, maintaining a separation between the Executive (monarch) and the Legislative-Judicial (kritarchy) branches of Judaic government.
Another is
shura - where Islamic rulers conferred with varying levels of councilors and community representatives in their adjudication and interpretation of
sharia. This ranges in scope from within the family unit to the royal council advising a monarch or Caliph. Many modern Muslims have compared and contrasted this with modern liberal democracy, noting that God is sovereign and not the People. (I am still learning about this and know very little; it would be invaluable for a Muslim on this board to expand on this concept.)
In both systems, to the best of my understanding, the development of various schools of jurisprudence indicate some degree of community-driven interpretation of scriptural law and regionalism in its application.
Both can be analogized, however roughly, to the development of constitutional monarchy and parliamentary democracy in the Anglosphere: God, the sovereign monarch, adheres and instructs our society to adhere to the laws in scripture, analogous to a constitution, and various institutions of community leadership adjudicate conflicts within society pursuant to that constitution.
