If God is the arbiter of morality, if morality is whatever he decides, then he could designate murder or torture or whatever horrible crime you can imagine as moral and it would then be moral by definition, since morality has been defined as whatever God decides it is. In brief, asserting that God is the source of morality is the same as asserting that morality is arbitrary.
If one disagrees with this and says that God cannot invent morality however he wishes then he is unavoidably committed to the idea that God obeys a law higher than himself (besides also denying the omnipotence of God, since one thing that God cannot have power over is the invention of morality), namely the Law of Morality to which even God must adhere. To say that God is the source of morality while holding that he himself is bound by that morality is to speak nonsense. If God had to spend effort arriving at a certain moral system then one can assume he had many possible moral systems from which to chose, and he chose from them one particular right one for very good reasons. (Good reasons can not include arbitrary declarations for then there would literally be no way of telling good reasons from bad.) If so, then God did not freely chose that moral system but was forced (being perfectly good) to chose only the one truly good moral system. Again this implies that God is beholden to a Moral Law that he cannot overturn.
In questions of morality, 'who decides?' The answer is that no ONE decides, including God. Morality must be a democratically derived system involving and accommodating multiple points of view. This is independent of the content of any given moral system. The concept of a legitimate moral system assumes perforce a plurality of input.
© K Michau 2006