If we believe that God is sovereign, and if we agree with Paul in his letter to the Romans, we are also forced to believe that "everyone must submit himself to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God." (Romans 13:1)

If that's the case, why vote? Or why get disheartened if the vote doesn't go the way we would like? Isn't God ultimately sovereign over such things? Or do we assume that our electoral system somehow thwarts God's sovereignty and Paul's claim in his letter to the church in Rome?

I personally believe that the American system of democracy actually lends away from clearly seeing the sovereignty of God. When the apostles needed to replace Judas Iscariot after he died, they drew lots to determine between two men that they had proposed. (Acts 1:23-25). Drawing lots is basically throwing dice. They threw dice to determine who should be a part of the 12 disciples, and by doing so, they had a clear picture of the sovereignty of God. When human wisdom cannot determine the correct path to take, and scriptures do not reveal what should be done, casting lots was the ultimate act of "let God decide."

By voting, it's not as though God becomes non-sovereign. God is ALWAYS sovereign, and God's will is not thwarted. But by voting, it appears as though the decision is in the hands of man and not the hand of God. But that is an illusion, since God remains sovereign.