Where are we told that God puts in an individual human being's hands the right to assess guilt and innocence and assign punishment? "Vengeance is Mine, sayeth the Lord: I will repay." Given that God knows that we need, in human affairs, to take action to protect ourselves, he lays out institutions and processes for trying to bring His will into the process of administering justice. In all of these processes the hand of the prosecutor and the accuser is stayed, in some way, by collective and unbiased decision making. This is one of God's great gifts to us.
*sigh*
... among other places...
For rulers hold no terror for those who do right, but for those who do wrong. Do you want to be free from fear of the one in authority? Then do what is right and he will commend you.
For he is God's servant to do you good. But if you do wrong, be afraid, for he does not bear the sword for nothing. He is God's servant, an agent of wrath to bring punishment on the wrongdoer. (Romans 13:3,4)
Rulers are given authority and responsiblity to make the call in secular dealings, but will bear the judgment of God for their calls - both for good and evil.