What role does conscience play in brutus decision?

Brutus relies heavily on his own conscience and will not agree to do anything unless he completely believes in the cause. This is why it takes so long for Cassius to convince him to kill Caesar. Eventually though, he believes that their cause is right and therefore goes into the murder with a clear conscience.

He also keeps the other men (especially Cassius) in check while planning the murder, because his conscience is so strong. He says "Let us be sacrificers, but not butchers, Caius." He is making sure they stay on track and are doing things for noble reasons, not just blindly killing.

This is why he refuses to let Cassius plan to kill Antony as well as Caesar, because he does not feel Antony has done anything wrong.