All Prefects, Head Boys and Girls, Team Captains, and Professors have the ability to give and deduct points. These are based on merits. By order of power:
Head Boy and Girl
Prefects and Head Students cannot change something Professors have done to points. Team Captains only have jurisdiction in Quidditch related points.
For the points to count, there needs to be a proof of log, and a comment here with this format: