As I have already written in that answer the points system works well as a tool for evoking social pressure on students, but it is often exploited when it comes to actual numbers. There is a lot of examples of the teachers awarding or deducting arbitrary number of points. It is likely that prefects are no better than teachers and sometimes take advantage of their powers.
In HP and the Order of the Phoenix we could see Draco Malfoy (who was at the moment both prefect and the member of the Inquisitorial Squad) clearly abuse his power:
So, Granger, I’ll have five from you for being rude about our new
headmistress... Macmillan, five for contradicting me... Five because I
don’t like you, Potter... Weasley, your shirt’s untucked, so I’ll have
another five for that... Oh yeah, I forgot, you’re a Mudblood,
Granger, so ten for that...
On the other hand, prefects are still students, so their own misbehaviors can be punished by the teachers. If a teacher learns about the prefect misusing her/his power, they should discipline such prefect or in extreme cases escalate the issue to Headmaster who can elect someone else for the role. Obviously that was not the case in the time of Umbridge.
Prefects seem to be quite independent in their roles, but in HP and the Chamber of Secrets there is one passage which might indicate the opposite:
“Harry!” said Percy loudly. “No magic in the corridors. I’ll have to
report this, you know!”
But Harry didn’t care, he was one-up on
Malfoy, and that was worth five points from Gryffindor any day.
It makes clear Percy had to report the incident, but we don't know who specifically deducted the points. So it's possible that prefects have to report to one of the teachers every time they punished another student.