A common rule in exams is to require them being written with permanent (non-erasable) pens, which includes usually ballpoint pens and fountain pens filled with special ink. The rule forbids using fountain pens with erasable ink, ink erasers, pencils, correction tape, or fluid.
What is the point of such a rule?
I’ll give my answer according to my own research and understanding below, but I am interested in anything that adds to it or refutes it.
I see three reasons for this (roughly sorted by relevance):
The forbidden tools increase the opportunities for the student to tamper with the exam when they get to review it and remark marking mistakes.¹ While examiners can make a point by completely ignoring anything using forbidden tools, this would be disproportionately strict and also just creates extra work for the examiners. However, examiners have good reason to refuse to correct their markings on an exam or part thereof where forbidden tools were used.
Most, if not all of the forbidden tools are more susceptible to accidental damage: Non-permanent ink dissolves better, correction tape can be rubbed off, some correctable ink is susceptible to light and temperature, etc. Should any of these things happen and not using forbidden tool could have avoided the loss or distortion of answers, the examiner can more easily (and often justifiably) refuse any claims based on this. For example, anybody can claim that correction tape with relevant content written on top somehow rubbed off during the correction of the exam.
It is more difficult for the correctors to tamper with the exam and thus it is more difficult for the student to demonstrate that this happened. (Thanks to Federico Poloni for adding this point.)
So, from the examiner’s point of view, students use the the forbidden tools at their own risk.
¹ Of course, it is never possible to fully exclude that somebody improves their solution by simply adding something, but such things can only be done with suitable mistakes and corrections. For example, a student may fix a mistake by changing “x” to “x²”, but only if the latter happens to be correct and the correction wasn’t adding a “²” in red (or whatever colour is used for correction). On top, the exam review should be surveilled to spot if anybody is writing in their exams.
The answer by Wrzlprmft focuses on exam integrity reasons for this instruction. I'm more familiar with an academic system in the US that does not treat most exams quite as seriously as is common in Europe, so while I think everything in this answer is accurate I've also heard reasons related to the type of work expected and practical issues with erasing.
If the instructor is expecting a stream-of-consciousness sort of answer and not an edited manuscript, they do not want students to go back over and erase and edit their work because this will cost them time "improving" things that don't matter for the grade at the cost of time not spent on those that do.
Practically, erasers (particularly for pencil) often do not work well and it can take substantial effort to erase and the results may not be legible. A simple strike through and re-write in ink, if necessary, takes less time and is more legible anyways.
In addition to concerns about cheating, I think there are more mundane practical concerns:
(I think correction tape may suffer from similar problems but to a lesser extent.)
On Cambridge International exams (example), the instructions contain this line: Do not use staples, paper clips, glue or correction fluid.
Putting correction fluid together with staples, paper clips, and glue strongly suggests the concern is less about cheating and more about the above practical concern.
Also from the Cambridge International exam instructions: Write in dark blue or black pen.
We know markers use red pens. But the above also specifically prohibits pens of any other colors (e.g. light blue/pink/purple/green), suggesting there is a desire for exam-takers' writing to be clearly legible.
Also, nowadays, exam scripts are sometimes scanned (where again any writing in pencil might be less clear than writing in dark blue/black pens).
All our exams (a Norwegian university) that's still conducted on paper are done on triplicate carbon copy paper. This means that erasing isn't possible, so using erasable tools are just asking for trouble if the student try to erase anything (or use correction tools like tape or fluid). And ballpoint pens work better for getting a proper copy on all three layers than pencils do.
