(Note: I'm not talking about the same kind of redundancy as in this question).
Is "may or may not" correct, or is it a redundant version of "may or not"? I've seen both, and I don't know which one(s) is (are?) correct:
If you take the phrase as a whole idiom—rather that the sum of its parts—it is not redundant. The point of its use is to highlight a common assumption that does not apply. In your example, it could be assumed that a lecturer would need a doctoral degree, and the idiom dispels this notion.
If I read "may or not", I would suppose that it was an error. I am startled to find that other people find it acceptable. (UK English, in case that is relevant).
The "may or not" version generates problems like: "He must do what he may or not a thing will come of it" vs. "He says he will fish; he may or not like the experience." You have to read on too far into the sentence to resolve whether the "or not" goes with the "may" or the rest of the text.
Perhaps because of this, the form I've heard most often is "may or may not" (which requires more exotic conditions before it becomes difficult to parse).
If you make the verb explicit: "may fish or not", then the "or not" form is quite common also.
May or may not is redundant; may or not is indecipherable; may by itself communicates both possibilities. In this instance, the idea of may is not relevant. “The position of lecturer is occasionally given to individuals [...] who do not have a doctoral degree.” Which implies that, most of the time, the position is given to individuals who do have a doctoral degree. This is more straightforward.
I think both usages are correct. In the US, it's far more common to hear "may or may not". The extra "may" might feel too wordy for some, but because I'm used to hearing it "may or not" sounds very uneven to me.
The answer here is the same as it was in the other question - that is to say, the certainty is unknown, which is why an apparent 'double modifier' is needed. In your case, the lecture being given may be attended by those with doctorate degrees, OR it may not. THe lecturer does not know, and their uncertainty about this is reflected in the construct "may or may not".
"May or not" doesn't quite work, because it would imply certainty that at least one individual does not have a doctorate degree where there is not any.
