Many students, when faced with a test or homework question that they cannot answer, will attempt to get some credit for the answer using a palinesque approach of “I don’t want to answer that question (because I don't know the answer), but I will answer a different, perhaps even unrelated question, for which I do know the answer and maybe you will forget that I am not answering the actual question and give me some points.”
Speaking as someone who does a fair amount of grading, I know that it is in fact psychologically much easier to give zero points for a question left blank than it is to give a zero for an attempt at an answer. Even so, a totally wrong answer is a totally wrong answer.
I am happy to give partial credit for a partially correct answer, but I do not consider the presence of random markings in graphite or ink sufficient for partial credit.
A related phenomenon is when a speaker (e.g. a professor giving a department seminar; a student giving a talk or oral exam) feels that every question must have some answer, even if the answer if not known (to the speaker). It can be painful to say “I don’t know”, especially in some circumstances, but is giving a bad/random/wrong answer better than saying that you don’t know?
A better alternative to a flat-out "I don't know" might be“I don’t know, but..” and then talking about possible answers or ways to approach figuring out the answer. Or is that like asking for partial credit?
I can understand a student’s wish to write something and not leave an answer blank, on the off chance of getting some points, and I can understand a speaker's not wanting to seem stupid or lacking knowledge in front of an audience. These are facts of academic life. Even so, for some reason the 'partial credit' attempt bothers me when it permeates debates and interviews involving candidates for major political office.