To reduce chance of students complaining:
Grade fairly each question/problem and write the score next to each question; write onto the top of the exam a sum-total score that is slightly greater (e.g., by 1-2%) than the actual sum if scores were tallied correctly for all questions. Students typically figure out that there is a discrepancy between what they deserve (based on correct sum total from all questions), and what was recorded incorrectly as the total; students then tend not complain about individual questions because they don’t want to risk discovery of the 2% grading “error” that benefits them. This works great for the professional complainers who would try to argue points no matter how fair you grade.
I hate that it assumes an adversarial relationship with students. I can live with that, I suppose, because there can be conflicts between instructors and students. I don’t think it should be assumed from the start, but it happens.
But what I can’t get over that an instructor thinks it’s useful to lie to students, routinely, just to avoid a conversation with as student about grades. It’s an instructor’s job to talk to students about grades.
There are few things that piss students off more than unfairness. This sounds like a situation where students who are close to the dividing for a letter grade are more likely to get that extra point than those who are not. If they were ever to find out that an instructor gave extra points to some students but not others (which sounds like the scenario here) to shut up “complainers,” instead of one complainer, you would have a whole classroom full of them.
When students find out that one instructor is pulling fast ones like this, they take that lesson into every other learning situation. “If one instructor is willing to fake an exam total to keep me quiet, will another one give me a lower grade because she didn’t like some random thing about me?”
Ultimately, the lesson students will take from this is complaining about grades gets you extra points, that grades reflect instructor bias more than actual achievement, and that instructors are lazy and uninterested in talking to students.
Don’t do this, instructors. And don’t say that you are looking forward to doing this on social media, like some I’ve seen.