It sounds like your fellow students understood the concept of a guessing penalty, but did not realise that the guessing penalty was too low in this case. One approach to convince them might have been:
Assume you get −0.0001 points for guessing an incorrect answer. Obviously, you should answer every question, because the penalty for guessing is so low. Now, assume that the guessing penalty is −20 points. Again, you obviously shouldn’t guess. What would the penalty have to be where you’re indifferent between guessing and not guessing? Obviously, when the penalty is −1 point. You guess two answers, one is correct and the other not, and your expected score is 0. In this case the penalty is −0.5, which is closer to −0.0001 than to −20, therefore you should always guess.
NB At my university, multiple choice exams always feature four possible answers, and you lose .33 for guessing incorrectly. Every student understands this concept perfectly. If they had to take your exam, they would’ve guessed every single time.
It’s strange to see that there are universities where the guessing penalty is not well calibrated. It seems like an elementary thing to do.
What would the penalty have to be where you’re indifferent between guessing and not guessing? Obviously, when the penalty is −1 point. You guess two answers, one is correct and the other not, and your expected score is 0.
Caveat: This is only true if you have no idea at all which is correct. If you think there’s a 60% chance you know the right answer, you’re still better off guessing.
It sounds like your fellow students understood the concept of a guessing penalty, but did not realise that the guessing penalty was too low in this case. One approach to convince them might have been:
Assume you get −0.0001 points for guessing an incorrect answer. Obviously, you should answer every question, because the penalty for guessing is so low. Now, assume that the guessing penalty is −20 points. Again, you obviously shouldn’t guess. What would the penalty have to be where you’re indifferent between guessing and not guessing? Obviously, when the penalty is −1 point. You guess two answers, one is correct and the other not, and your expected score is 0. In this case the penalty is −0.5, which is closer to −0.0001 than to −20, therefore you should always guess.
NB At my university, multiple choice exams always feature four possible answers, and you lose .33 for guessing incorrectly. Every student understands this concept perfectly. If they had to take your exam, they would’ve guessed every single time. It’s strange to see that there are universities where the guessing penalty is not well calibrated. It seems like an elementary thing to do.
Caveat: This is only true if you have no idea at all which is correct. If you think there’s a 60% chance you know the right answer, you’re still better off guessing.
Indeed. As a consequence, once you can narrow the answer down to two or three choices, you’re always better off guessing.