I’m bemused when I see today’s exams. Many are just multiple choice tests. There’s a question like “Who said ‘Never was so much owed by so many to so few’?” and you have to guess who said it: Franklin Roosevelt, Mahatma Gandhi, Adolf Hitler or Winston Churchill?
Of course I’m exaggerating. Even multiple choice tests can be complex! For example, you might have to answer 100 such questions in 30 minutes; so there’s time pressure. Or there could be negative marks; so you have to be circumspect.
There’s also a philosophical sort of objection: if the answer picked is wrong, you know for sure that the candidate doesn’t know the answer. But if the answer picked is right, can you be sure that the candidate truly knows the correct answer? Could it just be a lucky guess?
That’s the crux of the matter. How do we conquer the scourge of guessing? How do we ensure that we select a winner, and not a gambler?
A candidate once explained his strategy rather well: “I ask if there are negative marks. If there are no negative marks, then I first attempt all the questions for which I know the answer … and then I randomly guess all the remaining answers!”
That’s a smart thing to do. Imagine that there are 100 questions — with four choices — each carrying 1 mark. Imagine that there are two candidates … let us call them Hemant Satyavadi and Rohan Khiladi. Imagine that both Hemant and Rohan know only 40 answers. Hemant attempts only 40 questions and leaves. What’s the highest mark Hemant can get? 40/100! Rohan however reacts differently: he first ticks off the 40 answers he knows, and then randomly guesses the other 60 answers. If Rohan is very very very lucky he could get 100/100, but even if he is very very very unlucky he’ll still get 40/100. On the average expect Rohan to get 25% (one out of four) of his guesses right; so he should get about 15 marks more to end up with 55/100.
Now that’s unfair! Both Hemant and Rohan deserved to get 40/100. If 50/100 was the qualifying mark, both should have been out. Instead we now have a situation in which Hemant is out and Rohan is very probably in.
The preferred way to discourage guessing is to introduce negative marks. So what sort of a negative mark would be right? How about -1 for a wrong answer?
A moment’s reflection will show that this is a very stiff penalty. Even if the candidate has the slightest doubt, he will choose not to attempt an answer, because every wrong guess will ‘undo’ a correct answer.
So what about a lower negative penalty? What about -1/4 for a wrong answer? It is easy to see that -1/4 may not be a sufficient deterrent to prevent guessing. Imagine that Hemant and Rohan don’t know answers for any of the 100 questions. Hemant — who never guesses — will leave with 0/100. Rohan — who always guesses — will, on the average, get 25 guesses right and 75 wrong. The 25 correct guesses will fetch him 25 marks but the 75 wrong guesses will now take away 75/4 = 18.75 marks. So Hemant will end up with 25 – 18.75 = 6.25/100 when he too deserved 0/100! Some simple arithmetic will now show that if we give -1/3 for a wrong answer both Hemant and Rohan get the 0/100 that they truly deserve.
So to summarize: In a multiple choice test with four options, always guess if there are no negative marks; continue to guess till the negative mark drops to -1/3; and don’t guess if the negative mark falls below -1/3. If the negative mark is exactly -1/3, it doesn’t matter what you do.