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Why do Sasanka(students) study even though its relative grading?


Contributions: Shreyas Adiyodi & Tanuj Choudhary

Disclaimer: Sasanka Bhagabati, here, is a fictional character. If, from his character sketch, you draw any resemblance with a namesake residing in A-122, that’s sheer brilliance on your part :D.

Observing is an art of making curious, obvious.
Aim

So like any other sincere student of an IIT, I have often been plagued by this innocent question, Why the hell do we need to study? As most of us have long forgone our scholarly pursuits, it seems even more illogical to mug for long hours before examination. Don’t you think, it would have been amazing to score grades without messing with your sleeping schedules? And yes we all think it’s possible as grades are relative, yet due to some muggers we are all forced to bear the plight of studying every time before the exams. So, the aim of this blog is to determine why students study for exams when they can all manage good grades if none of them study?

Prerequisites:

I don’t know why I have written it but may be after writing so many practical files I am habituated to write PREREQUISITES after AIM. First of all, to read this blog there is no prerequisite, all you need is logical sanity. I have drawn an analogy from a situation called prisoners’ dilemma used in Game Theory but it is really basic so you don’t need to go through all that to comprehend this blog. Moreover, it would ironic to endorse any form of study in this blog when we are discussing its purpose on the first place, isn't it? 

Sample:

A group of sleep deprived IITians who are forced to mug PowerPoint slides for their end terms. None of them have any interest in learning the subject and they are driven solely by the need for good grades. We assume they have similar primitive understanding (which is enough to fetch passing marks) but different learning abilities i.e. all of them will score same grades if none of them are studying but if they study, everyone will score differently depending on their learning abilities. 

Grading System:

Grading System is a 10 point scale on which students’ performances are rated with 10 being the best. However, it not an absolute scale but a relative one so a student’s performance is measured against the performance his classmates. So if you score well and yet others score better, you might get poor grades and vice-versa. However, to score 10 you need to score above a threshold marks but there are no such thresholds for any other grade i.e. grades from 1-9 are purely relative. No grade is awarded if someone fails.

Subject: 
Our Subject
Utmost discretion has been
maintained to prevent his
identity from being revealed.

Our subject, Sasanka Bhagabati, is a religious and punctual student (I really mean it). He dedicates 8-10 hours every day for his studies. But, like many other IITians he has no interest in engineering and grades are his only motivation. In spite of all this hard work Sasanka Bhagabati has never been the batch topper. He is frustrated and believes that return on his investments is not good enough. Out of desperation, he has sought professional help from the author (who somehow holds expertise in earning without learning) on whether he should continue studying or not?




Solution:
Assumption: Everyone is driven by the selfish motive of getting better grades.

To precisely determine what the best course of action is for Sasanka, we need to make a list of all possible situations and respective outcomes. For simplicity, let us assume that samples behave identically i.e. if one student in the sample is not studying then the entire sample is not studying and likewise. So now there are four possible situations: Both Sasanka and Sample are not studying, Sasanka is studying but Sample is not, Sample is studying but Sasanka is not and both Sasanka and Sample are studying. Now we draw a possibility matrix representing all the above mentioned situations and depicting the possible outcomes in terms of grade of Sasanka and average grade of Sample. It is represented as (X,Y) with X being Sasanka’s grade and Y being samples average grade.

Possibility Matrix for Sasanka


Now, when no one is studying, we assume that everyone will score same marks which would obviously be less than the threshold thus securing a grade of 9. Now if Sample is not studying but Sasanka is, he can cross the threshold and secure 10. On the other hand everyone else’s grade will fall as their performance compared to Sasanka is now poor. If the situation is reversed, Sasanka’s grade will fall drastically as his performance compared to others is much worse. However, it must be noted that Sample’s average is not 10 as everyone has different reading abilities so their grades will lie in wide spectrum with Sasanka’s grade being the lowest of all. Now, the last section is left as (X,Y) as we can no longer predict anyone’s grades in this situation as it would depend on their reading abilities. 


Let us try to what is the favorable action in two independent situations for Sasanka i.e. When sample is studying and when it isn't. 

Case-1: Sample is not studying.
Even though (9,9) is a favorable situation for all but, since, Sasanka is driven by the selfish motive of getting good grades he will always try to make use of this easy opportunity to score a 10. Thus, it is evident that he should study when no one else is.


Case-2: When Sample is studying
Now, even though we can’t determine what Sasanka’s grade are going to be in the last case. But when he was not studying he was at bottom with minimum grades so it is self-evident that by studying Sasanka can only improve his grades not worsen it.So, once again, studying is the favored option.

Conclusion:
So, here we have come across a strange observation, popularly, known as condition of strict dominance i.e. when one choice in a situation clearly dominates the other choices for a person irrespective of what others involved in the situation decide to do. Here, too, the choice of studying is always a better choice irrespective of what others do. So, unfortunately, we are forced upon with the conclusion that our subject Sasanka Bhagabati’s studying was justified(and yet I am writing this blog while my end semesters are on). At the same time, this result helps you in appreciating the effectiveness of this grading system which leaves you with no rational choice other than studying if you seek good grades. 


There are several amazing concepts in our day to day life behind which are veiled simple explanation and ingenious thoughts. All you need to do is observe intently, search inquisitively and you may stumble upon the logic of life.

   
     

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