Students get class-wide As by boycotting test, solving Prisoner's Dilemma

Johns Hopkins computer science prof Peter Fröhlich grades his students' tests on a curve -- the top-scoring student gets an A, and the rest of the students are graded relative to that brainiac. But last term, his students came up with an ingenious, cooperative solution to this system: they all boycotted the test, meaning that they all scored zero, and that zero was the top score, and so they all got As. The prof was surprisingly cool about it:

Fröhlich took a surprisingly philosophical view of his students' machinations, crediting their collaborative spirit. "The students learned that by coming together, they can achieve something that individually they could never have done," he said via e-mail. “At a school that is known (perhaps unjustly) for competitiveness I didn't expect that reaching such an agreement was possible.”

The story of the boycott is a sterling example of how computer networks solve collective action problems -- the students solved a prisoner's dilemma in a mutually optimal way without having to iterate, which is impressive:

“The students refused to come into the room and take the exam, so we sat there for a while: me on the inside, they on the outside,” Fröhlich said. “After about 20-30 minutes I would give up.... Then we all left.” The students waited outside the rooms to make sure that others honored the boycott, and were poised to go in if someone had. No one did, though.

Andrew Kelly, a student in Fröhlich’s Introduction to Programming class who was one of the boycott’s key organizers, explained the logic of the students' decision via e-mail: "Handing out 0's to your classmates will not improve your performance in this course," Kelly said.

"So if you can walk in with 100 percent confidence of answering every question correctly, then your payoff would be the same for either decision. Just consider the impact on your other exam performances if you studied for [the final] at the level required to guarantee yourself 100. Otherwise, it's best to work with your colleagues to ensure a 100 for all and a very pleasant start to the holidays."

Fröhlich's changed the grading system -- but he's also now offering the students a final project instead of a final exam, should they choose.

Dangerous Curves [Zack Budryk/Inside Higher Ed]


  1. Doesn’t prisoner’s dilemma assume that the other prisoner(s) is/are not privvy to what is going on in the other room? If the students can see each other and police the situation, it’s not really a prisoner’s dilemma, no?

    1. It’s not. Prisoner’s Dilemma is an interesting game. Turns out the only winning move is not to play. These students decided to play a different game instead.

    2. Exactly.  

      Moreover, the students were ready to directly intervene if/when someone decided it would be in their best interests to actually take the exam.  

    3. It’s the lack of communication that makes it such a dilemma. :-)

      The ‘problem’ is created because the players cannot communicate and cannot see what the other one is up to.
      The problem is ‘solved’ by opening up communications for a combined strategy and moderating to see that it’s carried through.

      To mix allusions, it’s a Gordion solution. But the dilemma is certainly solved.

      Most of the naive solutions to the PD involve coming up with clandestine ways to pass notes or collude in some way. Maybe those solutions were right all along!

    4. There are multiple versions of the prisoner’s dilemma, some of which involve limited communication but all of which involve some degree of trust.

      This situation does require some trust in the organizers (who if they were sneaky could skip out on class and take a makeup test, guaranteeing someone a perfect score, not to mention the possibility of someone refusing to go along with the idea but only near the end of the test with, say, 30 seconds left to go), so I think you can chalk it down to “prisoner’s dilemma variant.”

      Most real life examples of prisoner’s dilemmas involve some chance for communication anyway (the last article BB did about a gameshow PD being solved involved communication)

      1. This was not a PD for several reasons: communication (which you and others here have addressed), non-PD payoffs, N asymmetric players, and ability to retaliate (kinda like iterated PD). The Defect strategy would be unattractive, as it would offer no increase gain (like an A+). OK, assume that some sadist might like not just to get an A, but for everyone else to get an F, so he gets a utility bump for defecting. But what if others did that? Then the sadists are taking a chance. Presumably the students are not identical, but fall into a bell curve of abilities, so the best of them (and probably that information is common knowledge) would have an advantage. If the top student was also a sadist…he might defect. But the other students would still be around, not stuck in prison, so they’d throw him a blanket party. They probably all signed this agreement in blood. Lots of communication going on in this PD variant….

        1. Like I said before, there’s nothing significant about including multiple players or even direct communication. Various social psych PD experiments use multiple players (my psych 101 teacher had a hilarious PD class demonstration that we *almost* managed to win), and the aforementioned gameshow had lots of communication (I wish I could remember the name… I think it was British) The payout structure works if you either account for multiple participants (e.g. as you add people the anticipated payout goes down), OR grade the entire class on a curve as well. 

          The last factor, the policing, is probably the most disrupted, but it could be avoided by a sufficiently clever “sadist” (such as promising to go along and not showing up that day, but having already taken the test in advance). 

    5. They were presented with a situation that was intended to be a prisoners’ dilemma, but like James Kirk they modified the conditions of the test allowing everyone to win.  A beautiful implementation of a Nash equilibrium.

  2. Any one of the students could have walked into the class and sat the test, guaranteeing herself an automatic A and all her classmates an automatic F.

    1. But for the holy spirit of John Nash shining a little light down on every one of their innocent heads.

    2. But in that case all the other students, who were poised outside for just such an occurrence, would also have taken the test. It’s still impressive, but it’s impressive as a simple strike, not as a prisoner’s dilemma situation.

      1. Yeah, I don’t see the payoff benefit for the first person to enter the room.  If they stay out, they get an A.  If they enter, so does everyone else and their chances of getting an A decrease.

        I think what would make it more of a traditional prisoner’s dilemma would be if all students were separated without any form of communication (like in cubicles or different rooms), and if the payoff for everyone boycotting wasn’t an A, but say, a B. (like if the curve was such that the median score was a B and everyone was graded relative to that, in which case, all 0’s = all B’s).

        1. >Yeah, I don’t see the payoff benefit for the first person >to enter the room.  If they stay out, they get an A.  If >they enter, so does everyone else and their chances >of getting an A decrease.

          Well…there may be things other than just the grade that are perceived to have value –
          1) Taking the test to get a grade that feels deserved.  2) Being the person to get the only A grade, which could e.g. improve their chances when competing for a scholarship/job.

          1. I’ve never met a student that didn’t feel they deserved an A.  I’ve also never met a 1000 level course I couldn’t sleep through and achieve said result.

    3. True, but their story wouldn’t end there. Comp Sci typically involves group work, and making enemies of your peers is a bad strategy for success. 

    4. These kids today and their socialist values.  Doing what is best for the group as a whole.  Commies!

      1. Just so happens that what is best for the group is best for themselves. Would they have done it the same way if everyone else was going to benefit and they would be left out though? Then you would have true commies. This is just more self-interest.

        1.  Well, for the brainiacs in the class it is clearly *NOT* self interest. They consciously allowed everyone else in the class to catch up to them, which by most metrics would be seen as individually harmful.

          1. Even if you were a “brainiac”, you would still not get a perfect score under the professor’s system of grading all people off of the top score. This enabled all of the “brainiacs” to get the perfect mark. It’s still self interest, even for them. Sorry.

          1. That’s why everyone waited outside of the door. If one selfish person went in then they would all go in and take the test. If this had been an online test then we would have had something to really talk about because all would have to separately depend on the other to keep their word. That would have been impressive. This is just students with solid analysis that saw a flaw in the professor’s system and came together to guarantee themselves good grades. Since it was a one time thing (for the final) they all came out of it well. The professor changed his grading after this, which is good. His grading system was douchey.

      1. I didn’t even notice it. Maybe that’s because I’m a woman and I take for granted that I exist. How “progressive” of me.

        1. Given the context, my original statement stands.

          Yours is erroneous, however.  “Sarcastic” would have been a more appropriate term to use. 

          1. What’s erroneous of mine? That I didn’t notice it, that I take for granted that I exist, or that I’m progressive?

            Read this sarcastically, by the way. For great effect, roll your eyes as you do so. That’s what I’m doing.

          1. Seems like any reaction except acceptance is overreacting here. The comment was pointless, was it not? Why draw attention to the pronoun unless you wanted to make a point?

            Well. The point was made, and I responded to it because it was, all in all, a useless thing to say unless you *wanted* to draw attention to it.

            So I’d say that the comment got exactly the response it was fishing for. Glad everyone is happy now!

          2. The point is that it is a sorely overlooked point.  

            Yes, I want to draw attention to the fact that science and technology can be associated by feminine contexts.  Don’t you?  Why did Cory specifically chose a feminine pronoun despite it being atypical?  Was it a conscious decision — if so, bravo. Was it unconscious — if so, even bigger bravo.

            The kudos were for making an atypical association in the first place.  If more people do it, it might not be so atypical.

            Or we can carry on with preconceived notions and gender bias, if you’d like…

    5. This seems more like a classic strike/anti-scab line outside a factory than prisoner’s dilemma. Sure, it’s not so much the rough-and-tumble union-buster of the early 20th cen. as a rarefied classroom, but there’s still that risk of harm (social only instead of social and physical) you take on breaking the union line.

      (NB: This is not to denigrate unions; I’m just drawing a comparison that I think is more apt.)

  3. I recall a story about a teacher who wrote trick questions, graded on a curve, and penalized wrong answers.  Eventually, the cutoff between A and B dropped below zero.  At the next exam, one student wrote her name at the top of the exam and handed it in otherwise blank.  She got the high score.

  4. > The students waited outside the rooms to make sure that others honored the boycott, and were poised to go in if someone had.  

    That phrase can be read several ways. One way is anyone who attempted to enter the room was blocked which, if true, undoes the kumbayesque aspect of the story.

    1.  According to other articles I have read, the students were ready to take the test if anyone person elected to do so, not to try and block anyone from entering.

  5. I see no prisoner’s dilemma here.

    There’s no benefit to defecting unless you think the teacher will change the rules retroactively.

    Furthermore, they were there and could go back to normal behavior if there was a defector.

    1. Students cooperated with each other. If anyone were to defect they would go into the exam room and write it, earning the highest grade and ensuring that everyone else failed the exam because of this act.

      But since they all decided to cooperate by not writing the exam, all of them benefited.  It is clearly a prisoner’s dilemma.

      1. Yes, but if they DO cooperate, they still get the highest grade in the class. In a Prisoner’s Dilemma, it is always beneficial to defect (screw your friend). In this case, defecting doesn’t help you (you have an A if you don’t defect, and an A if you do), so it’s not a prisoner’s dilemma.

      2. There are a few things that make PD.  The most important element in my mind is a reward if you defect and others cooperate.  This didn’t have that.  Defect, and everyone defects with you, and you battle for an A with blood and tears.  Cooperate, knowing that you can change to defecting if anyone enters the room, and you all get an A.  Cooperation is the only rational choice.  Not only does it offer the best reward, an A, but if you see someone being stupid and defecting, you can go defect with them.

        If the prof wanted to make it more of a PD type scenario, he could say that if everyone gets a zero, everyone will get a B.  Further, the test will be a take home test that is e-mailed in.  Now, you have no chance to know if someone is defecting and thus can’t switch to defect yourself, and the reward for defecting if everyone cooperates is an A, which is better than cooperating that gets you only a B and the possibility of an F if someone defects.

    2. Not to mention they could see what each was doing, and there was a fair amount of peer pressure involved to boot.

  6. Spock: Furthermore, you have failed to divine the purpose of the test.

    Kirk: [seething with anger] Enlighten me again.

    Spock: The purpose is to experience fear. Fear in the face of certain assessment. To accept that fear, and maintain control of oneself. This is a quality expected in every computer-science student.

  7. The linked article doesn’t seem to say–was this a protest of some sort, or more of an intellectual goof/”let’s see if we can do this” thing?

  8. Is grading on a curve still common? I’m pretty sure it was against the rules at my University. If it wasn’t against the rules, it must have at least been frowned upon, since none of my teachers did it.

    1. For some of the more challenging tests I’ve taken, it was a way of insuring that at least somebody passed the test.  

      1. Yeah, curves can be a good thing on tests where scoring 80% is a sign of astounding effort and talent. But I remember curves giving me a lot of stress because I could not depend on other students doing poorly so it motivated me to study obsessively to try to ensure that if anyone was breaking the curve it was going to be me.

        BTW, I’m pretty sure this is an effective strike, but not a prisoner’s dilemma because there was open communication. Collusion makes everything better!

      2. It seems to me that it’s more of a cop-out for bad teaching though.  If the whole class fails a test (or only achieves a lowish mark) then either the teacher did a bad job teaching or the test did a bad job of testing. Either way, the prof should be held responsible, not just fiddle with marks so that it looks like they did a competent job.

        1. It makes me wonder what the point of grading is if you’re not going to have some established standards. As someone who’s been in a number of hiring interviews, I’m not that thrilled about college graduates whose skills are at grammar school level.

          1. The test I’m thinking of were graduate school level.  In some ways, the professors were experimenting on us to see if we could do phenomenally difficult problems.  If we all could, great,  If we couldn’t, that’s what the curve was for.  

          2. To a scientist, the point of the curve is obvious. Imagine trying to study the length of lizards, but you only had a 6″ ruler. You’d have this big list of “lizard lengths” ranging from 2″ to 6″, then a huge number of “more than 6 inches” – the data would be useless.

            The same is true for grading, if people get 100% scores, then you can’t really analyze the performance of the group because they have brickwalled your dataset. If the test is designed to result in a 70% score for someone who really understands the material, it allows you to see who is above that (and maybe why), while not giving Cs to the people who have done what you asked them to do.

            It is uncommon for the curve to be so arbitrary (like in this professors example) – usually it is a bit more structured, and still centered around some pre-determined standard of success (that just may be a value less than 100%).

          3. What’s the point? For the professor to have some intricately detailed knowledge of the capabilities of the students is useless to anything except the professor’s sense of self. Grades should be objective (for material that can be graded objectively.)

        2. At the college I went to, the rate for passing O-Chem the first time through was 33%.
          Some subjects are very difficult, even for smart people. Having to go over the material a couple of times to really learn it is a reasonable requirement.  No one has the right to assume they will pass every test and every class just because they “studied”.

        1. A particularly difficult test I’m thinking of went beyond simple regurgitation of facts, consisted of complicated sets of word problems on biophysical chemistry of water.  The class was taken by PhD candidates and MD/Phd candidates. Simply having read  the textbook (written by the professor who taught), was no guarantee of passing.  Open book test.    The members or the class had also taken basic biochem with the medical students, we used to make fun of their poor grasp of biochemistry. Nobody in the class was fucking stupid.

    2. There was the way the school I went to that did it, all of the upsides, none of the down.

      Some scores were guaranteed. 80 was always (at least) a B, 90 was always at least an A. If a prof wanted to move it down, they were welcome to, but they couldn’t make it any worse for the student.

    3.  I’m not sure how common it might be today but I’ll relate a brief experience from my freshman year at Johns Hopkins.

      As an engineering student I was subject to mandatory freshman physics 101 held a few days a week at 8am in a large lecture hall. All my fellow students were convinced this was by design – easy to miss, easy to sleep through. Weed out the uncommitted fast.

      But, tests were graded on a curve. I’m not proud of it but on the first test of the fall semester I received a score of 17%. Luckily that was a passing grade on the curve . It also scared the hell out of me, having never scored so poorly on anything in my life. By junior year I was generally over 90% for all tests in my core curriculum classes. Still remember that 17% mark though. Ouch!

  9. “Yes, vell, zee shtudents may heff beaten me zis time, but next shemeshter’s test shall not be zo easily eshcaped from.  No vun makes a fool of Dr. Peter Fröhlich, *lightning strike, clap of thunder* Professor of Computing Shciences!”

  10. FALSE.  In the prisoner’s dilemma the prisoners are NOT allowed to communicate with each other — this was just *stupid* college kid scheming and peer pressure (would you go in to the class with a bunch of your classmates staring you down at the door?).

    Why is it stupid?  Now bunch of kids who can’t program can go on to the next level course — let that sink in — an accredited university is claiming a bunch of kids who can’t program CAN program — that NOT ONLY lowers the value of any degree they may have — but also of their schools reputation — and their potential employability…

    But let’s take a more short-term look at it — now, the next level course, is going to be filled with kids who couldn’t pass the first level course (it always is with programming classes, somehow the idiots get to move on before they finally give up — but I imagine this makes the problem an order of magnitude worse — at the least) — this means the professor and the rest of the class have to spend more time reexplaining the basics over and over; and just imagine — what if one of these dunces is paired up with you for the end-of-semester project?  I mean, there was always the chance that you’d get stuck with one of the few kids that some how mad it to level 2 or 3 without actually understanding programming — but now — at level 2 you’re going to have twice as many idiots, and a few might even make it to the level 4 course…  what a waste of time and money.

    School isn’t about grades — grades are a metric to judge how well you did in a subject.  This is like a fat person writing down that they weigh 120 lbs on their driver’s license — it doesn’t change anything — they’re STILL fat; “the map is not the territory”.

    1. I counter that by merit of gaining admission to John’s Hopkins alone, these kids are more than capable of passing a 1000 level Comp Sci course.

      1.  As a grad, I’d like to thank you for remembering the oft-forgotten “s” but instead I’ll (gently) chastise you for the apostrophe. The gentleman’s first name was simple “Johns.”

      2. The professor was a Johns Hopkins professor — it did not say the students were enrolled at Johns Hopkins as well — many professors have more than one school they teach at — usually news articles just grab the one with the biggest name and publish it as that. (Journalists are notorious for these kinds of errors.)

        At any rate — anyone who thinks that what was described in this article is somehow related to the prisoners’ dilemma is not fit to be passing any university level courses — let alone programming ones.

        EDIT: And seriously — by your logic — anyone who takes the class, by virtue of being in the class, is able to pass said class — if that were /really/ the case why have a final exam at all? — Spoiler Alert: the harder the school is, the more drop-outs it has — the level 100 and 200 courses are there to weed out the fucktards (i.e. your reasoning is completely the opposite of reality).

    2. Now bunch of kids who can’t program can go on to the next level course — let that sink in — an accredited university is claiming a bunch of kids who can’t program CAN program

      You’re talking nonsense: where is your evidence they can’t program? Not taking a test is not the same as failing a test. Their professor gets to make up the testing rules as he goes along, and evidently his judgement is that the entire class is fit to pass. If he hadn’t spent a year teaching them, he’d have nothing to base his judgement on and he’d be a fool. How much information are you basing your judgement on?

      1. There’s always someone who passes a course without the skill (the prof. graded on a curve for gods’ sakes) — this just makes the problem worse. — I mean, fuck, they can’t even tell that what they did was completely unrelated to the prisoner’s dilemma, what makes you think they *can* program?

        As a professional programmer, I interview people all the time who claim to be the next digital messaiah, and yet when asked to demonstrate their skills, they can’t program their way out of a wet paper bag!

        Call me a skeptic, but I’m not going to just assume on faith that someone has a highly specialized skill without any demonstration or proof of said skill (especially when most of the people who claim to have said skill — even at the university level — don’t actually have it) — And again — these guys apparently aren’t even bright enough to figure out that this isn’t the actual prisoners’ dilemma.

        This is complete bull donk, yo’.

    3. You make the point that this could allow underqualified students to slip on to the next level course, but it is also entirely possible that the students paid attention in class and would have done pretty well on the test if they took it.  You have no evidence that these are, “A bunch of kids that can’t program.”  For all we know they could be great programmers.  They simply were intuitive enough to see that there was no advantage in taking the test.  Why would we expect a rational person to do something which we know confers them no benefits?  Fröhlich realized that his students were employing the optimal strategy for his rules and adjusted his rules so that the students would no longer have an incentive not to take his test.  Overall I’d say that both the professor and the student’s showed insight when solving a problem in unconventional ways.  Being able to address a problem in a way that hasn’t been done before is a good quality for an engineer to have.

      1. I already outlined several benefits.  A rather big short term advantage would be being able to take the next level class without the dunces from the previous level holding everyone back.

        A good quality engineer also knows how much damage unqualified idiots can cause.

    4. I’m guessing there have been other grades (midterm, final?) and also I can’t help but imagine the students will end up being testing one way or another within the program. Furthermore, since they were all there ready to go in and take the test if one of them wanted to, there is an implication that most of them had studied to the extent they were going to anyway. 

      This is a bunch of kids getting to work together in order to test a social experiment and feel on top of the world for a few days during what is likely the only time in one’s life where that is possible. Kudos to them.

  11. Read this a week or so ago via Stephen Downes.  Was particularly interested in some of the comments critical of the students receiving an A since the aptitude they demonstrated was unrelated to the learning objectives of the class itself.  

    I’m not so sure.

    The students effectively formed what can be thought of as an ad hoc optimizing compiler: They minimized both the time and memory required to execute a task by altering the instructions based on known values and achieved an equivalent (perhaps better) output while employing fewer resources to do so.

    Seems quite reasonable to me. 

  12. I can’t help but sense a Ferris Bueller character leading the pack.  Ed Rooney would’ve responded differently, and more amusingly.

  13. Is there any data on how they performed on their other exams? I’d be curious to see if the decision to abdicate/boycott the exam let them focus on the other exams that term with greater intensity, or if the stress of pulling such an audacious stunt just made things tougher. 

    1. You exclude the possibility that they studied exactly as they otherwise would have because they couldn’t know for sure that they wouldn’t have to sit the exam.

  14. Cool teacher being accepting of his student’s ingenuity.  Still though, I would’ve said “No, seriously you need to take a test so I can see if you actually learned the material.”

    Maybe they just need to go back to the old system of score x to y is this grade, y-z is this grade, etc.

  15. So at my university any student with learning issues or any kind of accomidation would not be privy to this. Thus the 2-3 students who used the accomidation services would screw over the rest.

    Furthermore, when grad studies comes calling usually your RANKING in a class matters more. If you’re even ranked that’s not useful either.

    1. Meh. First of all, every department/discipline is different. Second of all, grad school picks people for a variety of reasons, of which ranking is NOT necessarily number one. Third, it is who you know. Finally, this will not affect their rank. They all get As and it will be as if having no impact on that group of individuals. 

  16. This is all well and good for academic purposes, but these students should be prepared for the “real world” where corporate performance reviews (essentially working life’s test scores) can be an absurd curve. Where I work, each manager has to assign X% of her employees a “far exceeds expectations”; X% an “exceeds expectations”…and so on to the lowest level.  Thereby, everyone who is not in the top percentile is scored relative to the top.  And, trust me, every group has an over-achiever workaholic who regularly takes on extra projects and works 60-80 a week.

    1. I hate those corporate score matrices with a vengeance.  They kill productivity and even the little creativity needed in fields like finance. They teach people to lie, burn, kick and stab their competitors, which overall brings the entire firm down a notch.  I’ve seen people at the top of the ratings bankrupt their division by getting their sums wrong.  Analysts who are proud of their 80 hour week, but who take three days to turn around the easiest thing.

      And by ranking people within management groups, you get a total schism with the true capabilities of people outside those groups.

      I’m hoping the advance of information capabilities and manufacturing technologies means large corporations are headed for the bin.

  17. The Science/Math teacher (he taught: Algebra-Calculus, Physics, Chemistry and advanced Geology) at the tiny high school used the example of “test-curving” as the basis for his discussion of the bell curve and it’s general scientific applications.

    Then he plotted the standard distribution of test scores from all of his classes.  They formed a distinct reverse bell curve, with clustering at the ends and sparse points in the middle.  “In my classes, people either seem to get it, or they don’t.”  I observed that is almost every rigorous class I ever took: a majority clustering around the top of the decimal scale, a minority clustering at the bottom.  His argument, which convinced me, was that Pass/Fail was a more meaningful grading system than our “competitive” or “ladder” system.

  18. If the students are graded on a curve and this test was only one of the components of the final grade, then the fact that they all got an A on this test would not change their class grade at all. 

  19. If nobody took the test, couldn’t the Prof have just failed the lot of them?

    The true prisoner’s dilemma is if all students had agreed to go in and sit the test, but just write their name at the top of the page. Assuming none writes anything more, they will all score the same, but if one answers just one question then they will get the A.
    Still not quite a true dilemma, as the students can observe if one of them is going to betray the others. All it would take is one to start doodling in the margin for everybody to start furiously answering the questions.

  20. ‘Kelly said the boycott was made possible through a variety of technological and social tools.  Students used a spreadsheet on Google Drive to keep track of who had agreed to the boycott, for instance.  And social networks were key to “get 100 percent confidence that you have 100 percent of the people on board” in a big class.’

    Was attendance taken?  If they had ‘100 percent confidence’ that no one would break their agreement, why sit outside and watch each other?  They used social tools to take a poll, but these are not a guarentee against a sudden bout of grade point insecurity. 

     I’d have been interested in reading the argument from which they decided to either succeed together, or fail together (except the Judas).  We have a few social problems in this country in need of such voter solidarity.  The professor can change his own rules against ‘gaming the system’, government moves more slowly.

  21. The communication and observability have nothing to do with this not being a prisoner’s dilemma. For it to be a PD, it has to be a strictly dominant strategy for the students to deviate. If students only value their grade and not their relative grade then deviating to sitting the exam does not provide a strict incentive: in either case they get an A. As described this is simply an equilibrium of a game. 

    If however, the students value their relative grade/position then they would have a strict incentive to deviate and get the only A. This would move it to something closer to a PD. However, there would still exist private information and uncertainty about the outcome. Given the observability of deviations, a student may not wish to deviate. Deviation triggers everyone to write the test and the student may end up with a grade less than an A. This interpretation adds richness and detail absent from the classical PD (for example this is now a dynamic game and not a simultaneous move game.)

  22. Grading curves generally suck.  They do not grade the student’s ability to show they know the material or not.  Nor, if the intent was to grade merit, show the work the student put in.

    These students should be given academic distinction and commendated for original thinking(for the trekies, though it’s not a no-win situation).

    And more importantly the entire grading system should be revised.  Because the only real solution is to game the system for everyone to be graded A.

    1. I have manual disabilities which can sometimes make it painful to write or type. I learned to do a lot of problems in my head, if need be, and I got burned for not showing my work.

  23. “Excellent… this really is an ingenious solution.  Who came up with it?”  (no one answers) “Oh, come on, I like it.  It shows you’re working together.  I give you my word of honor, the person who came up with it will not be penalized for it.”
    “It was Bill, sir.”
    “Great.  Don’t worry, I won’t penalize you.  For your ingenuity, you get a bonus point! 

    Oh, look at that.  That means Bill got one more point than everybody else.

    Which I guess means he gets the A.

    The rest of you unfortunately have zeroes.”

      1. Well, to me, that’s less interesting.  All that shows is “don’t even bother trying to get clever, I’ll just arbitrarily change the rules to screw you over.”  Which is probably a fair lesson to learn in life, but it reflects badly on the teacher. 

        Sending a message “it’s all well and good to game the system, but always remember others can game it too, so you’d better be REALLY clever about how you do it” is more appealing to me.

        (And of course, if I were the teacher in question, I’d offer a make-up test for the zeros, with a new set of rules for the grading curve… Bill would still get the A though, because it is a brilliant well-executed solution)

  24. In art school, the best artist in class might not get the best grade because the teacher thinks that he’s “trying too hard” or possibly “needs to explore a looser paradigm” or maybe the teacher “has higher expectations of him.”  Or possibly the student is too hot.  Or not hot enough.  Or made the tragic error of being a much better artist than the teacher.

  25. That the teacher let this stand is bogus.  Does he really value his course so lightly that he allows his students to get grades they don’t deserve due to a math trick combined with social coercion?

    He should’ve just changed the structure right then:   all 0 grades get an F, all non-zero grades are graded on the curve.  Or he shouldn’t be teaching at all.

    Also: You kids– get off my lawn!

  26. This illustrates “divide and conquer” versus the power of group action.

    If one person refuses to pay his taxes he will likely go to jail. But if everybody refuses to pay what will the authorities do then?

    This is how centralized authority succeeds. If you keep the governed population separated into individuals and small groups you can easily subjugate them through fear. But if they organize into larger groups it becomes more difficult to pick them all off.  

  27. They won’t feel quite so bright if any future tight-ass employer ever asks for their transcript, the list of raw scores for all of their courses over all of their years along with the break down of weightings as it will show they received a zero score. This will almost certainly be questioned at which point said tight-ass employers (who also tend to be the best when it comes to salary) will discover that their future potential employee is quite happy to strike, which whilst I might consider a perfectly sensible course of action tends to get frowned at in the US as I understand these things?

    1. I am paid very well, and have never had someone pick over my transcript like that. If they did, I’d probably not be interested in them as an employer, since they also probably want your facebook password and keys to your bedroom (both of which cost far more than they are willing to pay). Smart employers value teamwork, communication, creativity and problem solving – people who are good at that are expensive. People who just sit down and do as they are told are a dime a dozen.

  28.  In my university you don’t receive a grade if you don’t take the exam. In this case it would have been a prisoners dilemma because everybody would have been required to enter the room and return blank exams. And then it would have been only trust between them.

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