Why I give my students a ‘tragedy of the commons’ extra credit challenge

https://www.washingtonpost.com/posteverything/wp/2015/07/20/why-i-give-my-students-a-tragedy-of-the-commons-extra-credit-challenge/

by nkurz • 11 years ago

66 86 11 years ago

washingtonpost.com

justonepost2• 11 years ago

Don't the students just get together and do a lottery? And in RL tragedy of commons, it's rarely anonymous.

moistgorilla• 11 years ago

And then one person says that they chose 6 points and haven't won it via lottery. The other students can't retaliate because the only way to get back at her would be to take away points from the entire group

6d0debc071• 11 years ago

They can retaliate, there's simply a cost associated. That's one of the reasons this is a poor exercise: In iterative games it's often worth making sure people know that certain kinds of behaviour don't work - even where you have to harm yourself in order to do so. Otherwise you'll always be held hostage by those willing to move the costs closest in time.

I suspect this is why hatred and resentment are part of our make up.

andresmanz2• 11 years ago

I’ve been giving it to students since 2008, and only one class has successfully mastered the challenge.

That's a real surprise. The 2 points option is the safe one, so everyone should go with that. Sure, I could assume that all (or most) of the other students think so and just get the 6 points myself. But then again, chances are that the other students think the same. So let's just go with the safer 2 points.

justonepost2• 11 years ago

No, the safe option is to get organized and plan out who is going to chose the 6 points. That way, you know if you secretly chose the 6 points when you were supposed to get 2, you will get nothing. Then it doesn't become tragedy of commons, but rather an experiment with vandalism.

The experiment, IMO, isn't valid. In RL tragedy of commons, the selfish don't really suffer that much .. it's usually everyone else that does.

scottfr• 11 years ago

You could have an auction for the 6 point slots, with the proceeds being divided and distributed to the group.

andresmanz2• 11 years ago

I'm sorry, I assumed you're not allowed to organize. You're right, of course, at least if everyone in the group is reliable.

fweespeech• 11 years ago

The experiment, IMO, isn't valid. In RL tragedy of commons, the selfish don't really suffer that much .. it's usually everyone else that does.

Actually, I'd say that increases the validity since they do it even tho they know it is more likely to have negative consequences than RL.

Amorymeltzer2• 11 years ago

No, the safe option is to do well in the class and thus not give a fuck about a measly 2 or 6 points on one (admittedly important) paper.

I've had teachers offer various concepts like this over the years. One gave out simple vouchers for various points as awards for "fun" "games". I asked him if I applied ten points toward a 97/100 exam, would it cap at 100 or go to 107? He told me to sell the voucher to someone who needed it more.

Best lesson I ever got.

bradleyjg• 11 years ago

You want something that is perceived to be fair in order to minimize the chances of someone deciding he'd rather get nothing than 2 points.

If I were in the class I'd propose a weighted lottery where everyone had a chance to be one of the sixes but those with worse grades had a somewhat better chance. While there might be disgruntlement over the weight, I'd guess it'd be less severe than if someone that an entire fairness factor was being ignored.

An interesting questions would be what to do if someone issued an ultimatum to the group "give me one of the sixes or I will ruin it for everyone". I'd think in that case every move ends with no one getting any points.

s73v3r4• 11 years ago

"No, the safe option is to get organized and plan out who is going to chose the 6 points."

If you think that's a safe option, you've clearly never dealt with large groups.

deelowe2• 11 years ago

Yep. A better example would be to make it so that 10% of the students get 6 extra points and the rest get none if more than 10% choose 6 extra points. This way everyone that chooses 2 is punished if the go over.

baddox• 11 years ago

I'm wondering what "mastered the challenge" means. To maximize utility (naively assuming that points == utils), you want exactly 10% of the class to choose 6 points, and the rest to choose 2. Perhaps a "perfectly cooperative" class would give the larger payout to the students with the lowest grades.

vm• 11 years ago

"People conformed to the group’s positive behavior."

People are more likely to respond to social pressure, than to appeals to "do the right thing." Valuable lesson for startup marketing... and maybe even pricing.

TimPC• 11 years ago

I think this would be more interesting if there was a way to explicitly declare the marks post-curve. In the event the distribution of marks is smoothed to any sort of typically college distribution it's entirely rational to just select 6 points and not care whether 10% of the others do or not. Selecting 2 leaves you open to a worse result on a curve, but selecting 6 is nearly risk free if the distribution of marks is precisely controlled anyway. 2 marks when the average pre-curve goes up more than 2 and the average needs to be fixed post-curve is a really crappy proposition.

warkdarrior• 11 years ago

The article specifically state that the grades are not curved.

cortesoft• 11 years ago

It says in the very first paragraph of the article: "All selections are anonymous, and the course grades are not curved."

aaronchall• 11 years ago

I suspect that professors aren't upset that the game theory is validated, but rather they're upset that the students haven't done the analysis and thus choose to change the game by introducing structural changes.

Smushman2• 11 years ago

I see it as a simple equation. I don't think it says more than that about people.

Can someone enlighten me as to why a 90% break point? Why not for example 50%? Is it because 90% introduces some level of collaboration or vice versa?

Sans collaboration or any other useful information (people I may already know in the class, etc.), I would say at best you have a 50/50 chance of a total stranger choosing the option that is better for the common good. That number is based on it being college age students. If it were the general public at large I would estimate at least 60% would choose the more personally beneficial option.

Am I just extremely pessimistic? Please give your thoughts.

Amorymeltzer2• 11 years ago

I imagine it's because 10% kicks in really easy and requires the you to stop and think about your actions. If you need a full 50%, screw it, go for 6, almost everyone else will. At 10%, though, you stand a fairly good chance of being the tipping point.

Smushman2• 11 years ago

With the given caveat that any more than 10% of the group requesting 6 voids the whole thing, it seemed a foregone conclusion to expect 0 points. On the off chance I am wrong about that, I would end up with 6.

So the final conclusion I had == highly likely 0, but a very small chance of 6.

2 points were statistically ruled out the moment I heard 10%.

I see how the thinking re: screw it though also is valid. Thanks.

nadams• 11 years ago

I think we are missing some context - and that is very important to show if the students could communicate/collaborate (such as a homework question) or a test question.

I would say at best you have a 50/50 chance of a total stranger choosing the option that is better for the common good.

It depends on factors such as the student's current grade. I would argue you are more likely to choose 6 if you have a lower grade.

If it were the general public at large I would estimate at least 60% would choose the more personally beneficial option.

Here is an related experiment. Choose N random people, and offer 2 choices: $50 or $200 and run the same experiment.

Here is an interesting question - are people less "greedy" if the prizes/points have a greater span? Such as instead of 2 points and 6 what about 2 points and 20 points.

I think the experiment is interesting any way you think about it.

hcurtiss2• 11 years ago

Cooperative behavior is particularly difficult when the stakes are very high. In the context of climate change, increased energy costs have very real impacts on people day to day, particularly in developing countries. For this reason, it's difficult to imagine those countries would behave cooperatively (even if a figurehead signs a document promising they will). It may be that the better strategy is to have the best grades in the first instance, knowing that noone will get extra credit. That is, build a strong and resilient economy so that you are better prepared to deal with, and adapt to, the inevitable challenges associated with global climate change.

pitt19802• 11 years ago

I wonder if the prof has given any thought to what made that one class unique, if there were any factors that distinguished it from his other classes

off the top of my head, I wonder if it was a particularly small class

though I could imagine a lot of other potentially relevant factors

sosuke2• 11 years ago

But the challenge doesn't make sense, there isn't much risk, no fear of being known. Economic studies have covered this before, would you rather make $50k where everyone else makes $75k? or make $40k where everyone else makes $30k and people pick the latter because they want to have more than their peers. Everyone getting the same points doesn't change anything relative to those around me.

In a paper score, assuming 100, 2 to 6 points just doesn't mean much. 6 points is greater than 5, it could take me from 84 to 90! I'll go for the gusto and try for 6. 2 points just doesn't make any difference, and I wouldn't feel any better getting 2 points.

hcurtiss2• 11 years ago

Agreed, but your assumption may not be correct.

sosuke2• 11 years ago

You're right I vaguely remember seeing a very wide range of top scores possible. From 25 - 200

notahacker• 11 years ago

To pick up on the point about positional goods, everyone failing the class actually improves the ranking of [up to] half the classmates. If the points count towards some total score and there's some kind of calculation to normalize grades across the student population, everyone failing the class might actually bump up the overall grades of some of the weaker students in that class. Conversely, in this situation nobody benefits from everyone being awarded two additional points.

xg15• 11 years ago

I wonder if jealously could also play a role here. The option to choose 2 points doesn't seem completely risk-free to me from an "emotional" point of view:

Suppose you choose the 2 and the class was actually disciplined enough that the points weren't lost. Then you might think that there might very well be a small group of students who got 6 additional points because they were greedy and you were not.

If students underestimate the risk of all points getting lost, they might in turn overestimate the "risk" of getting less than others if they play it safe.

haberman• 11 years ago

Congratulations, you just independently discovered the sixth paragraph of the article!

"But many students choose the seemingly selfish option. Why? Perhaps to increase their own grades, or perhaps because they fear that they will be taken advantage of. No one wants to be the chump that chooses fewer points when they could have had more."

jedmeyers2• 11 years ago

Get together, auction the 6 point slots. Then, depending on whether it works or not, either evenly distribute proceeds to everyone or return the money to the auction winners.

ryan-c• 11 years ago

Or more generally allocate the 6 point slots in advance - how they're allocated doesn't really matter. The point is that everyone knows that if they are supposed to choose 2 points and instead choose 6, nobody gets anything. Someone still might blow it for everyone out of spite, though.

jedmeyers2• 11 years ago

By involving the auction you are adding an additional incentive to not blow it for everyone - you are getting money from the person who will get higher extra grade than you.

overpaidgoogler• 11 years ago

Really odd that the professor does not mention carbon taxes in the story. It doesn't make sense to borrow game theory from economics but completely ignore the idea of taxing externalities

MatthewWilkes• 11 years ago

Perhaps it's just cultural differences, but nobody getting extra points sounds like the most desirable outcome to me. Perhaps in a setting where the exam doesn't count for anything it'd be okay, but it just seems so juvenile.

paulsutter• 11 years ago

The professor omitted the sole interesting number: what percentage of students choose 6 points. Is it typically 15% or is it typically 80%?

It makes a huge difference. Most likely, it's a percentage low enough to indicate that the 10% threshold is carefully chosen. Otherwise he'd tell us.

This is evidence that he has an agenda to promote (that people are too selfish), and that the facts don't support his agenda (most people actually cooperate). So he omits the facts.

bduerst4• 11 years ago

Or maybe it's 70% of the students who pick 6. Or 99%. Or maybe 10.01%.

The point is we don't know and can only speculate, just like the students in the experiment who don't have the signal either. It kind of sounds like you want to believe the professor has a bias, and are trying to speculate evidence to support that belief. Even in the article he talks about how picking 6 in the first round isn't viewed as selfish, just that this experiment demonstrates tragedy of the commons.

pitt19802• 11 years ago

I'm actually not convinced that making it a higher percentage threshold doesn't make cooperation less likely

at 10% (depending on class size) each student realizes that their noncooperation goes a good distance of the way towards that 10%

at say 50% threshold, each student thinks their noncooperation matters less, and thus is even less likely to cooperate

at least that's what I'd hypothesize, I suspect there is an interesting paper somewhere that explores this very phenomenon

pimlock• 11 years ago

He mentioned here: https://twitter.com/SelterMosby/status/619250594071638016 that for that particular group it was 20%.

alelefant• 11 years ago

Your speculation != evidence

fcbrooklyn5• 11 years ago

Actually, I think in this case the only rational choice is to ask for the 6 points. One of two things will happen:

1) Less than 10% will follow suit, in which case you'll get a 6 point boost, and you'll have secured an advantage over 90% of your classmates.

2) More than 10% will follow suit, and noone will get anything, in which case you will have no advantage over your classmates, and neither will any classmate have an advantage over you.

If you select 2 points, then either:

1) Less than 10% will opt for 6, in which case you'll have no advantage over at least 90% of the class, but some members of class may have a 4 point advantage over you, or

2) More than 10% will opt for 6, in which case the outcome is identical to choosing 6 in the first place.

Because the "points" have no intrinsic value except in comparison to your classmates (unlike a true tragedy of the commons, where the scarce resource such as food, etc, has real value), there is no reason not to roll the dice.

EDIT: Many people think the fact that the course is "not graded on a curve" makes a difference. It does not, at least considering the class in isolation. I took courses in college where an A was pretty much a dead certainty, and other courses where getting a B was actually quite an achievement. In all cases my performance within a course had to be judged based on my performance against the other students within that same class.

MagicWishMonkey• 11 years ago

Not every class is graded on a curve.

mturmon• 11 years ago

The first italicized paragraph of the OP says the scores are not curved, and the students are told this, so your analysis is incorrect.

makr17• 11 years ago

"points" have no intrinsic value except in comparison to your classmates

this would be true if the course was graded on a curve, but the article makes clear that

the course grades are not curved.

fcbrooklyn5• 11 years ago

Doesn't matter if there's a curve. Your grades are still only meaningful compared to your classmates. (ok, assuming you're not in danger of actually failing the class)

jccalhoun• 11 years ago

The points only matter in comparison to your classmates if there is a curve or something and the directions say there is no curve. If there is no curve then I don't see how the notion of having an advantage comes into play.

edwardy20• 11 years ago

Because the "points" have no intrinsic value except in comparison to your classmates

This is where your logic is wrong. The professor is not saying the class is graded on a relative scale (for example, top 10% of the class gets As). If everyone gets two points, and it bumps up everyone's GPAs, then of course it will benefit them all, especially in comparison to people who are not in the class.

gorena4• 11 years ago

This is not necessarily true. If you're already a good student, this devalues your GPA, mostly due to the generally awful GPA system. Assuming your school considers everything above a 92 to be a "4.0", if you're already in that range, you definitely don't want to help anyone else into that range.

Note that, of course, this would be fixed by just making GPAs decimal numbers out of 100, the average of all of your actual, numeric grades from each course (multiplied by credit hours?). You can divide it by 25 if you really want the weird 4.0 scale for some reason.

fcbrooklyn5• 11 years ago

Yes, it's true that it sort of benefits everyone in the class vs people who did not take the class, but some classes are easy A's and some aren't, and everyone knows that. If the class becomes a slightly easier A because we all picked 2 points, then the effect will be relatively small. It would be a better experiment if he was handing out cash, even small amounts of cash.

univerio• 11 years ago

It depends on whether you consider the points valuable per se, or in relation to other people's grades. If you choose two points and < 10% of the class choose 6, you are still better off than you were before, if the points have intrinsic value. The article says that the class is not curved, meaning 2 points for you is a better grade, regardless of what others get.

porter• 11 years ago

This is the rational choice in isolation. But collectively there is a better solution. The problem is that there's always the (rational) incentive to defect from the coordinated outcome, because as you point out, it's better for you...if you're the only one who defects.

tnorthcutt• 11 years ago

All selections are anonymous, and the course grades are not curved.

bduerst4• 11 years ago

From the article, the class isn't graded on a curve so your assumption that 2 points is worthless doesn't apply.

gorena4• 11 years ago

This assumes you haven't already maxed out the GPA value for the course. If you already have a 92 (I went to a school that didn't have "A+", YMMV), there's no reason to increase your grades, and anyone else increasing their grade has the potential to devalue yours.

Note that this is fixed by just averaging your actual grades out of 100 to form your GPA, instead of mapping from a 0-100 range to an enumeration to a 0-4 scale then averaging the results.

tolmasky5• 11 years ago

A lot of people are commenting on how the article said there would be no curve, but I interpreted your statement to mean a deeper comparison to other students: the intrinsic value of doing better or worse than them, that translates to actual physical results: better chance at valedictorian than them, better chance to stand out to the teacher, higher overall GPA, etc.

fcbrooklyn5• 11 years ago

Exactly. Curve or no curve it doesn't matter.

fcbrooklyn5• 11 years ago

"better chance to stand out to the teacher"

On reflection, this might make me stop and think about it. It's supposedly anonymous, but it can't be anonymous to the professor, can it, or how would the points be awarded? This professor believes he's simulating the tragedy of the commons, so to act rationally and take the 6 points might cast you in a negative light in his eyes, which might not be worth the 6 points after all.

lifeformed2• 11 years ago

I think it also depends on the class size. If there are only 10 students, then it's very risky to pick 6 points, since you have to be the only one who picks it. But if there are 1,000 students, then it'd make perfect sense to pick 6 points. Basically, the less of an effect your own decision has on the group outcome, the more rational it is to pick the selfish decision.

This is why I find voting hard to justify if you view it pragmatically (even though I do it). It's mathematically improbable that my vote will make any difference. Then why do it? Sure, if everyone thought that, it would be bad. But it doesn't matter what other people do: your vote still won't matter either way. It's such a huge pool of voters that it's literally impossible to put yourself in a position where your vote makes a difference. Basically, it's important that people vote. But it's not important that a particular person votes.

Can anyone convince me why I in particular should vote in an election of a quarter billion people? Are there any reasons other than following idealistic principles? I mean, following principles is important, but I was wondering if there are more pragmatic arguments.

mtVessel2• 11 years ago

If you live in the same country as I do, I definitely think you shouldn't vote. That way, my vote counts more.

Huh?

If everyone's vote carries the same weight, then in a large pool, everyone's vote is equally meaningless. So, logically, if my vote is almost certainly not going to cast the deciding ballot, then I should stay home. And so should everyone else.

If everyone stays home, then all it takes for my candidate to win is for me to go to the polls. All of a sudden, my vote is the most meaningful vote in the entire election!

"Everyone's vote counts equally" only applies to those who actually, y'know, vote.

Or, try this argument: The premise of voting is not that it matters whose vote tips the scales. The premise of voting is that the candidate who gets the most people to vote for him or her wins. So you only need to vote if you actually care who wins. And if you do care who wins, you don't actually care about the relative contribution of any individual vote, including your own.

jmmcd• 11 years ago

The challenge was recently discussed on HN: https://news.ycombinator.com/item?id=9874215

This new article is from the lecturer's point of view.

anti-shill• 11 years ago

The commons worked great in two situations--1) europeans and 2) villages.

Maybe if we could get back to small villages of european descent we could have a higher quality of life.

hwita• 11 years ago

Sure, the course grades are not curved, but the students are definitely competing academically, especially those in the same class. There's class rank, honors status, merit scholarships, internships, job opportunities, etc., that are technically at stake. It makes sense to choose 6 every time.

bsder• 11 years ago

This really doesn't work for me as an experiment.

10% is too easy to hit. Do 3 or more students need the 6 rather than the 2? Why should I choose the 2 if it won't do me any good?

In any class I teach, there are generally 10% on the line between grades that requires that I take into account a little more than just scores. Did they do all the homework? Did they improve on assignments or were they blowing them off? etc.

Given that 10% probably need the 6 and not the 2, this is likely to never work.

I had a tragedy of the commons that I hadn't intended. I had an extra credit programming assignment, but there was a catch--the students had to write the tests for the automated tester. If nobody wrote tests, nobody had the chance to get any extra credit. They were allowed to collaborate on the tests, but not the solution.

Everybody complained bitterly when nobody wrote tests.

My response was not terribly charitable: "This is extra credit, folks. Not charity. You all had two options.

First, write the tests yourself. Yes, writing tests is time consuming, but not horribly difficult. Some students started, realized the amount of work, and stopped. However, once somebody writes the tests, everybody get to benefit.

Second, encourage someone else to write the tests for you. Did any of you talk to the students most likely to write tests? Did any of you encourage these students to put in the work if you couldn't pull it off yourself? Did any of you offer to compensate them for their valuable time?

Many of you have been repeatedly asking for a group assignment since the beginning of the semester. THIS WAS A GROUP ASSIGNMENT AND YOU FAILED. It simply worked out that freeloaders weren't guaranteed to be carried by the best students. The best students realized the amount of work and simply opted out since they already had enough points.

Welcome to the real world. Figuring out how to get someone to do something that they don't really want to do is a fundamental problem of life."

Tossrock• 11 years ago

It's funny how many people are saying "oh just get everyone organized and have a lottery/auction". Yes, if we could perfectly organize large groups of people we could solve the tragedy of the commons. Unfortunately, organizing large groups of people is hard.

Even in the scenario where everyone is a rational actor (ie, fantasyland), effectively communicating to a group of > 20 people and obtaining unanimous consent is an exceedingly difficult problem.

bduerst4• 11 years ago

The anonymous nature of this removes the reputation cost for picking the six points.

Collusion isn't possible because there is no penalty for breaking an agreement, and the signals it creates (everyone is picking 2) only makes rationally self-motivated individuals more likely to break it.

tolmasky5• 11 years ago

I'm surprised no rich student ever just offered ahead of the tally that they'd pay everyone $x if no one choose 6, where x is more valuable than 4 points. He now has the ability to safely choose 6, and everyone else is paid for their cooperation.

drcross• 11 years ago

Great, except votes are anonymous.

tolmasky5• 11 years ago

It doesn't matter because the requirement is NO ONE choose it. There is nothing to gain by selecting 6. The second you are writing 6 down on your paper, you better hope the 4 extra points are worth more to you than $x because you have absolutely invalidated the game, not "maybe" invalidated it.

If x is big enough to trivialize 4 points, I am pretty sure no one would choose it (or at least fell well below 10%). For example, if Richy Rich was in your class and offered $1million to EVERYONE as long as NO ONE chose 2, I am quite certain that even the most selfish actors would not write down 6. If he offered 50 cents than I'm pretty sure some people would. Binary search and you'll know how much a point costs.

(apologies if you commented before my edit)

gorena4• 11 years ago

Well, rich students don't need good grades since they'll just live off their trust fund, I suppose? (or get a job at daddy's hedge fund)

theburg• 11 years ago

Doesn't take into account the student's standing in the class. If I am confident with the quality of my term paper and believe it is worthy of an A, what do I care if I get additional points?

zwrt• 11 years ago

what if you choose 6 and explain to your classmates that "It feels good to be cooperative both from a strategic and moral perspective" and the whole commons thing and convince them to choose 2?

tolmasky5• 11 years ago

Its funny because we see the tragedy of the commons "fail" (succeed?) all the time in national elections: people are so afraid to "selfishly" choose the candidate they actually want to win (and thus cause the opponent to win) that we all "cooperate" on a sort-of ok choice (just like cooperating on 2 vs 6). I guess that's argument for penalties.

justifier• 11 years ago

So you get all the grades from your fellow students and organise the bottom 9% to choose 6 and the rest of the class chooses 2

in 6 months 4 points on a random test will be completely forgot.. might as well game the professor that is trying to game you

acbart• 11 years ago

Alternative experiment: every day, students are allowed to do this voting. Assuming that the first few days run like this experiment, I wonder if we'll see a change in their behavior. This actually models reality more closely, to some extent.

Why I give my students a ‘tragedy of the commons’ extra credit challenge

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