6 ms·

Student’s Dilemma, a riff of the Prisoner version with extra credit

11 points by valleyhut 11y ago

ableal 11y ago
> What's your answer? I take the two. Any guesses about where (in society) one can find those who answer "I take the six"?
- vonklaus 11y ago
  I would choose 6. I will either get 6% of the test free, or have my original grade which would be decent as I would've studied.
- michaelt 11y ago
  At schools that do forced-curve grading or grade normalisation. If what matters is your relative rank in the class, rather than your absolute score, then "everyone takes the 2" and "everyone takes the 6" produce the same relative ranks for everyone - i.e. the same result for you - while "you take the 2 while some other people take the 6" reduces your relative rank. If there's a nonlinearity introduced by the mapping from points to a letter grade to a GPA, and you have an extremely detailed knowledge of your current grades, and you know 2 points won't bump you up a letter grade whereas 6 points will (i.e. 2 points and 0 points have the same effect on your GPA, only 6 points will improve your GPA). Among people who believe punishing defectors to produce fair outcomes is more important than producing the best average outcome. If you believe there are inevitably people who will take the 6 points, and those people are assholes, and you'd rather punch an asshole in the face (make them lose 6 points) even if it hurts your hand (you lose 2 points). The same logic that makes people brake for tailgaters. In parts of society that prize 'rational self interest' and believe everyone should look out for their own best interests and let market forces sort it out; or that it's inevitable that other people will do this and if you're not doing it, you're basically a sucker. The same logic that makes people take seven-figure salaries in finance instead of becoming school teachers - and makes salesmen push the product with the highest commission, not the one that's best for the customer.
  - reagency 11y ago
    Braking for tailgators reduces the probability and cost of a crash, at the expense of time to destination.
  - JesperRavn 11y ago
    To clarify, the theory behind the free market is that the seven figure salary in finance represents a greater contribution to the net social good than a teacher. You personally might not agree with this, but you are completely misrepresenting economic theory when you say that proponents of the free market consider it to be a prisoners dilemma situation. On the contrary they argue for the free market precisely because they believe that in the free market, individual and social goals are aligned
  - deleted 11y ago
    [deleted]
jmmcd 11y ago
SPOILER? The "correct" answer is to generate a random number in [0, 1]. If less than 0.1, then select 6, else select 2. For safety use 0.05 (say) instead of 0.1. This means that everyone is guaranteed 2, but some (as many as possible) get 6. It works without coordination.
- mikexstudios 11y ago
  Except that you need to coordinate everyone to use the random number generator system...
  - jmmcd 11y ago
    Everyone can work that out for themselves! In theory. Or else remember it from the course textbook. In context, "coordination" usually means communication after the game is set up, whereas the idea of the random number generator is a standard approach even in advance.
- nonotcorrect 11y ago
  Better strategy: Students who are highly likely to get an A in the class should choose 6 points, to try to ensure that lesser students do not get a free opportunity to catch up. Students who are likely to get less than an A should all choose 2 points, in the hopes that they'll get some free points.
  - JadeNB 11y ago
    Why should well performing students try to prevent poor performing students—'lesser' seems harsh—from 'catching up'? (This may be plausible in the classroom setting, but I think becomes more questionable if one thinks instead of, say, welfare grants.) Also, setting aside any ethical considerations, I'm not sure that the mathematics checks out: if there are very few students getting an A, then they don't have significant power to block 'lesser' students from catching up; whereas, if there are very many students getting an A, then this behaviour is guaranteed to reward none of them, whereas they could instead grant themselves all an extra 2 points.
- 11y ago
anastasds 11y ago
All of this is poorly defined (edit: I meant mathematically not well defined) as a game theory problem, from the premises to the suggestion that it's "the prisoner's dilemma with extra credit". First, the prisoner's dilemma is defined for two people, which this is not. Furthermore, the prisoner's dilemma assumes perfectly rational actors; we cannot assume that of students. Second (and related to the number of players), the 10% metric has different meanings based on the number of players (students). With two people, one person opting for six points constitutes 50%, which might be the case for an advanced elective at a small school. A first year biology class at a major university might have hundreds of students, in which case we can treat the 10% condition as stated. Third, the outcomes of the prisoner's dilemma are either absolute gain or absolute loss - either jail or freedom. In this case, no possible outcome constitutes loss relative to the starting state; a player can fail to gain, but cannot be worse from where he or she started before playing. A premise that would make this closer to the prisoner's dilemma would be that if more than some percentage of the students opt for the six points, then all students lose six points. Overall, this seems like something this instructor is doing for fun rather than as an experiment in a formal extension of the prisoner's dilemma. For my part, I'd opt for the 2, based on what I remember about undergraduate students. I have no formal reasoning to support this, however. tl;dr As stated, this is neither an extension of the prisoner's dilemma, nor is it well-defined in any case. It seems to me that any suggested solution will require either additional data or additional assumptions. Either way, I'd choose 2 points, and I would be interested to see the outcome of this instructor's survey.
- jmmcd 11y ago
  I'm afraid you need to re-read your notes :) N-player prisoner's dilemma is well-known. Neither 2-player nor N-player assumes rational actors. EDIT: It assumes that payoffs are in a reasonable unit of utility (so we don't need to think about whether $1000 is worth 10 times as much as $100, or more, or less). That's a related point but not the same. The second point doesn't make it undefined. If there are two people, and one opts for 2 points, then the 10% is exceeded and the condition is triggered. No confusion. The prisoner's dilemma arises just as well if the payoff matrix is all positive. You just need T > R > P > S [https://en.wikipedia.org/wiki/Prisoner%27s_dilemma https://en.wikipedia.org/wiki/Prisoner%27s_dilemma].
egillie 11y ago
Is the class still curved? Because if so, then choosing 6 points would always be the correct strategy.

11 points by valleyhut 11y ago

> What's your answer? I take the two. Any guesses about where (in society) one can find those who answer "I take the six"?

vonklaus 11y ago
I would choose 6. I will either get 6% of the test free, or have my original grade which would be decent as I would've studied.
michaelt 11y ago
At schools that do forced-curve grading or grade normalisation. If what matters is your relative rank in the class, rather than your absolute score, then "everyone takes the 2" and "everyone takes the 6" produce the same relative ranks for everyone - i.e. the same result for you - while "you take the 2 while some other people take the 6" reduces your relative rank. If there's a nonlinearity introduced by the mapping from points to a letter grade to a GPA, and you have an extremely detailed knowledge of your current grades, and you know 2 points won't bump you up a letter grade whereas 6 points will (i.e. 2 points and 0 points have the same effect on your GPA, only 6 points will improve your GPA). Among people who believe punishing defectors to produce fair outcomes is more important than producing the best average outcome. If you believe there are inevitably people who will take the 6 points, and those people are assholes, and you'd rather punch an asshole in the face (make them lose 6 points) even if it hurts your hand (you lose 2 points). The same logic that makes people brake for tailgaters. In parts of society that prize 'rational self interest' and believe everyone should look out for their own best interests and let market forces sort it out; or that it's inevitable that other people will do this and if you're not doing it, you're basically a sucker. The same logic that makes people take seven-figure salaries in finance instead of becoming school teachers - and makes salesmen push the product with the highest commission, not the one that's best for the customer.
- reagency 11y ago
  Braking for tailgators reduces the probability and cost of a crash, at the expense of time to destination.
- JesperRavn 11y ago
  To clarify, the theory behind the free market is that the seven figure salary in finance represents a greater contribution to the net social good than a teacher. You personally might not agree with this, but you are completely misrepresenting economic theory when you say that proponents of the free market consider it to be a prisoners dilemma situation. On the contrary they argue for the free market precisely because they believe that in the free market, individual and social goals are aligned
- deleted 11y ago
  [deleted]

jmmcd 11y ago

SPOILER? The "correct" answer is to generate a random number in [0, 1]. If less than 0.1, then select 6, else select 2. For safety use 0.05 (say) instead of 0.1. This means that everyone is guaranteed 2, but some (as many as possible) get 6. It works without coordination.

mikexstudios 11y ago
Except that you need to coordinate everyone to use the random number generator system...
- jmmcd 11y ago
  Everyone can work that out for themselves! In theory. Or else remember it from the course textbook. In context, "coordination" usually means communication after the game is set up, whereas the idea of the random number generator is a standard approach even in advance.
nonotcorrect 11y ago
Better strategy: Students who are highly likely to get an A in the class should choose 6 points, to try to ensure that lesser students do not get a free opportunity to catch up. Students who are likely to get less than an A should all choose 2 points, in the hopes that they'll get some free points.
- JadeNB 11y ago
  Why should well performing students try to prevent poor performing students—'lesser' seems harsh—from 'catching up'? (This may be plausible in the classroom setting, but I think becomes more questionable if one thinks instead of, say, welfare grants.) Also, setting aside any ethical considerations, I'm not sure that the mathematics checks out: if there are very few students getting an A, then they don't have significant power to block 'lesser' students from catching up; whereas, if there are very many students getting an A, then this behaviour is guaranteed to reward none of them, whereas they could instead grant themselves all an extra 2 points.
11y ago

anastasds 11y ago

All of this is poorly defined (edit: I meant mathematically not well defined) as a game theory problem, from the premises to the suggestion that it's "the prisoner's dilemma with extra credit". First, the prisoner's dilemma is defined for two people, which this is not. Furthermore, the prisoner's dilemma assumes perfectly rational actors; we cannot assume that of students. Second (and related to the number of players), the 10% metric has different meanings based on the number of players (students). With two people, one person opting for six points constitutes 50%, which might be the case for an advanced elective at a small school. A first year biology class at a major university might have hundreds of students, in which case we can treat the 10% condition as stated. Third, the outcomes of the prisoner's dilemma are either absolute gain or absolute loss - either jail or freedom. In this case, no possible outcome constitutes loss relative to the starting state; a player can fail to gain, but cannot be worse from where he or she started before playing. A premise that would make this closer to the prisoner's dilemma would be that if more than some percentage of the students opt for the six points, then all students lose six points. Overall, this seems like something this instructor is doing for fun rather than as an experiment in a formal extension of the prisoner's dilemma. For my part, I'd opt for the 2, based on what I remember about undergraduate students. I have no formal reasoning to support this, however. tl;dr As stated, this is neither an extension of the prisoner's dilemma, nor is it well-defined in any case. It seems to me that any suggested solution will require either additional data or additional assumptions. Either way, I'd choose 2 points, and I would be interested to see the outcome of this instructor's survey.

jmmcd 11y ago
I'm afraid you need to re-read your notes :) N-player prisoner's dilemma is well-known. Neither 2-player nor N-player assumes rational actors. EDIT: It assumes that payoffs are in a reasonable unit of utility (so we don't need to think about whether $1000 is worth 10 times as much as $100, or more, or less). That's a related point but not the same. The second point doesn't make it undefined. If there are two people, and one opts for 2 points, then the 10% is exceeded and the condition is triggered. No confusion. The prisoner's dilemma arises just as well if the payoff matrix is all positive. You just need T > R > P > S [https://en.wikipedia.org/wiki/Prisoner%27s_dilemma https://en.wikipedia.org/wiki/Prisoner%27s_dilemma].

egillie 11y ago

Is the class still curved? Because if so, then choosing 6 points would always be the correct strategy.