3 ms·

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.

by 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.
JadeNB 11y ago
> This means that everyone is guaranteed I don't think that this usage of 'guaranteed' is strictly correct (although I understand the informal sense in which it is meant). I don't know a formal definition of "random number" that would allow me to back up what I'm about to say, but it seems to me impossible to guarantee that exactly 10% of all generated random numbers are less than 0.1. For example, it can't possibly be true if (some, but) fewer than 10 numbers are generated. (For example, consider jmmcd (https://news.ycombinator.com/item?id=9874773 https://news.ycombinator.com/item?id=9874773 )'s hypothetical classroom with 2 students.) The best guarantee that I can imagine is some sort of "law of large numbers", which won't help in a class of, say, 30 people, 4 of whom happen to generate a small number! EDIT: Also, I think that the use of a random-number generator should probably count as co-ordination. Consider, for example, a situation where some outside observer picks floor(10%*$classsize) of the class, and the random-number generator is replaced by this person. (Let's say he has an auxiliary random-number generator, for which he generates a number up to 0.1 for the chosen students, and a number past 0.1 for the unchosen.) This is clearly co-ordination, but it is also indistinguishable to anyone who can't peer behind the curtain; so it seems to me that your situation should count as co-ordination, too. EDIT 2: Also also, let's ignore the fact that there are only finitely many distinguishable floating-point numbers in [0, 1] (so that, in particular, it makes a difference what we instruct the student to do who generates 0.1 exactly), and suppose that there's some clever output scheme that gives infinitely many possibilities.

by jmmcd 11y ago

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.

JadeNB 11y ago

> This means that everyone is guaranteed I don't think that this usage of 'guaranteed' is strictly correct (although I understand the informal sense in which it is meant). I don't know a formal definition of "random number" that would allow me to back up what I'm about to say, but it seems to me impossible to guarantee that exactly 10% of all generated random numbers are less than 0.1. For example, it can't possibly be true if (some, but) fewer than 10 numbers are generated. (For example, consider jmmcd (https://news.ycombinator.com/item?id=9874773 https://news.ycombinator.com/item?id=9874773 )'s hypothetical classroom with 2 students.) The best guarantee that I can imagine is some sort of "law of large numbers", which won't help in a class of, say, 30 people, 4 of whom happen to generate a small number! EDIT: Also, I think that the use of a random-number generator should probably count as co-ordination. Consider, for example, a situation where some outside observer picks floor(10%*$classsize) of the class, and the random-number generator is replaced by this person. (Let's say he has an auxiliary random-number generator, for which he generates a number up to 0.1 for the chosen students, and a number past 0.1 for the unchosen.) This is clearly co-ordination, but it is also indistinguishable to anyone who can't peer behind the curtain; so it seems to me that your situation should count as co-ordination, too. EDIT 2: Also also, let's ignore the fact that there are only finitely many distinguishable floating-point numbers in [0, 1] (so that, in particular, it makes a difference what we instruct the student to do who generates 0.1 exactly), and suppose that there's some clever output scheme that gives infinitely many possibilities.