11 Plus Exams Forum

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Seems to me that the girl gave this rather dubious moral reasoning for not attempting the question to divert from the fact that she probably just didn't know how to solve it! This girl will probably go far!

Anyway ignoring the date-night question for a minute, a far more interesting question IMO is quoted further down the article.

Its the "cruel exam question" set by the University of Maryland.

Select whether you want 2 points or 6 points added onto your final paper grade.
But there’s a small catch: If more than 10% of the class selects 6 points, then no one gets any points. Your responses will be anonymous to the rest of the class, only I will see the responses.

Assuming a reaonsably large number of people taking the exam, and assuming that your primary objective is to try and maximise your own score, I think that from an individidual's point of view, the logical choice is to select 6 additional points. (I'll explain why I think this is true if anyone disagrees).

The paradox is though, that if everyone follows the same rigorous logic to maximise their score, they will all end up with a lower score than if they'd all made the "illogical" choice of an additional 2 points.

Which all makes my brain hurt a bit!

What would other people do if faced with a question like this?

Choose 2 points - no loss, even though gain might be lower if 90% or more also choose 2 points.

tiffinboys wrote:Choose 2 points - no loss, even though gain might be lower if 90% or more also choose 2 points.

You would still get nothing if more than 10% of the others chose 6 points regardless of whether you yourself chose 2 or 6.

Imagine you're one of a 100 students taking this exam. There's no way for you to communicate with or arrange a deal with the other students to influence what they choose. Everyone's choice is independant of all the others.

First consider the case where more than 10 other students choose 6 points. It doesn't matter what you choose, you and everyone else will still get zero, so your choice is completely irrelevant in this scenario .

Now consider the case where 10 or less students choose 6 points. If the number of other students who choose 6 is between 0 and 9 and you choose 6, the total will still not be more than 10% so you'll get your 6 extra points and everyone else will also get what they selected.

The only scenario in which you choosing 6 points would have a negative effect on your or anyone elses score is if exactly 10 other students also choose 6 points. Your selection of 6 points tips the balance over 10% and everyone gets zero. This is a very unlikely scenario though. Its 10 times as likely that the number of other students who choose 6 is between 0 and 9 than exactly 10. Also if you choose 6 and are successful you gain +4, whereas if you are unsuccessful you only lose -2.

So logically the odds are heavily in favour of you choosing 6 rather than 2.

Only problem is everyone else goes through the same logical thought process, 100 students choose 6 points and you all get zero!

I'd have gone with the 6 points on the basis that all my class mates are a lot nicer and would be more likely to pick the 2 points!