some thoughts
I was listening to NPR on the way home today when a story about college entrance essays got me thinking. How do admissions officers judge the merits of an entrance essay? Is it based on some fixed scale? I can’t imaging that something as subjective as an essay can be effectively judged on a fixed scale. Is it judged relative to the other essays? This makes more sense to me, but I don’t understand the logistics. So I thought of a simpler problem that has the same elements, but is easier to identify with.
Suppose I were to come to you and offer you 100 boxes. In each box is a random amount of money between $0.01 and $100. After each box is offered to you, you must decide to keep it or to return it to me. If you return it to me, I will show you the amount of money in the box, but you will never see it again (and you won’t get the money). You are allowed to keep the first 10 boxes you choose. If you have not taken all of your 10 boxes by the time I offer the last boxes, you must take the remaining boxes to round out your total of 10. When you pick your tenth box, I will not offer any more boxes. What strategy optimizes your earnings?
Or suppose you are in a fishing tournament. At the end of the day, you must weigh in with your 10 biggest fish. If the game warden catches you with more than 10 fish in your boat, you will be disqualified from the competition. What strategy will assure your highest total weight?
Justin Allison
I’m going to think about this one. When I’m tired – like now, I would probably just take the first ten, and then go to sleep.
Jon
Well, since I’ve been in education for a while, maybe I can share a plausible essay rating strategy.
First, read each on and grade it somehow (could include grammar, substance, etc.). Then, when all are graded as such, use a simple bell curve to stratify them. Then, simply send acceptance letters to the top percentage.
Sorry, I have no idea of how to do the boxes either, though I find that far harder than grading app essays.
John
@Jon
I think that’s probably how the essays are graded. It makes a lot of sense. When I first heard it, though, I thought about it from a computer science perspective, and, as always in CS, the issue is scale. A few hundred papers to grade would be tedious, but not impossible. A few thousand gets really difficult, and over ten thousand gets close to impossible. (But what happens if you have a few million?) Even if (or especially if) there are multiple graders, how do you ensure that the best get in? Perhaps you need to adjust each grader’s results and then adjust all of the graders together, but that doesn’t seen like a fair system to those who are on the edge–those that are either right above or right below the cutoff.
clay
The fishing one is easy. You only keep 10 fish in the pot at all times – as you catch another you throw out the smallest. (If the warden counts 11 fish in the boat as disqualify, you may only be able to hold onto 9 at a time)
I actually would expect acceptance slots to filled in the same manor. Each time you want to add a new candidate beyond the limit of available seats – you have to decide who you’re going to toss out.
I’m unclear on the boxes problem. Do you (when offering me a box) know before hand the amount of money in it? Or it’s a surprise to us both after I choose to pass? If I don’t know the amount of the money in the box until after I choose – how could I possibly strategize? Can I shake them like a Christmas gift? ;)