Chocolate and Gold Coins

Tuesday, January 10, 2006

The Homework Option

My son came home with some homework and a curious option. It was a slip of paper from his teacher excusing him from one homework assignment, which my son could use at his discretion.

“I won’t use it now, Daddy, because this homework is easy. I will save it for a really hard homework.”

“But what if you use it for a really hard homework and the next day the teacher gives an assignment that is three times harder. You would have wasted your option.”

This made me think. How would one use such an option optimally? It is like an option to marry someone or to buy a house or take a job opportunity or some other decision that is nearly impossible reverse (at least in the short term). You never know what better choices might lie ahead, but you also may be throwing away great opportunities in the present.

There is a theory that deals with such options. You never exercise the option early on. You use the first few opportunities to create an estimate of the probability distribution of future opportunities. Once you have an estimated probability distribution, you then can make a decision rule which is always: accept the option if the opportunity is better than or equal to x(t). The variable x(t) declines with t – at some point you accept almost anything.

The curious thing about the homework option is that the distribution of homework assignments is not random. The instructor creates the homework and decides how hard to make it. He might, in fact, purposefully hide a really hard assignment way near the end of the semester just to trip everybody up. Students who still had the option would then avoid the trap.

I have been trying to convince my son that this is exactly his teacher’s strategy. Even if it isn’t, I don’t really care: I just want my son to do all of his homework.

1 Comments:

  • I hope you keep us posted of how and when your son exercises this option.

    Btw how did he manage to get this 1-time exemption?

    By Anonymous Varun, at 10:32 AM  

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