Oct
17
A Negative Score On A Homework Reveals Some Interesting Things About Myself
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As I woke up today, I received an email from the Stanford class I’m taking. Ah ha! Homework grades are available online for the first homework of the class. “Oh good,” I thought, “Let’s see what I got”.
I loaded up the Stanford Decision Analysis course page, logged in, and it took me a full minute before I realized what my grade was. I got -1.07. That’s right – I scored lower than if I hadn’t actually done the homework!!
“How can this happen?” you may think. Well, this class has an interesting grading policy. The homeworks are multiple choice, but instead of picking the correct answer, you assign probabilities to the answers. For example, if the question was, “Which of the following adds up to 4? a) 1+1 b) 2+2 c) 1+1 d) 4+1″, I would have the answer in the form a) .01 b) .97 c) .01 d).01. Then, the score for the question is calculated as 1 + log(p)/log(4), where p is the probability I’d put down for the correct answer. So for this question, I would get +.978 if I got it right and -2.32 if I got it wrong.
This means that if you put 0 as the probability to any answer, you get negative infinity on the homework (so you’re kind of screwed for the course)!
I’d chosen .003/.003/.004 for the questions that I was sure about (making the correct answer .99). Unfortunately, I got two of these questions wrong! Since I get about -3 points for each of those two questions, my score came out to a “nice” -1.07.
Some people might think this is a horrible situation, but I think it was well worth the price. I learned two important lessons from this.
First, I am overconfident about the correctness of my answers. When I am 99% sure, I actually am only correct about 80-95% of the time! This really made me wonder about situations where there are disagreements with other people. If I am only right so little on a test, am I really right the 99% I think am when dealing with other people? Add in the fact that most of the time, I think I am only about 90% right; also add in differences in perspectives between people, and I can’t help but think “thinking I’m right” means almost next to nothing! Realistically, I’m probably only right like 60% (if even that) in those situations. Wow!
This reminds me of a quote by someone famous (I think it was either Roosevelt, Churchill, or Franklin) that said even he, a great leader of people, is only right about 70% of the time, and that’s on a good day! I never fully appreciated that quote until I got this test result. It really makes me think I need to be open minded when dealing with other people’s opinions. While one really good person can make correct decisions maybe 70% of the time, 10 people who make correct decisions 60% of the time can easily combine to make correct decisions 90% of the time. It has really opened my eyes to just how valuable other people’s insights may be.
The second lesson is that I haven’t been taking the class seriously enough. If we take my score literally, I know less than 0! This is for a class I’d walked into scoffing at how easy the subject is. That is precisely the type of mistake that I try really hard to guard against. When you think things are easy, you are very likely to do well. However, that’s only assuming you give it your full attention! What a shame it is to not spend the short amount of attention it requires and get poorer results than if it was something hard!
Two very important lessons learned.
Not a bad price I’d say!
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