My Decision Analysis midterm exam is super weird...
First off, it's designed to make you fail. There are about 20 multiple choice questions, each worth 5 points. However, for every question you answer you have to put the probability of it being right. Say you think A is right, and you're pretty sure it's the answer, so you put a probability of 0.7 beside it. That'll be how sure you are the answer is. Since you think A has a 70% chance of being correct, then the other options will either be assigned equal values of the remaining probability or you can assign values for yourself, just as long as they all add up to 1.
Anyhow, your mark for each question depends on the probability you put beside the correct answer. And if it so happens that A was correct and you put a probability of 0.7, then you gain 3.71 marks. If it wasn't, and instead was C (which you put a probability of, say, 0.1) you get -3.30. You don't get the full 5 unless you put a probability of 1. Duh. Now this is because the points are determined by an exponential curve. Which mathematically proves that
if A was correct (and you put a 0.7), then 5+3.60674 log(0.7) = 3.71 points
if C was correct (and you stupidly put a 0.1) then 5+3.60674 log(0.1) = -3.30 points
Now, due to the logic of this exponential curve and the fact that we know maths can never lie, it is also true that if you're super confident, you might also be super stupid. An example....
You look at a question and think, "Why, I know the answer for this! I'll put a probability of 1 'cos I'm frickin sure it's A! ". I'm sure we've all felt this way at some time or another while doing an exam, and when we get back our paper, it turns out we're wrong. Don't lie. It's happened to all of us. BUT...if you did this in THIS exam, and put a 1 beside the answer you thought was right, then obviously all the other options B, C and D would have a probability of 0. And using our trusty log system, that would give you a....let's see..
if C was the answer (and you had a probability of 0 for it, since you already put a 1 beside A) then 5+3.60674 log(0) = - infinity
Woohoo! This, obviously, will cause you to flunk the exam. And it's pretty hard to pull up. heh.
So now what? Put a probability of 0.25 for all answers? This'll give me a 0 for the exam, but hell it's a whole lot better than getting a negative infinity!