Subjective Probability and the de Finetti Game

Ask any AP student how they did on their exam, they will give you an estimate of how they "feel" about their performance. How do you know if the student is giving you the whole truth and nothing but the truth?

The Italian statistician, Bruno de Finetti, found a way to measure subjective probability. Say you ask a student how they did on the AP Micro exam, and they say the aced it. How did they really do? Tell your student, "We are going to play a game. You have a choice. You can either draw a ball from a bag that have 98 red balls and 2 black ones, or you can wait and see how you did on the test. If you happen to draw a red ball out of the bag, I'll give you $300. If you wait to see your test results and you earn a 5, then I'll give you $300. If your student says, she will draw from the bag, that means she doesn't think the probablity is 98% that she'll earn a 5. You then ask questions like, now their are 80 red balls and 20 black ones. Do you want to draw from the bag or wait for the exam results?

When you ask students if they are interested in learning about a topic, they will less than truthful. When residents are asked how much they will use a new park, they will over-estimate the amount of time they will use at the park. When teachers are asked to complete a survey about administrative performance, they will offer words that do not convey their true feelings. When obtaining subjective data from a population, the de Finetti Game will help extract the truth.