Bruno de Finetti heard of [the author’s empirical Bayes method for grading tests] and he wrote to me suggesting that the student should be encouraged to state their probability for each of the possible choices. The appropriate score should be a simple function of the probability distribution and the correct answer. An appropriate function would encourage students to reply with their actual distribution rather than attempt to bluff. I responded that it would be difficult to get third graders to list probabilities. He answered that we should give the students five gold stars and let them distribute the stars among the possible answers.
- Herman Chernoff (pg 34 of Past, Present, and Future of Statistical Science, available here)
- Herman Chernoff (pg 34 of Past, Present, and Future of Statistical Science, available here)
Actually, if you do this with something besides a test, this sounds like a really good way to teach a third-grader probabilities.