Cascading Problem Sets
Those of us engineering have plenty of experience with the weekly problem sets that so frequently take over our lives, keeping us in Duffield atrium until the sun starts to rise in the morning. Typically we have 3 or 4 problem sets a week, and often they are graded based upon the correctness of each answer, rather than being effort-based. While homework scores don’t count for a large portion of the final grade in most classes, it is enough to boost you up or drop you down that half letter grade that can often matter significantly in a society where jobs are not easy to come by. Students worrying about their GPAs spend countless hours trying to get each and every answer correct. This is done through a combination of using textbooks, lecture notes, online resources, office hours, and fellow students. If posted solutions to the problems are not available students often compare answers to determine whether they have arrived at the right answer. The determination of whether one has actually gotten the correct answer is an interesting example of an informational cascade.
The process begins with the engineers that start their problem sets early, with early typically considered more than a day or two before they’re due. The first person to finish will have a set of answers that may or may not be correct. They compare with whoever is the next person they know to finish. There can then be one of two cases: either they both have the same answer or they have different answers, without knowing the correctness of their answers. When these two students are then approached by others, the others are more likely to believe that the answers the first two students got are the right answers. This then results in an informational cascade, with all subsequent students basing the correctness of their answers off of the answers obtained by the first two students. If the first two students are truly right, then everyone gets good grades. If the first two students happened to make the same mistake and got the same incorrect answer, then many, many students will have the wrong answer, as they believed in the correctness of the answers found by the first two students and based their calculations off of those results. Students with different answers may be less likely to change their answers, even if they have what is truly correct, to fit what the crowd is writing down as the answers.
This informational cascade happens quite frequently in many settings in engineering, with problem sets being one of the most common scenarios. Personally I have been part of many groups and conversations where I have compared my results to those of other students, and if we all had the same answer we were fairly confident we were correct. The answer that was seen the most frequently was most often deemed the correct answer. I have also been in the opposite situation, where a vast majority of a class made exactly the same mistake that resulted in the same incorrect answer. Most often this is not a result of a methodical error but an incorrect data measurement, unit, or conversion factor, or using an incorrect equation. While this situation is less than ideal for students it has the potential to improve their engineering practices by identifying common mistakes that professors, TAs, or the students themselves can correct and avoid making in the future. It also teaches students to be confident in their calculations, as it has been the case in the past where students have changed their answers to conform to the crowd and then got the incorrect answer, having originally had the correct one. Recognizing the formation of informational cascades an important consideration when comparing results.