We have this problem, especially since the Covid educational chaos, that examiners are under pressure to inflate grades. This is understandable and happening for good reasons.
It predictably creates the problem that there are too many people scoring 100% on tests. With many people on identical marks, universities cannot select the students with the best aptitudes.
They are starting to do lotteries. This is unfair. It means that the whole leaving cert has failed to do its job of testing students for eligibility for university. It is not properly filtering students into courses by aptitude. If universities are going to do lotteries to select students, we don’t need a leaving cert at all.
The solution is old and well known. the exams are written using whatever scoring system is deems appropriate for that subject. It does not need to be out of 100. Then the results are converted into percentiles, using the bell curve. This means that the best 1% of students get a mark of 100, the worst 1% get 1, and the median/average students get 50. All the other marks follow the same pattern.
(To be kind, it might be decided to give all the worst 10% of students a mark of 10. There might be gaps where for example a mark of 71 does not exist, only 70 and 72, but that is easily dealt with by the simple algorithm.)
There will be no grade inflation. The whole annual stress and debate becomes obsolete and we can focus on the many real issues and problems with the leaving cert.
Percentiles and statistics (L-estimators in this case) are very common in the adult world. L-estimators are fundamental to medicine, engineering, science, etc. It is good that students and teachers become familiar with them. This method is not complex or weird or confusing. If students get used to it, it will help them understand the world better and perform in their careers.
Then people’s standards change, so that anything below 93% creates feelings of failure. This is just extra grade inflation. It doesn’t really help.
It would at least take some time (possibly many years) for the student population to acclimate and associate the low end of the new scale with failure. But you are right, it doesn’t really help in the long run.
I’m not convinced that there is a mathematical solution to perception problem like this.
If your goal is to fool people, to give them a false perception of themselves, that is very difficult.
What you can do is allow the exam to do its job - filtering students into the most appropriate university courses. My solution does that.
I don’t even think it’s a very original idea. I’m sure this is already done in some forward-thinking places.