80/20 Rule partially explains 7+/-2 law: general system-based analysis

The 80/20 rule and the 7 ± 2 law are examples of difficult to explain empirical facts. According to the 80/20 rule, in each activity, 20% of the people contribute to the 80% of the results. The 7± 2 law means that we divide objects into 7 ± 2 groups – i.e., into 5 to 9 groups. In this paper, we show that there is a relation between these two facts: namely, we show that, because of the 80/20 rule, the number of classes cannot be smaller than 5. Thus, the 80/20 rule explains the lower bound (5) on the 7 ± 2 law. 1 Formulation of the Problem Difficult-to-explain empirical facts. There are several difficult-to-explain empirical facts. • For example, there is a ubiquitous 80/20 rule, according to which, in each human activity, 80% of the results come from 20% of the participants. For example, 20% of the people own 80% of all the wealth, 20% of researchers publish 80% of all the papers, etc.; see, e.g., [1, 2] and references therein. • There is a known phenomenon in psychology called a 7 ± 2 law (see, e.g., [4, 5]), according to which each person usually classifies everything into a certain number of classes C; depending on the person, this number ranges from 7 − 2 = 5 to 7 + 2 = 9 classes.