On maximal social preference

Abstract

Mathematics and physics are based on two numbers: Archimedes' constant  = 3,14… and e = 2,71… - Napier's constant. The former reflects the ratio of the perime- ter of a figure to its diameter and maximizes the area, given the diameter. The solutions are the disk and the circle. The latter represents the accumulated capital paid by a bank after one year from investing one unit of money at an annual interest rate of 100% under con- tinuous compounding. The ratio of the disk's perimeter to its diameter, i.e. , governs omnipresent cyclical motion, whereas Napier's constant determines natural growth - exponential growth. Nature mixes both kinds of behaviour: there is equilibrium - vortices, and the cobweb model, dynamic growth. Our general remarks are corroborated by the theory of linear differential equations with constant coefficients. Social life - democracy and quality - despite the deceptive chaos of accidental behaviour, is also governed by a beautiful numeral law. This social number is λ = ⅔ whose notation is derived from the Greek  meaning crowd, people, assembly. The social number, Łyko's number, is defined by the fundamental theorem. If each alternative of a maximal relation of a given profile has its frequency in this profile greater than ⅔, then such relation is a group prefer- ence. This sufficient condition separates a decisional chaos from a stable economic and voting order - the preference. Also our everyday language makes use of . We distinguish with it upper states - elitist ones, from ordinary standards. The ⅔ rule implies that in each group one third of the population prevails, while the rest are just background actors. The number  also appears, a bit of a surprise, in classical theorems of geometry.