Poster F128, Tuesday, March 27, 8:00-10:00 am, Exhibit Hall C
Distribution of Relative Quantities in Nature and Human Culture
Santiago Alonso-Diaz1, Luis Alejandro Lee-Penagos1, Gabriel Ignacio Penagos-Londoño1; 1Department of Economics, Universidad Javeriana, Bogotá Colombia
The comparison of relative quantities is central for behavior (prey over occupied area), perception (Weber law), and human culture (math). Little is known about the distribution of their components. For instance, when a ratio is the larger in a pair it could have the larger numerator and smaller denominator, or perhaps, the smaller numerator and denominator. We present evidence that the distribution is not uniform across the potential cases. In a large array of databases we found that natural occurring proportions, such as the ones computed from animal morphology, neuron morphology, food distribution, and others, the larger (or smaller) proportion always had some numerosity advantage in one of its components. A similar pattern emerged in human-related activity. In economic measures (e.g. GDP per capita), intellectual activity (e.g. citations per paper), and education (e.g. ratios in Physics textbooks), it was not possible to find a uniform distribution. Numerical results revealed that if the numerator and denominator are independent and identically distributed then the probability that one of them is bigger in the larger fraction is greater than chance. We further test with a simulation that such statistical structure in the natural world induces numerosity-based strategies that are optimal. The non-uniformity of the distribution in such large array of databases suggests the existence of a previously unknown constrain in how ratios emerge (akin to Benford’s Law) and suggest that numerosity-based strategies in education and decision-making have a rationale.
Topic Area: THINKING: Decision making