The golden section and an algebraic model of ethical cognition

Abstract

In experimental investigations related to Kelly's theory of constructs (1955. The psychology of personal constructs. New York: Norton) a special constant was discovered. It was found that subjects on the average choose a positive over a negative pole with the probability 0.62. (Adams-Webber and Benjafield 1973. Canadian Journal of Behavioral Science 5, 234–241). The same constant was also found in other experiments related to the choice of elements marked “good” and “bad.” Benjafield and Adams-Webber (1976. British Journal of Psychology 67, 11–15) hypothesized that the precise value of this constant coincides with “golden section” ≈0.6180. In this paper it is shown that if we suppose that the subjects actualize mechanisms of choice described by the algebraic model of ethical cognition (which was constructed without any relation to the constant 0.62), then the existence of this constant is mathematically explained. Under very broad assumptions its value is 0.625, and under more constrained conditions it is equal to the golden section ratio precisely.