Challenge Theory: The Structure and Measurement of Risky Binary Choice Behavior

Challenge Theory (Shye \u0026 Haber 2015; 2020) has demonstrated that a newly devised challenge index (CI) attributable to every binary choice problem predicts the popularity of the bold option, the one of lower probability to gain a higher monetary outcome (in a gain problem); and the one of higher probability to lose a lower monetary outcome (in a loss problem).  In this paper we show how Facet Theory structures the choice-behavior concept-space and yields rationalized measurements of gambling behavior. The data of this study consist of responses obtained from 126 student, specifying their preferences in 44 risky decision problems. A Faceted Smallest Space Analysis (SSA) of the 44 problems confirmed the hypothesis that the space of binary risky choice problems is partitionable by two binary axial facets: (a) Type of Problem (gain vs. loss); and (b) CI (Low vs. High). Four composite variables, representing the validated constructs: Gain, Loss, High-CI and Low-CI, were processed using Multiple Scaling by Partial Order Scalogram Analysis with base Coordinates (POSAC), leading to a meaningful and intuitively appealing interpretation of two necessary and sufficient gambling-behavior measurement scales.