  Challenge Theory (Shye & 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.
