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Pearson Correlation Coefficients, r, between Challenge Index, CI, (Eq. 3) and Observed Proportion, P b , of Bold Responses for All (Gain & Loss) Problems of This Study and of Kahneman & Tversky's (1979) Study *
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Challenge Theory (CT) is a new approach to decision under risk that departs significantly from expected utility and is based firmly on psychological, rather than economic, assumptions. The paper demonstrates that a purely cognitive-psychological paradigm for decision under risk can yield excellent predictions, comparable to those attained by more c...
Contexts in source publication
Context 1
... course, if the entire sample of 44 gain and loss problems is processed together (i.e., imposing the same set of four parameters on both, gain and loss problems), a lower correlation (r=-.87) is found between CI and P b . See first row in Table 2. The second row in Table 2 shows a very high correlation (r=-.99) for Kahneman & Tversky's (1979) sample of 11 gain and loss problems. ...Context 2
... first row in Table 2. The second row in Table 2 shows a very high correlation (r=-.99) for Kahneman & Tversky's (1979) sample of 11 gain and loss problems. However, this sample of problems is small, and the CI values are not well spread over their range. ...Context 3
... course, if the entire sample of 44 gain and loss problems is processed together (i.e., imposing the same set of four parameters on both, gain and loss problems), a lower correlation (r=-.87) is found between CI and P b . See first row in Table 2. The second row in Table 2 shows a very high correlation (r=-.99) for Kahneman & Tversky's (1979) sample of 11 gain and loss problems. ...Citations
... 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 Challenge Theory (CT) for decision under risk is a dual system stochastic model for binary choice behavior, based on the assumption that in decision under risk, two cognitive processing systems, the automatic system and the analytic system operate sequentially (Shye & Haber 2015;2020). The automatic system reacts rapidly, providing the initial, default response which according to CT is based on the probabilities alone (initially disregarding the amounts of gain or of losses). ...
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.
Hereunder we analyse of the cognitive performance of New Zealand robins (Petroica longipes) using smallestspace analysis and partial order scalogram analysis with base co-ordinates using a data set was originally analysed using principle component analysis. We propose a two facet, rather than a single principle component, solution and we characterized individual birds by their scores on all tasks. We survey attitudes about how we talk about birds and propose a revised mapping sentence for avian cognition based on these. We call for replications of our study using a larger sample of birds and for the development of further test items. We suggest that facet theory and the mapping sentences are research approaches suitable for avian cognitive research.
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.
