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Relational Information Theory

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Abstract

“Pseudodiagnostic" patterns of information search were first classified by Doherty et al. (1979), predicated on their assertion that only the selection of data that allow for the calculation of Bayseian probability ratios may be considered rational. However, with the exception of Crupi et al. (2009), who have argued for an epistemological explanation loosely based on the de Finetti theorem of exchangeable probability assignments (see, eg., Heath and Sudderth, 1972), the Doherty et al. interpretation of information search patterns has gone unchallenged. This thesis seeks to answer three questions: can people make reasonable inferences from probabilistic information; is there an identifiable common approach to information selection; and, if not Bayes' theorem, then what mathematics might underlie human decision-making? A series of experiments demonstrate that people appear to select data not only for their ordinal values, but also to establish the relationships between them. However, since such a holistic approach to decision-making lies beyond the scope of the naïve Bayes' classifier, an alternative expression for the calculation of likelihood ratios is presented. By rejecting the Kolmogorov axioms of classical statistics in favour of the von Neumann mathematical axioms of quantum mechanics, it is shown that not only may probabilistic information be reconceptualised as isomorphic representations of quantised and entangled statistical systems, but that it is only this approach which allows for the assumption free calculation of likelihood ratios. Further, the mathematical derivation demonstrates that Bayes' theorem is a special case of this more general quantum expression, applicable only where the conditional independence of data is guaranteed. Mathematical modelling, combined with the results of another experiment, is used to investigate the plausibility of this expression as an explanation for both information search patterns, and people's estimation of probability. The nature of this “relational information theory" is both discussed and situated within the wider psychological field of mental models.
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