Coherent lower and upper conditional previsions defined by Hausdorff inner and outer measures to represent the role of conscious and unconscious thought in human decision making

The model of coherent lower and upper conditional previsions, based on Hausdorff inner and outer measures, is proposed to represent the preference orderings and the equivalences, respectively assigned by the conscious and unconscious thought in human decision making under uncertainty. Complexity of partial information is represented by the Hausdorff dimension of the conditioning event. When the events, that describe the decision problem, are measurable is represented to the s-dimensional Hausdorff outer measure, where s is the Hausdorff dimension of the conditioning event, an optimal decision can be reached. The model is applied and discussed in Linda's Problem and the conjunction fallacy is resolved.