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On the Cycle-Transitivity of the Dice Model

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Abstract

We introduce the notion of a dice model as a framework for describing a class of probabilistic relations. We investigate the transitivity of the probabilistic relation generated by a dice model and prove that it is a special type of cycle-transitivity that is situated between moderate stochastic transitivity or product-transitivity on the one side, and Łukasiewicz-transitivity on the other side. Finally, it is shown that any probabilistic relation with rational elements on a three-dimensional space of alternatives which possesses this particular type of cycle-transitivity, can be represented by a dice model. The same does not hold in higher dimensions.

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De Schuymer, B., De Meyer, H., De Baets, B. et al. On the Cycle-Transitivity of the Dice Model. Theory and Decision 54, 261–285 (2003). https://doi.org/10.1023/A:1027378124173

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