On the Cycle-Transitivity of the Dice Model

Theory and Decision 54 (3):261-285 (2003)
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 Lukasiewicz-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
Keywords Dice model  Probabilistic relation  Stochastic transitivity   T-transitivity  Utility model
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