On the cycle-transitivity of the dice model (Q1420801)

The paper deals with modifications of the dice model to generate, describe and analyze a class of probabilistic relations. Attention is focused on their transitivity and it is shown that it is a special type of cycle-transitivity, the properties of which rather combine the features of moderate stochastic transitivity and Lukasiewicz-transitivity. Moreover, even the opposite relation is shown -- any probabilistic relation with rational elements on a 3-dimensional space of alternatives and with the specific cycle-transitivity as considered in the paper can be represented by a dice model. The above conclusion is not fulfilled for higher dimensions.