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This work analyses decision making situations, where the quantity of the value function associated with the alternatives is a random number with known distribution. The main contribution of the paper is that alternatives are grouped into pseudo indifference classes, where the alternatives are indifferent to at least one of the other alternatives in the class. However, not all elements in the set are indifferent to each other, unlike classical indifference classes. Since the resulting relation of strict preference over pseudo indifference classes turns out to be non-transitive, it is demonstrated both in theory and in terms of an example that it is strongly dependent on the significance level of comparisons in order to allocate alternatives into groups.

Non-Transitive Binary Relation of Preference in the Case of Random Value Functions, Derived from REPOMP