Rank Reversal and Uncertainty of Probabilistic Preference Relations

Probabilistic preference relations (PPRs) are a type of preference relations in which judgements are uncertain and represented by several possible values associated with their probabilities. Consistencies and priorities of PPRs have been developed in literature. These results might not be admissible if the uncertain degree of a PPR is relatively high because of the existence of rank reversal. This paper presents a process to measure the uncertain degree of a PPR from the prospective of rank reversal. The process (i) estimates the rank acceptability indices of alternatives based on the idea of stochastic multi-criteria acceptability analysis, (ii) computes the likelihood ranks, and (iii) measures the probabilities of rank reversal and rank preserve from the matrix level. Moreover, the measures are introduced to the framework of preference analysis in the setting of PPRs. Being different from some similar strategies, the process does not depend on the specific probabilistic distributions of items in PPRs nor require the independence of the items of priority vectors.