Entropy production rate as a criterion for inconsistency in decision theory

Evaluating pairwise comparisons breaks down complex decision problems into tractable ones. Pairwise comparison matrices (PCMs) are regularly used to solve multiple-criteria decision-making (MCDM) problems using Saaty’s analytic hierarchy process (AHP) framework. There are two significant drawbacks of using PCMs. First, humans evaluate PCM in an inconsistent manner. Second, PCMs of large problems often have missing entries. We address these two issues by first establishing a novel connection between PCMs and time-irreversible Markov processes. Specifically, we show that every PCM induces a family of dissipative maximum path entropy random walks (MERW) over the set of alternatives. We show that only ‘consistent’ PCMs correspond to detailed balanced MERWs. We identify the non-equilibrium entropy production in the induced MERWs as a metric of inconsistency of the underlying PCMs. Notably, the entropy production satisfies all of the recently laid out criteria for reasonable consistency indices. We also propose an approach to use incompletely filled PCMs in AHP. Potential future avenues are discussed as well.