  Individual and group decisions are complex, often involving choosing an apt
alternative from a multitude of options. Evaluating pairwise comparisons breaks
down such complex decision problems into tractable ones. Pairwise comparison
matrices (PCMs) are regularly used to solve multiple-criteria decision-making
(MCDM) problems, for example, using Saaty's analytic hierarchy process (AHP)
framework. However, there are two significant drawbacks of using PCMs. First,
humans evaluate PCMs in an inconsistent manner. Second, not all entries of a
large PCM can be reliably filled by human decision makers. 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.
  keywords: analytic hierarchy process, markov chains, maximum entropy
