Geometric mean-based pairwise comparison method with the reference values -- statistical approach

For many years, pairwise comparison methods have been widely used for eliciting preferences and ranking alternatives in decision-making problems. These methods estimate priority weights from a pairwise comparison matrix and are now standard tools in multi-criteria decision analysis. In this paper, we present a statistical view of the pairwise comparison method using reference values and the geometric mean to calculate alternative priorities. Thanks to this approach, we can simultaneously capture the phenomenon of inconsistency in pairwise comparisons and the preference distance between different alternatives. In this paper, we define indicators that measure the quality of the obtained weight vector, which, thanks to the statistical approach, have an understandable interpretation.

Decision-Value Attribution in Predict-then-Optimize Systems

Predictive models are increasingly embedded in operational decision-making, yet standard explanation methods typically explain forecasts rather than the decisions those forecasts induce. This distinction is important in predict-then-optimize systems: large forecast changes may leave the optimizer's action unchanged, while small changes can alter the selected decision and its realized value. We propose Decision Value Attribution (DVA), a Shapley-based framework for attributing the value of a fixed prediction--optimization pipeline. The framework defines cooperative games whose payoff is the downstream decision value, allowing the players to be information sources, optimization or design parameters, or both. We present three variants: InfoDVA attributes value to features, DesignDVA attributes value to operational configurations, and Decision-Value Interactions (DVI) quantifies how information and design jointly create value. We further distinguish post-DVA, which evaluates decisions using realized outcomes, from pre-DVA, which evaluates decisions under the model's full prediction. This separation turns attribution into a decision-level diagnostic of whether the model's operational beliefs align with realized performance. The resulting attributions are expressed in the units of the operational objective and decompose the gain or loss relative to a baseline. Case studies in electricity storage arbitrage and emergency medical service coverage show that predictive explanations can be poor proxies for operational value, that DVA can guide targeted information-control interventions, and that optimization configurations determine when predictive information is decision-relevant.