Sufficient conditions for a Heuristic Rating Estimation Method application

For many years, the pairwise comparison method has been widely used for decision-making involving experts. The best-known example of this method is the Analytic Hierarchy Process (AHP). In this now classic approach, the weights of alternatives are calculated using the principal eigenvector of the comparison matrix. 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 both the phenomenon of inconsistency in pairwise comparisons and the preference distance between alternatives. In this paper, we define indicators that measure the quality of the obtained weight vector, which, thanks to the statistical approach, have a clear and intuitive interpretation.

The paper addresses several ranking-dependent decision support methods. Ordinal information on compared objects can be used to improve the quality of expert data during estimation and help reduce the number of comparisons that the experts need to perform. In the paper we compare three incomplete ranking-dependent pair-wise comparison patterns which can be used in the Analytic Hierarchy Process - Best-worst method, Best-Second Best (Top 2) method, and the original maximum difference method. The first two comparison patterns (and respective methods) are incomplete, while the third can be a complete one. We determine conditions under which these three methods can be compared in terms of stability to expert errors. We also present the results of a simulation-type experiment, in which the three methods are compared. The research allows us to define the most stable incomplete ranking-dependent pair-wise comparison pattern and reduce the number of comparisons without loss of credibility of expert session results. The research contributes to algorithmic, cognitive, and applied aspects of decision support in uncertain environments.

We study fixed-precision ranking-and-selection in structured settings where the answer may be non-unique and where noisy estimates may temporarily admit no valid answer at all. This phenomenon arises naturally in problems such as multi-fidelity ranking-and-selection and identifying a Condorcet winner from pairwise comparisons. To address this, we propose a unified framework based on answer-wise acceptance sets, restricted generalized likelihood ratio stopping, and an answer-pitfall decomposition that yields a max-max-min characteristic value and a common sampling principle. We introduce ENDS, a general procedure that combines estimation, nomination, pitfall detection, and cost-aware information-directed selection. We instantiate ENDS for various problems by deriving explicit formulas. Extensive numerical experiments show that this unified recipe performs well across a broad range of pure-exploration problems and offers a practical framework and proof-of-concept algorithmic recipe.