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AbstractIn many real‐world applications, designs can only be evaluated pairwise, relative to each other. Nevertheless, in the simulation literature, almost all the ranking and selection procedures are developed based on the individual performances of each design. This research considers the statistical ranking and selection problem when the design performance can only be simulated pairwise. We formulate this new problem using the optimal computing budget allocation approach and derive the asymptotic optimality condition based on some approximations. The numerical study indicates that our approach can reduce the number of simulations required to confidently identify the best design.

ABSTRACTThe Pairwise Comparison‐based Preference Measurement (PCPM) approach has been proposed for products featuring a large number of attributes. In the PCPM framework, a static two‐cyclic design is used to reduce the number of pairwise comparisons. However, adaptive questioning routines that maximize the information gained from pairwise comparisons promise to further increase the efficiency of this approach.This paper introduces a new adaptive algorithm for PCPM, which accounts for several response errors. The suggested approach is compared with an adaptive algorithm that was proposed for the Analytic Hierarchy Process as well as a random selection of pairwise comparisons. By means of Monte Carlo simulations, we quantify the extent to which the adaptive selection of pairwise comparisons increases the efficiency of the respective approach. Copyright © 2011 John Wiley & Sons, Ltd.

AbstractThis paper studies the properties of an inconsistency index of a pairwise comparison matrix under the assumption that the index is defined as a norm-induced distance from the nearest consistent matrix. Under additive representation of preferences, it is proved that an inconsistency index defined in this way is a seminorm in the linear space of skew-symmetric matrices and several relevant properties hold. In particular, this linear space can be partitioned into equivalence classes, where each class is an affine subspace and all the matrices in the same class share a common value of the inconsistency index. The paper extends in a more general framework some results due, respectively, to Crawford and to Barzilai. It is also proved that norm-based inconsistency indices satisfy a set of six characterizing properties previously introduced, as well as an upper bound property for group preference aggregation.