Pairwise comparison

About: Pairwise comparison is a research topic. Over the lifetime, 6804 publications have been published within this topic receiving 174081 citations.

Investigating Generalisations of Expected Utility Theory using Experimental Data

Abstract: A number of generalizations of the expected utility preference functional are estimated using experimentally generated data involving 100 pairwise choice questions repeated on two separate occasions. Likelihood ratio tests are conducted to investigate the statistical superiority of the various generalizations and the Akaike information criterion is used to distinguish between them. The economic superiority of the various generalizations is also explored and the paper concludes that, for many subjects, the superiority of several of the generalizations is not established. Copyright 1994 by The Econometric Society.

Estimation of pairwise relatedness with molecular markers

Abstract: Applications of quantitative genetics and conservation genetics often require measures of pairwise relationships between individuals, which, in the absence of known pedigree structure, can be estimated only by use of molecular markers. Here we introduce methods for the joint estimation of the two-gene and four-gene coefficients of relationship from data on codominant molecular markers in randomly mating populations. In a comparison with other published estimators of pairwise relatedness, we find these new "regression" estimators to be computationally simpler and to yield similar or lower sampling variances, particularly when many loci are used or when loci are hypervariable. Two examples are given in which the new estimators are applied to natural populations, one that reveals isolation-by-distance in an annual plant and the other that suggests a genetic basis for a coat color polymorphism in bears.

SDT: A Virus Classification Tool Based on Pairwise Sequence Alignment and Identity Calculation

Abstract: The perpetually increasing rate at which viral full-genome sequences are being determined is creating a pressing demand for computational tools that will aid the objective classification of these genome sequences. Taxonomic classification approaches that are based on pairwise genetic identity measures are potentially highly automatable and are progressively gaining favour with the International Committee on Taxonomy of Viruses (ICTV). There are, however, various issues with the calculation of such measures that could potentially undermine the accuracy and consistency with which they can be applied to virus classification. Firstly, pairwise sequence identities computed based on multiple sequence alignments rather than on multiple independent pairwise alignments can lead to the deflation of identity scores with increasing dataset sizes. Also, when gap-characters need to be introduced during sequence alignments to account for insertions and deletions, methodological variations in the way that these characters are introduced and handled during pairwise genetic identity calculations can cause high degrees of inconsistency in the way that different methods classify the same sets of sequences. Here we present Sequence Demarcation Tool (SDT), a free user-friendly computer program that aims to provide a robust and highly reproducible means of objectively using pairwise genetic identity calculations to classify any set of nucleotide or amino acid sequences. SDT can produce publication quality pairwise identity plots and colour-coded distance matrices to further aid the classification of sequences according to ICTV approved taxonomic demarcation criteria. Besides a graphical interface version of the program for Windows computers, command-line versions of the program are available for a variety of different operating systems (including a parallel version for cluster computing platforms).

Best-worst multi-criteria decision-making method: Some properties and a linear model

Abstract: The Best Worst Method (BWM) is a multi-criteria decision-making method that uses two vectors of pairwise comparisons to determine the weights of criteria. First, the best (e.g. most desirable, most important), and the worst (e.g. least desirable, least important) criteria are identified by the decision-maker, after which the best criterion is compared to the other criteria, and the other criteria to the worst criterion. A non-linear minmax model is then used to identify the weights such that the maximum absolute difference between the weight ratios and their corresponding comparisons is minimized. The minmax model may result in multiple optimal solutions. Although, in some cases, decision-makers prefer to have multiple optimal solutions, in other cases they prefer to have a unique solution. The aim of this paper is twofold: firstly, we propose using interval analysis for the case of multiple optimal solutions, in which we show how the criteria can be weighed and ranked. Secondly, we propose a linear model for BWM, which is based on the same philosophy, but yields a unique solution.

Relative measurement and its generalization in decision making why pairwise comparisons are central in mathematics for the measurement of intangible factors the analytic hierarchy/network process

Abstract: According to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which scales of measurement exist. The theme of this paper is that direct comparisons are necessary to establish measurements for intangible properties that have no scales of measurement. In that case the value derived for each element depends on what other elements it is compared with. We show how relative scales can be derived by making pairwise comparisons using numerical judgments from an absolute scale of numbers. Such measurements, when used to represent comparisons can be related and combined to define a cardinal scale of absolute numbers that is stronger than a ratio scale. They are necessary to use when intangible factors need to be added and multiplied among themselves and with tangible factors. To derive and synthesize relative scales systematically, the factors are arranged in a hierarchic or a network structure and measured according to the criteria represented within these structures. The process of making comparisons to derive scales of measurement is illustrated in two types of practical real life decisions, the Iran nuclear show-down with the West in this decade and building a Disney park in Hong Kong in 2005. It is then generalized to the case of making a continuum of comparisons by using Fredholm’s equation of the second kind whose solution gives rise to a functional equation. The Fourier transform of the solution of this equation in the complex domain is a sum of Dirac distributions demonstrating that proportionate response to stimuli is a process of firing and synthesis of firings as neurons in the brain do. The Fourier transform of the solution of the equation in the real domain leads to nearly inverse square responses to natural influences. Various generalizations and critiques of the approach are included.