Pairwise comparison

Pairwise comparison generally is any process of comparing entities in pairs to judge which of each entity is preferred, or has a greater amount of some quantitative property, or whether or not the two entities are identical. The method of pairwise comparison is used in the scientific study of preferences, attitudes, voting systems, social choice, public choice, requirements engineering and multiagent AI systems. In psychology literature, it is often referred to as paired comparison. Prominent psychometrician L. L. Thurstone first introduced a scientific approach to using pairwise comparisons for measurement in 1927, which he referred to as the law of comparative judgment. Thurstone linked this approach to psychophysical theory developed by Ernst Heinrich Weber and Gustav Fechner. Thurstone demonstrated that the method can be used to order items along a dimension such as preference or importance using an interval-type scale. Mathematician Ernst Zermelo (1929) first described a model for pairwise comparisons for chess ranking in incomplete tournaments, which serves as the basis (even though not credited for a while) for methods such as the Elo rating system and is equivalent to the Bradley–Terry model that was proposed in 1952. If an individual or organization expresses a preference between two mutually distinct alternatives, this preference can be expressed as a pairwise comparison. If the two alternatives are x and y, the following are the possible pairwise comparisons: The agent prefers x over y: "x > y" or "xPy" The agent prefers y over x: "y > x" or "yPx" The agent is indifferent between both alternatives: "x = y" or "xIy" In terms of modern psychometric theory probabilistic models, which include Thurstone's approach (also called the law of comparative judgment), the Bradley–Terry–Luce (BTL) model, and general stochastic transitivity models, are more aptly regarded as measurement models. The Bradley–Terry–Luce (BTL) model is often applied to pairwise comparison data to scale preferences.