Pairwise comparison

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

A Note on Two Methods for Estimating Missing Pairwise Preference Values

Abstract: This note analyzes two methods for calculating missing values of an incomplete reciprocal fuzzy preference relation. The first method by Herrera-Viedma appeared in the IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics [vol. 37, no. 1 (2007) 176-189], while the second one by Fedrizzi and Giove appeared later in the European Journal of Operational Research [vol. 183 (2007) 303-313]. The underlying concept driving both methods is the additive consistency property. We show that both methods, although different, are very similar. Both methods derive the same estimated values for the independent-missing-comparison case, while they differ in the dependent-missing-comparison case. However, it is shown that a modification of the first method coincides with the second one. Regarding the total reconstruction of an incomplete preference relation, it is true that the second method performs worse than the first one. When Herrera-Viedma 's method is unsuccessful, Fedrizzi-Giove's method is as well. However, in those cases when Fedrizzi-Giove's method cannot guarantee the successful reconstruction of an incomplete preference relation, we have that Herrera-Viedma 's method can. These results lead us to claim that both methods should be seen as complementary rather than competitors in their application, and as such, we propose a reconstruction policy of incomplete fuzzy preference relations using both methods. By doing this, the only unsuccessful reconstruction case is when there is a chain of missing pairwise comparisons involving each one of the feasible alternatives at least once.

A Method of Assigning Weights Using a Ranking and Nonhierarchy Comparison

Abstract: The analytic hierarchy process (AHP) has advantages that the whole number of comparisons can be reduced via a hierarchy structure and the consistency of responses verified via a consistency ratio. However, at the same time, the AHP has disadvantages that values vary according to the form of hierarchy structure and it is difficult to maintain consistency itself among responses. If the number of comparisons can be reduced, a comparison within a single level is optimal, and if comparison can be made while the priority among entities is maintained, consistency may be automatically maintained. Thus, in this study, we propose a method of assigning weights, which applies hierarchy structure of AHP and pairwise comparison but complements the disadvantages of AHP. This method has advantages that the number of comparisons can be reduced and also consistency is automatically maintained via determination of priorities first on multiple entities and subsequent comparisons between entities with adjoined priorities.

Learning Human Interactions with the Influence Model

Abstract: We are interested in quantitatively modeling the interactions between humans in conversational settings. While a variety of models are potentially appropriate, such as the coupled HMM, all require a very large number of parameters to describe the interactions between chains. We propose as an alternative the generative model developed in [1], the Influence Model, which parametrizes the hidden state transition probabilities by taking a convex combination of the pairwise transitions with constant “influence” parameters. We develop a learning algorithm for this model and show its abilities to model chain dependencies in comparison to other standard models using synthetic data. We also show early results of applying this model to human interaction data. 1 Int r o duct io n There is a long history of work in the social sciences aimed at understanding the interactions between individuals and influencing their behavior. In the psychology community, there are many instances of work studying these effects. For instance, Wells and Petty [2] show how a speaker's confidence could be significantly influenced by repeated head nodding from the audience. Studies of this kind give us interesting insights into the workings of human dynamics. In many cases, the * The first three authors contributed equally to this paper and are listed alphabetically. TR 539: Condensed version submitted to NIPS’01

Modeling Intransitivity in Matchup and Comparison Data

Abstract: We present a method for learning potentially intransitive preference relations from pairwise comparison and matchup data. Unlike standard preference-learning models that represent the properties of each item/player as a single number, our method infers a multi-dimensional representation for the different aspects of each item/player's strength. We show that our model can represent any pairwise stochastic preference relation and provide a comprehensive evaluation of its predictive performance on a wide range of pairwise comparison tasks and matchup problems from online video games and sports, to peer grading and election. We find that several of these task -- especially matchups in online video games -- show substantial intransitivity that our method can model effectively.