The problem of deriving a binary relation over alternatives based on paired comparisons is studied. The problem is tackled in the framework of belief functions, which is well-suited to model and manipulate partial and uncertain information. Starting from the work of Tritchler and Lockwood [8], the paper proposes a general model of mass allocation and combination, and shows how to practically de...

Researchers in the behavioural sciences have been presented with a host of pairwise multiple comparison procedures that attempt to obtain an optimal combination of Type I error control, power, and ease of application. However, these procedures share one important limitation: intransitive decisions. Moreover, they can be characterized as a piecemeal approach to the problem rather than a holistic...

We consider data in the form of pairwise comparisons of n items, with the goal of precisely identifying the top k items for some value of k < n, or alternatively, recovering a ranking of all the items. We analyze the Copeland counting algorithm that ranks the items in order of the number of pairwise comparisons won, and show it has three attractive features: (a) its computational efficiency lea...

This paper explores the preference-based top-K rank aggregation problem. Suppose that a collection of items is repeatedly compared in pairs, and one wishes to recover a consistent ordering that emphasizes the top-K ranked items, based on partially revealed preferences. We focus on the Bradley-Terry-Luce model that postulates a set of latent preference scores underlying all items, where the odds...

A new definition of consistency is introduced. It allows us to locate the roots of inconsistency and is easy to interpret. It also forms a better basis than the old eigenvalue consistency for selecting a threshold based on commnn sense. The new definition of consistency is applicable to expert systems and to knowledge acquisition. It is instrumental in applications of fuzzy sets and the theory ...

We present a regression formulation of the analytic hierarchy process (AHP) introduced by Saaty (1977) as a method of deriving a ratio scale of preferences (or priorities) concerning a set of m entities or attributes. This method involves a quantification of all m(m-1)/2 pairwise comparisons between the entities. The ratio scale is derived using an eigenvalue calculation on a matrix formed from...

In this paper we deal with the problem of nding the smallest and the largest elements of an ordered set of size n using pairwise comparisons if one of the comparisons might be erroneous and prove a conjecture of Aigner stating that the minimum number of comparisons needed is 87n 32 + c for some constant c. We also address some related problems.

We develop a Bayesian multivariate analysis of expert judgment elicited using an extended form of pair-wise comparisons. The method can be used to estimate the effect of multiple factors on the probability of an event and can be applied in risk analysis and other decision problems. The analysis provides variance predictions of the quantity of interest that incorporate dependencies amongst the v...

We introduce a two-alternative forced-choice experimental paradigm to quantify expressed emotions in music using the two wellknown arousal and valence (AV) dimensions. In order to produce AV scores from the pairwise comparisons and to visualize the locations of excerpts in the AV space, we introduce a flexible Gaussian process (GP) framework which learns from the pairwise comparisons directly. ...

The Heuristic Ratio Estimation (HRE) approach proposes a new way of using the pairwise comparisons matrix. It allows the assumption that the weights of some alternatives (herein referred to as concepts) are known and fixed, hence the weight vector needs to be estimated only for the other unknown values. The main purpose of this paper is to extend the previously proposed iterative HRE algorithm ...