Search results for "Kemeny distance"
showing 9 items of 9 documents
Towards the definition of distance measures in the preference-approval structures
2022
The task of combining preference rankings and approval voting is a relevant issue in social choice theory. The preference-approval voting (PAV) analyses the preferences of a group of individuals over a set of items. The main difference with the classical approaches for preference data consists in introducing, in addition to the ranking of candidates, a further distinction; candidates are subsetted in “acceptable” and “unacceptable”, or also in “good set” and “bad set” (a way to express the approval/disapproval). This work introduces the definition of a new measure to quantify disagreement between preference-approval profiles. For each pair of alternatives, we consider the two possible disag…
Recursive partitioning: an approach based on the weighted kemeny distance
2015
In the framework of preference rankings, the interest can lie in finding which predictors and which interactions are able to explain the observed preference structures. The possibility to derive consensus measures using a classification tree represents a novelty and an important tool, given its easy interpretability. This work proposes the use of a univariate decision tree for ranking data based on the weighted Kemeny distance. The performance of the methodology will be shown by using a real dataset about university rankings.
Classification trees for preference data: a distance-based approach
2014
In the framework of preference rankings, when the interest lies in explaining which predictors and which interactions among predictors are able to explain the observed preference structures, the possibility to derive consensus measures using a classi cation tree represents a novelty and an important tool given its easy interpretability. In this work we propose the use of a multivariate decision tree where a weighted Kemeny distance is used both to evaluate the distances between rankings and to de ne an impurity measure to be used in the recursive partitioning. The proposed approach allows also to weight di erently high distances in rankings in the top and in the bottom alternatives.
Consensus among preference rankings: a new weighted correlation coefficient for linear and weak orderings
2021
AbstractPreference data are a particular type of ranking data where some subjects (voters, judges,...) express their preferences over a set of alternatives (items). In most real life cases, some items receive the same preference by a judge, thus giving rise to a ranking with ties. An important issue involving rankings concerns the aggregation of the preferences into a “consensus”. The purpose of this paper is to investigate the consensus between rankings with ties, taking into account the importance of swapping elements belonging to the top (or to the bottom) of the ordering (position weights). By combining the structure of $$\tau _x$$ τ x proposed by Emond and Mason (J Multi-Criteria Decis…
A new position weight correlation coefficient for consensus ranking process without ties
2019
Preference data represent a particular type of ranking data where a group of people gives their preferences over a set of alternatives. The traditional metrics between rankings do not take into account the importance of swapping elements similar among them (element weights) or elements belonging to the top (or to the bottom) of an ordering (position weights). Following the structure of the τx proposed by Emond and Mason and the class of weighted Kemeny–Snell distances, a proper rank correlation coefficient is defined for measuring the correlation among weighted position rankings without ties. The one‐to‐one correspondence between the weighted distance and the rank correlation coefficient ho…
Weighted distance-based trees for ranking data
2017
Within the framework of preference rankings, the interest can lie in finding which predictors and which interactions are able to explain the observed preference structures, because preference decisions will usually depend on the characteristics of both the judges and the objects being judged. This work proposes the use of a univariate decision tree for ranking data based on the weighted distances for complete and incomplete rankings, and considers the area under the ROC curve both for pruning and model assessment. Two real and well-known datasets, the SUSHI preference data and the University ranking data, are used to display the performance of the methodology.
Element weighted Kemeny distance for ranking data
2021
Preference data are a particular type of ranking data that arise when several individuals express their preferences over a finite set of items. Within this framework, the main issue concerns the aggregation of the preferences to identify a compromise or a “consensus”, defined as the closest ranking (i.e. with the minimum distance or maximum correlation) to the whole set of preferences. Many approaches have been proposed, but they are not sensitive to the importance of items: i.e. changing the rank of a highly-relevant element should result in a higher penalty than changing the rank of a negligible one. The goal of this paper is to investigate the consensus between rankings taking into accou…
Consensus measures for preference rankings with ties: an approach based on position weighted Kemeny distance
2018
Preference data are a particular type of ranking data where some subjects (voters, judges, ...) give their preferences over a set of alternatives (items). It happens, in most of the real cases, that some items receive the same preference by a judge, giving raise to a ranking with ties. The purpose of our paper is to investigate on the consensus between rankings with ties taking into account the importance of swapping elements belonging to the top (or to the bottom) of the ordering (position weights). Combining the structure of the Taux proposed by Emond and Mason and the class of weighted Kemeny-Snell distances, we propose a position weighted rank correlation coefficient to compare rankings…
Ensemble methods for ranking data with and without position weights
2020
The main goal of this Thesis is to build suitable Ensemble Methods for ranking data with weights assigned to the items’positions, in the cases of rankings with and without ties. The Thesis begins with the definition of a new rank correlation coefficient, able to take into account the importance of items’position. Inspired by the rank correlation coefficient, τ x , proposed by Emond and Mason (2002) for unweighted rankings and the weighted Kemeny distance proposed by García-Lapresta and Pérez-Román (2010), this work proposes τ x w , a new rank correlation coefficient corresponding to the weighted Kemeny distance. The new coefficient is analized analitically and empirically and represents the main…