Measuring Consensus in Weak Orders

García-Lapresta, José Luis; Pérez-Román, David

doi:10.1007/978-3-642-20533-0_13

Cited by 40 publications

(49 citation statements)

References 20 publications

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“…Additionally, Bosch [5] and Alcalde-Unzu and Vorsatz [1] provided axiomatic characterizations of several consensus measures in the context of linear orders. García-Lapresta and Pérez-Román [15] extended that notion to the context of weak orders and they analyzed a class of consensus measures generated by distances. Alcantud et al [2] provided axiomatic characterizations of some consensus measures in the setting of approval voting.…”

Section: Consensusmentioning

confidence: 99%

Consensus-Based Agglomerative Hierarchical Clustering

García-Lapresta

Pérez-Román

2017

Fuzzy Sets, Rough Sets, Multisets and Clustering

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In this contribution, we consider that a set of agents assess a set of alternatives through numbers in the unit interval. In this setting, we introduce a measure that assigns a degree of consensus to each subset of agents with respect to every subset of alternatives. This consensus measure is defined as 1 minus the outcome generated by a symmetric aggregation function to the distances between the corresponding individual assessments. We establish some properties of the consensus measure, some of them depending on the used aggregation function. We also introduce an agglomerative hierarchical clustering procedure that is generated by similarity functions based on the previous consensus measures.

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Section: Consensusmentioning

confidence: 99%

Consensus-Based Agglomerative Hierarchical Clustering

García-Lapresta

Pérez-Román

2017

Fuzzy Sets, Rough Sets, Multisets and Clustering

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“…From the point of view of considering consensus among a family of voters, McMorris and Powers [48] characterised consensus rules defined on hierarchies, while García-Lapresta and Pérez-Román [29] focused on how to measure consensus using complete preorders on alternatives and introduced a class of consensus measures based on seven well-known distances. Subsequently, Alcalde-Unzu and Vorstatz in [1] characterised a family of linear and additive consensus measures, whereas in [2] new ways to measure the similarity of preferences in a group of individuals were suggested.…”

Section: Consensus Measurement In the Literaturementioning

confidence: 99%

“…In the Decision Making context, the use of aggregation functions to derive the degree of agreement among a group of experts has been justified (see for example [11,29,31,43,47]). Recall that the main aim of considering aggregation functions is to produce an overall output that can be considered representative of the aggregated values by incorporating desirable properties.…”

Section: A New Consensus Measure: Correlation Consensus Degreementioning

confidence: 99%

“…Up to now most studies on consensus measurement have focused on the use of distance/similarity function based measures and association measures, respectively. Among the distance functions used, and worth highlighting, are the Kemeny, Mahalanobis, Mannhattan, Jacard, Dice and Cosine distance functions [1,4,6,17,19,29,31]. Association measures are less widely used than distance functions but it is also possible to find the use of some of them such as the Kendall's coefficient, the Goodman-Kruskal's index and the Spearman's coefficient [18,24,35,44,58].…”

Section: Introductionmentioning

confidence: 99%

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A new measure of consensus with reciprocal preference relations: The correlation consensus degree

González-Arteaga

Calle

Chiclana

2016

Knowledge-Based Systems

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The achievement of a 'consensual' solution in a group decision making problem depends on experts' ideas, principles, knowledge, experience, etc. The measurement of consensus has been widely studied from the point of view of different research areas, and consequently different consensus measures have been formulated, although a common characteristic of most of them is that they are driven by the implementation of either distance or similarity functions. In the present work though, and within the framework of experts' opinions modelled via reciprocal preference relations, a different approach to the measurement of consensus based on the Pearson correlation coefficient is studied. The new correlation consensus degree measures the concordance between the intensities of preference for pairs of alternatives as expressed by the experts. Although a detailed study of the formal properties of the new correlation consensus degree shows that it verifies important properties that are common either to distance or to similarity functions between intensities of preferences, it is also proved that it is different to traditional consensus measures. In order to emphasise novelty, two applications of the proposed methodology are also included. The first one is used to illustrate the computation process and discussion of the results, while the second one covers a real life application that makes use of data from Clinical Decision-Making.

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“…, x n }, with n ≥ 2, be the set of alternatives which have to be evaluated. Under total and Pérez-Román [17] extended that notion to the context of weak orders and they analyzed a class of consensus measures generated by distances. certainty, each agent assigns a linguistic term to every alternative within a linguistic ordered scale L = {l 1 , .…”

Section: Notation and Basic Notionsmentioning

confidence: 99%