Measuring consensus in a preference-approval context

We consider measuring the degree of homogeneity for preference-approval profiles which include the approval information for the alternatives as well as the rankings of them. A distance-based approach is followed to measure the disagreement for any given two preference-approvals. Under the condition that a proper metric is used, we propose a measure of consensus which is robust to some extensions of the ordinal framework. This paper also shows that there exists a limit for increasing the homogeneity level in a group of individuals by simply replicating their preference-approvals

Measuring consensus in a preference-approval context

Producción CientíficaWe consider measuring the degree of homogeneity for preference-approval proles which include the approval information for the alternatives as well as the rankings of them. A distance-based approach is followed to measure the disagreement for any given two preference-approvals. Under the condition that a proper metric is used, we propose a measure of consensus which is robust to some extensions of the ordinal framework. This paper also shows that there exists a limit for increasing the homogeneity level in a group of individuals by simply replicating their preference approvals.Ministerio de Economía, Industria y Competitividad (ECO2009- 07332)Ministerio de Economía, Industria y Competitividad (ECO2008-03204-E/ECON

Consensus-Based Agglomerative Hierarchical Clustering

Producción CientíficaIn 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 measuresMinisterio de Economía, Industria y Competitividad (ECO2012-32178)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA066U13

Approval consensus measures

In many realistic group decision making problems where a “representative” collective output must be produced, it is relevant to measure how much consensus this solution conveys to the group. Many aspects influence the final decision in group decision making problems. Two key issues are the experts’ individual opinions and the methodology followed to compute such a final decision (aggregation operators, voting systems, etc.). In this paper we consider situations where each member of a population decides upon approving or not approving each of a set of options. The experts express their opinions in a dichotomous way, e.g., because they intend to use approval voting. In order to measure the consensus or cohesiveness that the expression of the individual preferences conveys we propose the concept of approval consensus measure (ACM), which does not refer to any priors of the agents like preferences or other decision-making processes. Then we give axiomatic characterizations of two generic classes of ACMs

Approval consensus measures

In many realistic group decision making problems where a “representative” collective output must be produced, it is relevant to measure how much consensus this solution conveys to the group. Many aspects influence the final decision in group decision making problems. Two key issues are the experts’ individual opinions and the methodology followed to compute such a final decision (aggregation operators, voting systems, etc.). In this paper we consider situations where each member of a population decides upon approving or not approving each of a set of options. The experts express their opinions in a dichotomous way, e.g., because they intend to use approval voting. In order to measure the consensus or cohesiveness that the expression of the individual preferences conveys we propose the concept of approval consensus measure (ACM), which does not refer to any priors of the agents like preferences or other decision-making processes. Then we give axiomatic characterizations of two generic classes of ACMs

Medidas de consenso en contextos preferenciales generadas por distancias

En esta tesis se ha analizado cómo medir el consenso entre agentes que muestran sus preferencias sobre alternativas en diversos escenarios. El concepto de medida de consenso, introducido por Bosch para órdenes lineales, se ha extendido a órdenes débiles, órdenes dicotómicos y preferencias aprobatorias. Se han propuesto varias clases de medidas de consenso que tienen en cuenta las distancias entre las preferencias individuales; además, se ha desarrollado un procedimiento para que las distancias entre preferencias sean generadas por distancias entre vectores. Se han introducido distancias ponderadas sobre órdenes débiles, órdenes dicotómicos y preferencias aprobatorias que son sensibles a dónde se producen desacuerdos en la ordenación de las alternativas. Se ha llevado a cabo un estudio de las propiedades de las correspondientes medidas de consenso en los escenarios mencionados. Por otra parte se han utilizado medidas de consenso para la creación de conglomerados mediante un nuevo criterio, denominado método del consensoDepartamento de Economía Aplicad