Some measures of consensus generated by distances on weak orders (original) (raw)

Measuring Consensus in Weak Orders

In this chapter we focus our attention in how to measure consensus in groups of agents when they show their preferences over a fixed set of alternatives or candidates by means of weak orders (complete preorders). We have introduced a new class of consensus measures on weak orders based on distances, and we have analyzed some of their properties paying special attention to seven well-known distances.

Consensus measures generated by weighted Kemeny distances on weak orders

2010 10th International Conference on Intelligent Systems Design and Applications, 2010

In this paper we analyze the consensus in groups of decision makers that rank alternatives by means of weak orders. We have introduced the class of weighted Kemeny distances on weak orders for taking into account where the disagreements occur, and we have analyzed the properties of the associated consensus measures.

On measuring consensus

2008

Abstract The cohesion of a group depends to large extend on the degree to which its members coincide in their preferences (what will be called the consensus). This paper proposes axioms a consensus measure should satisfy from a normative point of view and characterizes first a class of linear and additive measures which fulfills an ordinal property similar to the concept of Lorenz curve domination in the literature on income inequality measurement.

Comparing distance to consensus of collective relations using OWA operators

Consensus is understood as a unanimous agreement by all experts in a group. The goal of consensus is not the selection of several options but to develop one decision that suits the interests of the entire group under consideration. In this paper, it is assumed that collective preferences are developed with the help of commonly used ordered weighted averaging operators but resultant relations do not exhibit any property of a consensus type. That is, consensus is not reached at the first attempt of ranking alternatives. Under such circumstances, the measure of distance to consensus can be successfully used to determine how far a group collectively is from consensus. The aim of this paper is to compare, where possible, the distance to consensus of collective relations compiled with the help of most commonly used ordered weighted averaging operators. The innovative part is that this measure helps in defining an upper and lower bound of distance to consensus of the resultant collective relations. With such an analysis at hand, experts can choose a suitable ordered weighting averaging operator to formulate a collective relation that exhibits a lower distance to consensus.

Consensus measures constructed from aggregation functions and fuzzy implications

Knowledge-Based Systems, 2014

We focus on the problem of constructing functions that are able to measure the degree of consensus for a set of inputs provided over the unit interval. When making evaluations based on inputs from multiple criteria, sources or experts, the resulting output can be seen as the value which best represents the individual contributions. However it may also be desirable to know the extent to which the inputs agree. Does the representative value reflect a universal opinion? Or has there been a high degree of tradeoff? We consider the properties relating to such consensus measures and propose two general models built component-wise from aggregation functions and fuzzy implications.

Majoritarian decisions. Penalizing the disagreement

In this paper we introduce some classes of consensus measures based on distances on weak orders and we analyze some of their properties. We also propose indices of contribution to consensus for each decision maker for prioritizing the decision makers in order of their contribution to consensus. Consider a set of decision makers or voters V = {v 1 , . . . , v m } (m ≥ 3) who show their preferences over a set of alternatives X = {x 1 , . . . , x n } (n ≥ 3). With L(X) we denote the set of linear orders on X (reflexive, antisymmetric and transitive binary relations on X), and with W (X) the set of weak orders on X (complete and transitive binary relations on X).

Some results on consensus: extended abstract

We will show how reaching consensus among n individuals communicating in pairs depends on the topology of the communications graph. In particular we show that the consensus on the value of union consistent function is guaranteed in any non-cyclic fair protocol. We also anylyze protocols where individuals exchange (simultaneously) information in pairs. Finally we prove a surprising result that a certain non-trivial level of common knowledge of some formula which was not initially common knowledge is a necessary condition for a disagreement.

Measuring consensus in a preference-approval context

Information Fusion, 2014

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 preferenceapprovals.

On the Relation between Centrality Measures and Consensus Algorithms

2012

This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed method is motivated by the robustness and optimality of leaf-venation patterns. We introduce a new class of centrality measures which are built based on the degree distribution of nodes within network graph. Furthermore, the proposed measure is used to select the appropriate weight of the corresponding consensus algorithm. To this end, an implicit hierarchical structure is derived that control the flow of information in different situations. In addition, the performance analysis of the proposed measure with respect to other standard measures is performed to investigate the convergence and asymptotic behavior of the measure. Gas Transmission Network is served as our test-bed to demonstrate the applicability and the efficiently of the method.