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Miguel Rebollo

Publications and source records attributed to Miguel Rebollo.

3 recordsLinked to original sources

Decentralized Value Systems Agreements

One of the biggest challenges of value-based decision-making is dealing with the subjective nature of values. The relative importance of a value for a particular decision varies between individuals, and people may also have different interpretations of what aligning with a value means in a given situation. While members of a society are likely to share a set of principles or values, their value systems--that is, how they interpret these values and the relative importance they give to them--have been found to differ significantly. This work proposes a novel method for aggregating value systems, generating distinct value agreements that accommodate the inherent differences within these systems. Unlike existing work, which focuses on finding a single value agreement, the proposed approach may be more suitable for a realistic and heterogeneous society. In our solution, the agents indicate their value systems and the extent to which they are willing to concede. Then, a set of agreements is found, taking a decentralized optimization approach. Our work has been applied to identify value agreements in two real-world scenarios using data from a Participatory Value Evaluation process and a European Value Survey. These case studies illustrate the different aggregations that can be obtained with our method and compare them with those obtained using existing value system aggregation techniques. In both cases, the results showed a substantial improvement in individual utilities compared to existing alternatives.

cs.MA

On the convergence of weighted-average consensus

In this note we give sufficient conditions for the convergence of the iterative algorithm called weighted-average consensus in directed graphs. We study the discrete-time form of this algorithm. We use standard techniques from matrix theory to prove the main result. As a particular case one can obtain well-known results for non-weighted average consensus. We also give a corollary for undirected graphs.

math.OC

L-RCM: a method to detect connected components in undirected graphs by using the Laplacian matrix and the RCM algorithm

In this paper we consider undirected graphs with no loops and multiple edges, consisting of k connected components. In these cases, it is well known that one can find a numbering of the vertices such that the adjacency matrix A is block diagonal with k blocks. This also holds for the (unnormalized) Laplacian matrix L= D-A, with D a diagonal matrix with the degrees of the nodes. In this paper we propose to use the Reverse Cuthill-McKee (RCM) algorithm to obtain a block diagonal form of L that reveals the number of connected components of the graph. We present some theoretical results about the irreducibility of the Laplacian matrix ordered by the RCM algorithm. As a practical application we present a very efficient method to detect connected components with a computational cost of O(m+n), being m the number of edges and n the number of nodes. The RCM method is implemented in some comercial packages like MATLAB and Mathematica. We make the computations by using the function symrcm of MATLAB. Some numerical results are shown

cs.DM