Pairwise dichotomous cohesiveness measures

Producción CientíficaAbstract In a framework where experts or agents express their opinions in a dichotomous way, we analyze the cohesiveness of their opinions on axed set of issues in a population. A parametric family of related measures are introduced and axiomatically characterized. They are ordinally equivalent when the population isxed, and some further properties are proved. In order to argue that this restricted dichotomous situation is nevertheless versatile, the paper ends with several empirical illustrations based on real forecasts (for the 2012 American presidential election) and elections (with real data from referenda in two countries and from elections in several scientic societies).Ministerio de Economía, Industria y Competitividad (Project ECO2012-31933)Ministerio de Economía, Industria y Competitividad (Project ECO2012-32178)Ministerio de Economía, Industria y Competitividad (Proyect CGL2008-06003-C03-03/CLI)Ministerio de Economía, Industria y Competitividad (Project CGL2011-29396-C03-02)

The problem of collective identity in a fuzzy environment

Producción CientíficaWe define the problem of group identication in a fuzzy environment. We concentrate on the case where the society is required to self-determine the belongingness of each member to a speci_c group, characterized by a single attribute. In general terms, this case consists of a collective identity issue that can be regarded as an aggregation problem of individual assessments within a group. Here we introduce the possibility that both the original assessments and the resulting output attach partial memberships to the collectivity, for each potential member. We propose relevant classes of rules, and some are axiomatically characterized. Our new approach provides a way to circumvent classical impossibility results like Kasher and Rubinstein's.Ministerio de Economía, Industria y Competitividad (Project ECO2012-32178

A fuzzy hierarchical multiple criteria group decision support system - Decider - and its applications

Decider is a Fuzzy Hierarchical Multiple Criteria Group Decision Support System (FHMC-GDSS) designed for dealing with subjective, in particular linguistic, information and objective information simultaneously to support group decision making particularly on evaluation. In this chapter, the fuzzy aggregation decision model, functions and structure of Decider are introduced. The ideas to resolve decision and evaluation problems we have faced in the development and application of Decider are presented. Two real applications of the Decider system are briefly illustrated. Finally, we discuss our further research in this area. © 2011 Springer-Verlag Berlin Heidelberg

Establishing Herd Immunity is Hard Even in Simple Geometric Networks

We study the following model of disease spread in a social network. At first, all individuals are either infected or healthy. Next, in discrete rounds, the disease spreads in the network from infected to healthy individuals such that a healthy individual gets infected if and only if a sufficient number of its direct neighbours are already infected. We represent the social network as a graph. Inspired by the real-world restrictions in the current epidemic, especially by social and physical distancing requirements, we restrict ourselves to networks that can be represented as geometric intersection graphs. We show that finding a minimal vertex set of initially infected individuals to spread the disease in the whole network is computationally hard, already on unit disk graphs. Hence, to provide some algorithmic results, we focus ourselves on simpler geometric graph classes, such as interval graphs and grid graphs.Comment: This is an extended and revised version of a preliminary conference report that was presented in WAW 202

Group Control for Procedural Rules: Parameterized Complexity and Consecutive Domains

We consider {\sc{Group Control by Adding Individuals}} (\sc{GCAI}) for two procedural rules -- the consensus-start-respecting rule and the liberal-start-respecting rule. It is known that {\sc{GCAI}} for both rules are NP-hard, but whether they are fixed-parameter tractable with respect to the number of distinguished candidates remained open. We resolve both open problems in the affirmative. In addition, we strengthen the NP-hardness of GCAI by showing that, with respect to the natural parameter the number of added individuals, GCAI for both rules is W[2]-hard. Notably, the W[2]-hardness for the liberal-start-respecting rule holds even when restricted to a very special case where the qualifications of individuals satisfy the so-called consecutive ones property. However, for the consensus-start-respecting rule, the problem becomes polynomial-time solvable in this special case. We also study a duality restriction where the disqualifications of individuals fulfill the consecutive ones property, and we show that under this restriction {\sc{GCAI}} for both rules turn out to be polynomial-time solvable. Our reductions for showing W[2]-hardness also imply several other lower bounds concerning kernelization and exact algorithms

Broadening the Complexity-theoretic Analysis of Manipulative Attacks in Group Identification

In the Group Identification problem, we are given a set of individuals and are asked to identify a socially qualified subset among them. Each individual in the set has an opinion about who should be considered socially qualified. There are several different rules that can be used to determine the socially qualified subset based on these mutual opinions. In a manipulative attack, an outsider attempts to exploit the way the used rule works, with the goal of changing the outcome of the selection process to their liking. In recent years, the complexity of group control and bribery based manipulative attacks in Group Identification has been the subject of intense research. However, the picture is far from complete, and there remain many open questions related to what exactly makes certain problems hard, or certain rules immune to some attacks. Supplementing previous results, we examine the complexity of group microbribery on so-called protective problem instances; that is, instances where all individuals from the constructive target set are already socially qualified initially. In addition, we study a relaxed variant of group control by deleting individuals for the consent rules, the consensus-start-respecting rule, and the liberal-start-respecting rule. Based on existing literature, we also formalize three new social rules of the iterative consensus type, and we provide a comprehensive complexity-theoretic analysis of group control and bribery problems for these rules.Comment: 93 pages, 8 figures, 3 table