arXiv subjects

Jesús Aranda

Publications and source records attributed to Jesús Aranda.

4 recordsLinked to original sources

arXiv2026

Minimal Effort to Consensus (MEC) polarization measure

We introduce the Minimum Effort to Consensus (MEC), a measure that quantifies polarization as resistance to consensus: a population is highly polarized when much effort is needed to bring its members to a common position, and weakly polarized when little is needed. Given an opinion distribution, MEC is the minimum effort required to turn it into a consensus distribution, taken over all consensus points, and it returns both a scalar value and an endogenous optimal consensus point. In the basic case MEC equals the 1-Wasserstein distance (Earth Mover's Distance) to the nearest consensus configuration, so that polarization becomes proximity to maximum disagreement. A two-parameter family with exponents alpha, beta >= 1 writes MEC as a weighted L^beta cost whose weights are the alpha-power of the group masses, recovering mean absolute deviation and variance-like dispersion as special cases and giving alpha and beta natural readings as identification and alienation. We prove a Shifting Away from Consensus principle, by which displacing a whole group's mass away from the optimal consensus point strictly increases polarization, and use it to show that MEC is maximized by the extremal distribution that splits the population equally between the two extremes, establishing that MEC is a polarization measure in the standard sense. We also obtain a Minority Principle and a Tipping Point method, showing that polarization is not monotone in extremism. MEC further satisfies the three axioms of Esteban and Ray with a central-split monotonicity property. Empirically, MEC[2,1.15] attains Kendall's tau near 0.89 against a sixty-expert benchmark, matching the strongest Esteban-Ray parametrization and outperforming the Van der Eijk and Tastle-Wierman measures, and it is computable by bisection in O(n log(1/epsilon)) time.

cs.CY↗

arXiv2025

The Sound of Silence in Social Networks

We generalize the classic multi-agent DeGroot model for opinion dynamics to incorporate the Spiral of Silence theory from political science. This theory states that individuals may withhold their opinions when they perceive them to be in the minority. As in the DeGroot model, a community of agents is represented as a weighted directed graph whose edges indicate how much agents influence one another. However, agents whose current opinions are in the minority become silent (i.e., they do not express their opinion). Two models for opinion update are then introduced. In the memoryless opinion model (SOM-), agents update their opinion by taking the weighted average of their non-silent neighbors' opinions. In the memory based opinion model (SOM+), agents update their opinions by taking the weighted average of the opinions of all their neighbors, but for silent neighbors, their most recent opinion is considered. We show that for SOM- convergence to consensus is guaranteed for clique graphs but, unlike for the classic DeGroot, not guaranteed for strongly-connected aperiodic graphs. In contrast, we show that for SOM+ convergence to consensus is not guaranteed even for clique graphs. We showcase our models through simulations offering experimental insights that align with key aspects of the Spiral of Silence theory. These findings reveal the impact of silence dynamics on opinion formation and highlight the limitations of consensus in more nuanced social models.

cs.MA↗

arXiv2024

Fairness and Consensus in an Asynchronous Opinion Model for Social Networks (Technical Report)

We introduce a DeGroot-based model for opinion dynamics in social networks. A community of agents is represented as a weighted directed graph whose edges indicate how much agents influence one another. The model is formalized using labeled transition systems, henceforth called opinion transition systems (OTS), whose states represent the agents' opinions and whose actions are the edges of the influence graph. If a transition labeled $(i,j)$ is performed, agent $j$ updates their opinion taking into account the opinion of agent $i$ and the influence $i$ has over $j$. We study (convergence to) opinion consensus among the agents of strongly-connected graphs with influence values in the interval $(0,1)$. We show that consensus cannot be guaranteed under the standard strong fairness assumption on transition systems. We derive that consensus is guaranteed under a stronger notion from the literature of concurrent systems; bounded fairness. We argue that bounded-fairness is too strong of a notion for consensus as it almost surely rules out random runs and it is not a constructive liveness property. We introduce a weaker fairness notion, called $m$-bounded fairness, and show that it guarantees consensus. The new notion includes almost surely all random runs and it is a constructive liveness property. Finally, we consider OTS with dynamic influence and show convergence to consensus holds under $m$-bounded fairness if the influence changes within a fixed interval $[L,U]$ with $0<L<U<1$. We illustrate OTS with examples and simulations, offering insights into opinion formation under fairness and dynamic influence.

cs.SI↗

arXiv2014

Towards Formal Interaction-Based Models of Grid Computing Infrastructures

Grid computing (GC) systems are large-scale virtual machines, built upon a massive pool of resources (processing time, storage, software) that often span multiple distributed domains. Concurrent users interact with the grid by adding new tasks; the grid is expected to assign resources to tasks in a fair, trustworthy way. These distinctive features of GC systems make their specification and verification a challenging issue. Although prior works have proposed formal approaches to the specification of GC systems, a precise account of the interaction model which underlies resource sharing has not been yet proposed. In this paper, we describe ongoing work aimed at filling in this gap. Our approach relies on (higher-order) process calculi: these core languages for concurrency offer a compositional framework in which GC systems can be precisely described and potentially reasoned about.

cs.PL↗