arXiv subjects

Frank Valencia

Publications and source records attributed to Frank Valencia.

18 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

A Constraint Opinion Model

This paper introduces a generalised opinion model that extends the standard DeGroot model by representing agents' opinions and influences as soft constraints rather than single real values. This allows for modelling scenarios beyond the scope of the DeGroot model, such as agents sharing partial information and preferences, engaging in discussions on multiple topics simultaneously, and representing opinions with different degrees of uncertainty. By considering soft constraints as influences, the proposed model captures also situations where agents impose conditions on how others' opinions are integrated during belief revision. Finally, the flexibility offered by soft constraints allows us to introduce a novel polarisation measure that takes advantage of this generalised framework.

cs.LO↗

arXiv2024

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

Consensus in Models for Opinion Dynamics with Generalized-Bias

Interest is growing in social learning models where users share opinions and adjust their beliefs in response to others. This paper introduces generalized-bias opinion models, an extension of the DeGroot model, that captures a broader range of cognitive biases. These models can capture, among others, dynamic (changing) influences as well as ingroup favoritism and out-group hostility, a bias where agents may react differently to opinions from members of their own group compared to those from outside. The reactions are formalized as arbitrary functions that depend, not only on opinion difference, but also on the particular opinions of the individuals interacting. Under certain reasonable conditions, all agents (despite their biases) will converge to a consensus if the influence graph is strongly connected, as in the original DeGroot model. The proposed approach combines different biases, providing deeper insights into the mechanics of opinion dynamics and influence within social networks.

cs.SI↗

arXiv2024

A Multi-Agent Model for Opinion Evolution under Cognitive Biases

We generalize the DeGroot model for opinion dynamics to better capture realistic social scenarios. We introduce a model where each agent has their own individual cognitive biases. Society is represented as a directed graph whose edges indicate how much agents influence one another. Biases are represented as the functions in the square region $[-1,1]^2$ and categorized into four sub-regions based on the potential reactions they may elicit in an agent during instances of opinion disagreement. Under the assumption that each bias of every agent is a continuous function within the region of receptive but resistant reactions ($\mathbf{R}$), we show that the society converges to a consensus if the graph is strongly connected. Under the same assumption, we also establish that the entire society converges to a unanimous opinion if and only if the source components of the graph-namely, strongly connected components with no external influence-converge to that opinion. We illustrate that convergence is not guaranteed for strongly connected graphs when biases are either discontinuous functions in $\mathbf{R}$ or not included in $\mathbf{R}$. We showcase our model through a series of examples and simulations, offering insights into how opinions form in social networks under cognitive biases.

cs.MA↗

arXiv2024

Unified Opinion Dynamic Modeling as Concurrent Set Relations in Rewriting Logic

Social media platforms have played a key role in weaponizing the polarization of social, political, and democratic processes. This is, mainly, because they are a medium for opinion formation. Opinion dynamic models are a tool for understanding the role of specific social factors on the acceptance/rejection of opinions because they can be used to analyze certain assumptions on human behaviors. This work presents a framework that uses concurrent set relations as the formal basis to specify, simulate, and analyze social interaction systems with dynamic opinion models. Standard models for social learning are obtained as particular instances of the proposed framework. It has been implemented in the Maude system as a fully executable rewrite theory that can be used to better understand how opinions of a system of agents can be shaped. This paper also reports an initial exploration in Maude on the use of reachability analysis, probabilistic simulation, and statistical model checking of important properties related to opinion dynamic models.

cs.LO↗

arXiv2023

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↗

arXiv2023

A Formal Model for Polarization under Confirmation Bias in Social Networks

We describe a model for polarization in multi-agent systems based on Esteban and Ray's standard family of polarization measures from economics. Agents evolve by updating their beliefs (opinions) based on an underlying influence graph, as in the standard DeGroot model for social learning, but under a confirmation bias; i.e., a discounting of opinions of agents with dissimilar views. We show that even under this bias polarization eventually vanishes (converges to zero) if the influence graph is strongly-connected. If the influence graph is a regular symmetric circulation, we determine the unique belief value to which all agents converge. Our more insightful result establishes that, under some natural assumptions, if polarization does not eventually vanish then either there is a disconnected subgroup of agents, or some agent influences others more than she is influenced. We also prove that polarization does not necessarily vanish in weakly-connected graphs under confirmation bias. Furthermore, we show how our model relates to the classic DeGroot model for social learning. We illustrate our model with several simulations of a running example about polarization over vaccines and of other case studies. The theoretical results and simulations will provide insight into the phenomenon of polarization.

cs.LO↗

arXiv2022

A Rewriting Logic Approach to Stochastic and Spatial Constraint System Specification and Verification

This paper addresses the issue of specifying, simulating, and verifying reactive systems in rewriting logic. It presents an executable semantics for probabilistic, timed, and spatial concurrent constraint programming -- here called stochastic and spatial concurrent constraint systems (SSCC) -- in the rewriting logic semantic framework. The approach is based on an enhanced and generalized model of concurrent constraint programming (CCP) where computational hierarchical spaces can be assigned to belong to agents. The executable semantics faithfully represents and operationally captures the highly concurrent nature, uncertain behavior, and spatial and epistemic characteristics of reactive systems with flow of information. In SSCC, timing attributes -- represented by stochastic duration -- can be associated to processes, and exclusive and independent probabilistic choice is also supported. SMT solving technology, available from the Maude system, is used to realize the underlying constraint system of SSCC with quantifier-free formulas over integers and reals. This results in a fully executable real-time symbolic specification that can be used for quantitative analysis in the form of statistical model checking. The main features and capabilities of SSCC are illustrated with examples throughout the paper. This contribution is part of a larger research effort aimed at making available formal analysis techniques and tools, mathematically founded on the CCP approach, to the research community.

cs.LO↗

arXiv2022

Counting and Computing Join-Endomorphisms in Lattices (Revisited)

Structures involving a lattice and join-endomorphisms on it are ubiquitous in computer science. We study the cardinality of the set $\mathcal{E}(L)$ of all join-endomorphisms of a given finite lattice $L$. In particular, we show for $\mathbf{M}_n$, the discrete order of $n$ elements extended with top and bottom, $| \mathcal{E}(\mathbf{M}_n) | =n!\mathcal{L}_n(-1)+(n+1)^2$ where $\mathcal{L}_n(x)$ is the Laguerre polynomial of degree $n$. We also study the following problem: Given a lattice $L$ of size $n$ and a set $S\subseteq \mathcal{E}(L)$ of size $m$, find the greatest lower bound ${\large\sqcap}_{\mathcal{E}(L)} S$. The join-endomorphism ${\large\sqcap}_{\mathcal{E}(L)} S$ has meaningful interpretations in epistemic logic, distributed systems, and Aumann structures. We show that this problem can be solved with worst-case time complexity in $O(mn)$ for distributive lattices and $O(mn + n^3)$ for arbitrary lattices. In the particular case of modular lattices, we present an adaptation of the latter algorithm that reduces its average time complexity. We provide theoretical and experimental results to support this enhancement. The complexity is expressed in terms of the basic binary lattice operations performed by the algorithm.

cs.MA↗

arXiv2022

On the Computation of Distributed Knowledge as the Greatest Lower Bound of Knowledge

Let $L$ be a finite lattice and $\mathcal{E}(L)$ be the set of join endomorphisms of $L$. We consider the problem of given $L$ and $f,g \in \mathcal{E}(L)$, finding the greatest lower bound $f \sqcap_{{\scriptsize \mathcal{E}(L)}} g$ in the lattice $\mathcal{E}(L)$. (1) We show that if $L$ is distributive, the problem can be solved in time $O(n)$ where $n=| L |$. The previous upper bound was $O(n^2)$. (2) We provide new algorithms for arbitrary lattices and give experimental evidence that they are significantly faster than the existing algorithm. (3) We characterize the standard notion of distributed knowledge of a group as the greatest lower bound of the join-endomorphisms representing the knowledge of each member of the group. (4) We show that deciding whether an agent has the distributed knowledge of two other agents can be computed in time $O(n^2)$ where $n$ is the size of the underlying set of states. (5) For the special case of $S5$ knowledge, we show that it can be decided in time $O(nα_{n})$ where $α_{n}$ is the inverse of the Ackermann function.

cs.MA↗

arXiv2021

On the impossibility of non-trivial accuracy under fairness constraints

One of the main concerns about fairness in machine learning (ML) is that, in order to achieve it, one may have to trade off some accuracy. To overcome this issue, Hardt et al. proposed the notion of equality of opportunity (EO), which is compatible with maximal accuracy when the target label is deterministic with respect to the input features. In the probabilistic case, however, the issue is more complicated: It has been shown that under differential privacy constraints, there are data sources for which EO can only be achieved at the total detriment of accuracy, in the sense that a classifier that satisfies EO cannot be more accurate than a trivial (i.e., constant) classifier. In our paper we strengthen this result by removing the privacy constraint. Namely, we show that for certain data sources, the most accurate classifier that satisfies EO is a trivial classifier. Furthermore, we study the trade-off between accuracy and EO loss (opportunity difference), and provide a sufficient condition on the data source under which EO and non-trivial accuracy are compatible.

cs.LG↗

arXiv2021

A Multi-Agent Model for Polarization under Confirmation Bias in Social Networks

We describe a model for polarization in multi-agent systems based on Esteban and Ray's standard measure of polarization from economics. Agents evolve by updating their beliefs (opinions) based on an underlying influence graph, as in the standard DeGroot model for social learning, but under a confirmation bias; i.e., a discounting of opinions of agents with dissimilar views. We show that even under this bias polarization eventually vanishes (converges to zero) if the influence graph is strongly-connected. If the influence graph is a regular symmetric circulation, we determine the unique belief value to which all agents converge. Our more insightful result establishes that, under some natural assumptions, if polarization does not eventually vanish then either there is a disconnected subgroup of agents, or some agent influences others more than she is influenced. We also show that polarization does not necessarily vanish in weakly-connected graphs under confirmation bias. We illustrate our model with a series of case studies and simulations, and show how it relates to the classic DeGroot model for social learning.

cs.LO↗

arXiv2021

Algebraic Structures from Concurrent Constraint Programming Calculi for Distributed Information in Multi-Agent Systems

Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-preserving functions that represent the spaces of the agents in the group. We provide an alternative characterization of this notion as the greatest family of join-preserving functions that satisfy certain basic properties. For completely distributive lattices, we establish that distributed information of a group is the greatest information below all possible combinations of information in the spaces of the agents in the group that derive a given piece of information. We show compositionality results for these characterizations and conditions under which information that can be obtained by an infinite group can also be obtained by a finite group. Finally, we provide an application on mathematical morphology where dilations, one of its fundamental operations, define an scs on a powerset lattice. We show that distributed information represents a particular dilation in such scs.

cs.MA↗

arXiv2020

Polarization and Belief Convergence of Agents in Strongly-Connected Influence Graphs

We describe a model for polarization in multi-agent systems based on Esteban and Ray's classic measure of polarization from economics. Agents evolve by updating their beliefs (opinions) based on the beliefs of others and an underlying influence graph. We show that polarization eventually disappears (converges to zero) if the influence graph is strongly-connected. If the influence graph is a circulation we determine the unique belief value all agents converge to. For clique influence graphs we determine the time after which agents will reach a given difference of opinion. Our results imply that if polarization does not disappear then either there is a disconnected subgroup of agents or some agent influences others more than she is influenced. Finally, we show that polarization does not necessarily vanish in weakly-connected graphs, and illustrate the model with a series of case studies and simulations giving some insights about polarization.

cs.MA↗

arXiv2019

Semantic Structures for Spatially-Distributed Multi-Agent Systems

Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. They have been used to reason about beliefs, lies, and group epistemic behaviour inspired by social networks. They have also been used for proving new results about modal logics and giving semantics to process calculi. In this paper we will discuss the theory and main results about scs.

cs.MA↗

arXiv2012

Reducing Weak to Strong Bisimilarity in CCP

Concurrent constraint programming (ccp) is a well-established model for concurrency that singles out the fundamental aspects of asynchronous systems whose agents (or processes) evolve by posting and querying (partial) information in a global medium. Bisimilarity is a standard behavioural equivalence in concurrency theory. However, only recently a well-behaved notion of bisimilarity for ccp, and a ccp partition refinement algorithm for deciding the strong version of this equivalence have been proposed. Weak bisimiliarity is a central behavioural equivalence in process calculi and it is obtained from the strong case by taking into account only the actions that are observable in the system. Typically, the standard partition refinement can also be used for deciding weak bisimilarity simply by using Milner's reduction from weak to strong bisimilarity; a technique referred to as saturation. In this paper we demonstrate that, because of its involved labeled transitions, the above-mentioned saturation technique does not work for ccp. We give an alternative reduction from weak ccp bisimilarity to the strong one that allows us to use the ccp partition refinement algorithm for deciding this equivalence.

cs.PL↗

arXiv2011

Proceedings 18th International Workshop on Expressiveness in Concurrency

This volume contains the proceedings of the 18th International Workshop on Expressiveness in Concurrency (EXPRESS 2011), which took place on 5th September 2011 in Aachen, as a satellite workshop of CONCUR 2011. The EXPRESS workshop series aim at bringing together researchers who are interested in the expressiveness and comparison of formal models that broadly relate to concurrency. In particular, this also includes emergent fields such as logic and interaction, game-theoretic models, and service-oriented computing.

cs.LO↗