arXiv subjects

André C. R. Martins

Publications and source records attributed to André C. R. Martins.

At least 19 recordsLinked to original sources

arXiv2025

Annealing approximation in master-node network model

This paper investigates absorbing-state phase transitions in opinion dynamics through a master-node network model analyzed using annealing approximation. We develop a theoretical framework examining three fundamental regimes: systems converging to complete disagreement, complete consensus, or both states depending on initial conditions. The phase behavior is governed by two key chiral parameters: $R$ measuring right-oriented influence and $L$ measuring left-oriented influence in the network interactions. Our analysis reveals a rich phase diagram featuring both continuous and discontinuous transitions between disordered and ordered phases. The discontinuous transition emerges in systems with two absorbing states, where the final configuration depends critically on initial opinion distributions. The annealing approximation provides fundamental insights into how asymmetric social influences (chirality) shape collective opinion formation, acting as a symmetry-breaking element that drives the system toward polarization or consensus.

physics.soc-ph↗

arXiv2022

Critical Exponents of Master-Node Network Model

The dynamics of competing opinions in social network play an important role in society, with many applications in diverse social contexts as consensus, elections, morality and so on. Here we study a model of interacting agents connected in networks to analyze their decision stochastic process. We consider a first-neighbor interaction between agents in a one-dimensional network with a shape of ring topology. Moreover, some agents are also connected to a hub, or master node, that has preferential choice or bias. Such connections are quenched. As the main results, we observed a continuous non-equilibrium phase transition to an absorbing state as a function of control parameters. By using the finite size scaling method, we analyzed the static and dynamic critical exponents to show that this model probably cannot match any universality class already known.

physics.soc-ph↗

arXiv2021

Opinions and dark energy: A mechanism of long-range repulsion in a toy opinion particle model

The concept of opinion particles can be introduced by studying time-continuous versions of Bayesian-inspired opinion dynamics methods. Here, we use opinion particles to further explore how information and Bayesian methods can contribute new ideas to physical problems. Continuous-time limits are shown to correspond to the case with little trust between the original agents, and a synchronous version of the model is studied. The interaction between two particles is defined as attractive. However, space and distances are not well represented in the model. We define a local measure of distances based on the parameters. That allows distant particles to be repelled in the natural coordinates of any central particle, similar to the observed cosmological effects identified as dark energy. Keywords: Opinion dynamics, Opinion particles, Dark energy, Bayesian methods, CODA

physics.soc-ph↗

arXiv2020

Senescence, change, and competition: when the desire to pick one model harms our understanding

The question of why we age is a fundamental one. It is about who we are, and it also might have critical practical aspects as we try to find ways to age slower. Or to not age at all. Different reasons point at distinct strategies for the research of anti-ageing drugs. While the main reason why biological systems work as they do is evolution, for quite a while, it was believed that aging required another explanation. Aging seems to harm individuals so much that even if it has group benefits, those benefits were unlikely to be enough. That has led many scientists to propose non-evolutionary explanations as to why we age. But those theories seem to fail at explaining all the data on how species age. Here, I will show that the insistence of finding the one idea that explains it all might be at the root of the difficulty of getting a full picture. By exploring an evolutionary model of aging where locality and temporal changes are fundamental aspects of the problem, I will show that environmental change causes the barrier for group advantages to become much weaker. That weakening might help small group advantages to add up to the point they could make an adaptive difference. To answer why we age, we might have to abandon asking which models are correct. The full answer might come from considering how much each hypothesis behind each existing model, evolutionary and non-evolutionary ones, contributes to the real world's solution.

q-bio.PE↗

arXiv2020

Embracing undecidability: Cognitive needs and theory evaluation

There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Goëdel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things get even harder. We want to compare the results of our mathematical theories to observations, and that means the use of inductive methods. While we can demonstrate how an ideal probabilistic induction should work, the requirements of such a method include a few infinities. Furthermore, it would not be even enough to be able to compute those methods and obtain predictions. There are cases where underdeterminacy might be unavoidable, such as the interpretation of quantum mechanics or the current status of string theory. Despite that, scientists still behave as if they were able to know the truth. As it becomes clear that such behavior can cause severe cognitive mistakes, the need to accept our limits, both our natural human limits and the limits of the tools we have created, become apparent. This essay will discuss how we must accept that knowledge is almost only limited to formal systems. Moreover, even in those, there will always be undecidable propositions. We will also see how those questions influence the evaluation of current theories in physics.

physics.hist-ph↗

arXiv2020

Extremism definitions in opinion dynamics models

There are several opinion dynamics models where extremism is defined as part of their characteristics. However, the way extremism is implemented in each model does not correspond to equivalent definitions. While some models focus on one aspect of the problem, others focus on different characteristics. This paper shows how each model only captures part of the problem and how Bayesian inspired opinion models can help put those differences in perspective. That discussion suggests new ways to introduce variables that can represent the problem of extremism better than we do today. Keywords: Extremism, Opinion dynamics, CODA, Sociophysics

physics.soc-ph↗

arXiv2019

Ideologically Motivated Biases in a Multiple Issues Opinion Model

It has been observed people tend to have opinions that are far more internally consistent than it would be reasonable to expect. Here, we study how that observation might emerge from changing how agents trust the opinions of their peers in a model for opinion dynamics with multiple issues. A previous Bayesian inspired opinion model for continuous opinions is extended to include multiple issues. In the original model, agents tended to trust less opinions that were too different from their own. We investigate the properties of the extended model in its natural form. And we also introduce the possibility the trust of the agent might depend not only on the specific issue but on the average opinions over the many issues. By adopting such a ideological point of view, we observe an important decrease in the spread of individual opinions.

physics.soc-ph↗

arXiv2019

Network generation and evolution based on spatial and opinion dynamics components

In this paper, a model for a spatial network evolution based on a Metropolis simulation is presented. The model uses an energy function that depends both on the distance between the nodes and the stated preferences. The agents influence their network neighbors opinions using the CODA model. That means each agent has a preference between two options based on its probabilistic assessment of which option is the best one. The algorithm generates realistic networks for opinion problems as well as temporal dynamics for those networks. The transition from a random state to an ordered situation, as temperature decreases, is described. Different types of networks appear based on the relative strength of the spatial and opinion components of the energy.

physics.soc-ph↗

arXiv2017

Don't choose theories: Normative inductive reasoning and the status of physical theories

Evaluating theories in physics used to be easy. Our theories provided very distinct predictions. Experimental accuracy was so small that worrying about epistemological problems was not necessary. That is no longer the case. The underdeterminacy problem between string theory and the standard model for current possible experimental energies is one example. We need modern inductive methods for this problem, Bayesian methods or the equivalent Solomonoff induction. To illustrate the proper way to work with induction problems I will use the concepts of Solomoff induction to study the status of string theory. Previous attempts have focused on the Bayesian solution. And they run into the question of why string theory is widely accepted with no data backing it. Logically unsupported additions to the Bayesian method were proposed. I will show here that, by studying the problem from the point of view of the Solomonoff induction those additions can be understood much better. They are not ways to update probabilities. Instead, they are considerations about the priors as well as heuristics to attempt to deal with our finite resources. For the general problem, Solomonoff induction also makes it clear that there is no demarcation problem. Every possible idea can be part of a proper scientific theory. It is just the case that data makes some ideas extremely improbable. Theories where that does not happen must not be discarded. Rejecting ideas is just wrong.

physics.hist-ph↗

arXiv2016

Stop the tests: Opinion bias and statistical tests

When statisticians quarrel about hypothesis testing, the debate usually focus on which method is the correct one. The fundamental question of whether we should test hypothesis at all tends to be forgotten. This lack of debate has its roots on our desire to have ideas we believe and defend. But cognitive experiments have been showing that, when we do choose ideas, we become prey to a large number of biases. Several of our biases can be grouped together in a single description, an opinion bias. This opinion bias is nothing more than our desire to believe in something and to defend it. Also, despite our feelings, believing has no solid logical or philosophical grounds. In this paper, I will show that if we combine the fact that even logic can never prove an idea right or wrong and the problems our brains cause when we pick ideas, hypothesis testing and its terminology are a recipe for disaster. Testing should have no place when we are thinking about hypothesis.

stat.OT↗

arXiv2015

Thou shalt not take sides: Cognition, Logic and the need for changing how we believe

We believe, in the sense of supporting ideas and considering them correct while dismissing doubts about them. We take sides about ideas and theories as if that was the right thing to do. And yet, from a rational point of view, this type of support and belief is not justifiable at all. The best we can hope when describing the real world, as far as we know, is to have probabilistic knowledge, to have probabilities associated to each statement. And even that can be very hard to achieve in a reliable way. Far worse, when we defend ideas and believe them as if they were true, Cognitive Psychology experiments show that we stop being able to analyze the question we believe at with competence. In this paper, I gather the evidence we have about taking sides and present the obvious but unseen conclusion that these facts combined mean that we should actually never believe in anything about the real world, except in a probabilistic way. We must actually never take sides because taking sides destroy out abilities to seek for the most correct description of the world. That means we need to start reformulating the way we debate ideas, from our teaching to our political debates, if we actually want to be able to arrive at the best solutions as suggested by whatever evidence we might have. I will show that this has deep consequences on a number of problems, ranging from the emergence of extremism to the reliability of whole scientific fields. Inductive reasoning requires that we allow every idea to make predictions so that we may rank which ideas are better and that has important consequences in scientific practice. The crisis around $p$-values is also discussed and much better understood under the light of this paper results. Finally, I will debate possible ideas to try to minimize the problem.

physics.soc-ph↗

arXiv2013

Opinion Particles: Classical Physics and Opinion Dynamics

A model for Opinion Particles, based on Bayesian-inspired models of Opinion Dynamics such as the CODA model is presented. By extending the discrete time characteristic of those models to continuous time, a theory for the movement of opinion particles is obtained, based only on inference ideas. This will allow inertia to be obtained as a consequence of an extended CODA model. For the general case, we will see that the likelihoods are associated with variables such as velocity and acceleration of the particles. Newtonian forces are easily defined and the relationship between a force and the equivalent likelihood provided. The case of the harmonic oscillator is solved as an example, to illustrate clearly the relationship between Opinion Particles and Mechanics. Finally, possible paths to apply these results to General Relativity are debated.

physics.gen-ph↗

arXiv2013

Applying a new method to the 2-d Ising transition

The Ising ferromagnetic model on a square lattice is revisited using the Galam Unifying Frame (GUF), set to investigate the dynamics of two-state variable systems within the frame of opinion dynamics. When combined with Metropolis dynamics, an unexpected intermediate "dis/order" phase is found with the coexistence of two attractors associated respectively to an ordered and a disordered phases. The basin of attraction of initial conditions for the disordered phase attractor starts from zero size at a first critical temperature $T_{c1}$ to embody the total landscape of initial conditions at a second critical temperature $T_{c2}$ with $T_{c1}\approx 1.59$ and $T_{c2}\approx 2.11$ in $J/k_B$ units. It appears that $T_{c2}$ is close to the Onsager result $T_{c}\approx 2.27$. The transition, which is first-order like, exhibits a vertical jump to the disorder phase at $T_{c2}$, reminiscent of the rather abrupt vanishing of the corresponding Onsager second order transition. However, using Glauber dynamics combined with GUF does not yield the intermediate phase and instead the expected single transition at $T_{c}\approx 3.09$. Accordingly, although the "dis/order" phase produced by the GUF - Metropolis combination is not physical, it is an intriguing result to be understood. In particular the fact that Glauber and Metropolis dynamics yield so different results using GUF needs an explanation. The possibility of extending GUF to larger clusters is discussed.

cond-mat.stat-mech↗

arXiv2013

Trust in the CODA model: Opinion Dynamics and the reliability of other agents

A model for the joint evolution of opinions and how much the agents trust each other is presented. The model is built using the framework of the Continuous Opinions and Discrete Actions (CODA) model. Instead of a fixed probability that the other agents will decide in the favor of the best choice, each agent considers that other agents might be one one of two types: trustworthy or useless. Trustworthy agents are considered more likely to be right than wrong, while the opposite holds for useless ones. Together with the opinion about the discussed issue, each agent also updates that probability for each one of the other agents it interacts withe probability each one it interacts with is of one type or the other. The dynamics of opinions and the evolution of the trust between the agents are studied. Clear evidences of the existence of two phases, one where strong polarization is observed and the other where a clear division is permanent and reinforced are observed. The transition seems signs of being a first-order transition, with a location dependent on both the parameters of the model and the initial conditions. This happens despite the fact that the trust network evolves much slower than the opinion on the central issue.

physics.soc-ph↗

arXiv2012

The building up of individual inflexibility in opinion dynamics

Two models of opinion dynamics are entangled in order to build a more realistic model of inflexibility. The first one is the Galam Unifying Frame (GUF), which incorporates rational and inflexible agents, and the other one considers the combination of Continuous Opinions and Discrete Actions (CODA). While initially in GUF, inflexibility is a fixed given feature of an agent, it is now the result of an accumulation for a given agent who makes the same choice through repeated updates. Inflexibility thus emerges as an internal property of agents becoming a continuous function of the strength of its opinion. Therefore an agent can be more or less inflexible and can shift from inflexibility along one choice to inflexibility along the opposite choice. These individual dynamics of the building up and falling off of an agent inflexibility are driven by the successive local updates of the associated individual opinions. New results are obtained and discussed in terms of predicting outcomes of public debates.

physics.soc-ph↗

arXiv2012

Discrete Opinion models as a limit case of the CODA model

Opinion Dynamics models can be, for most of them, divided between discrete and continuous. They are used in different circumstances and the relationship between them is not clear. Here we will explore the relationship between a model where choices are discrete but opinions are a continuous function (the Continuous Opinions and Discrete Actions, CODA, model) and traditional discrete models. I will show that, when CODA is altered to include reasoning about the influence one agent can have on its own neighbors, agreement and disagreement no longer have the same importance. The limit when an agent considers itself to be more and more influential will be studied and we will see that one recovers discrete dynamics, like those of the Voter model in that limit

physics.soc-ph↗

arXiv2011

Change and Aging Senescence as an adaptation

Understanding why we age is a long-lived open problem in evolutionary biology. Aging is prejudicial to the individual and evolutionary forces should prevent it, but many species show signs of senescence as individuals age. Here, I will propose a model for aging based on assumptions that are compatible with evolutionary theory: i) competition is between individuals; ii) there is some degree of locality, so quite often competition will between parents and their progeny; iii) optimal conditions are not stationary, mutation helps each species to keep competitive. When conditions change, a senescent species can drive immortal competitors to extinction. This counter-intuitive result arises from the pruning caused by the death of elder individuals. When there is change and mutation, each generation is slightly better adapted to the new conditions, but some older individuals survive by random chance. Senescence can eliminate those from the genetic pool. Even though individual selection forces always win over group selection ones, it is not exactly the individual that is selected, but its lineage. While senescence damages the individuals and has an evolutionary cost, it has a benefit of its own. It allows each lineage to adapt faster to changing conditions. We age because the world changes.

q-bio.PE↗

arXiv2009

The Importance of Disagreeing: Contrarians and Extremism in the CODA model

In this paper, we study the effects of introducing contrarians in a model of Opinion Dynamics where the agents have internal continuous opinions, but exchange information only about a binary choice that is a function of their continuous opinion, the CODA model. We observe that the hung election scenario still exists here, but it is weaker and it shouldn't be expected in every election. Finally, we also show that the introduction of contrarians make the tendency towards extremism of the original model weaker, indicating that the existence of agents that prefer to disagree might be an important aspect and help society to diminish extremist opinions.

physics.soc-ph↗