arXiv subjects

Arkadiusz Jędrzejewski

Publications and source records attributed to Arkadiusz Jędrzejewski.

15 recordsLinked to original sources

arXiv2026

Unified Framework for Binary-Choice Dynamics: Analysis and Applications

We demonstrate how the unified framework for binary-choice dynamics can be used to study the role of annealed and quenched disorders in homogeneous and heterogeneous systems. The framework defines the structure of interactions between agents without imposing their functional forms. Such a high level of generality allows us to connect many different models across disciplines and find universal rules that apply to all of them. Within this framework, agents update their states under the influence of two competing mechanisms chosen according to individual preferences. We review the literature to classify existing models as homogeneous or heterogeneous based on their preference distribution, and we discuss the role of annealed (changing) and quenched (fixed) disorders in modeling these preferences. Using the framework, we derive a constraint on the transition rates. When a model meets this condition, three major things happen: annealed and quenched dynamics become equivalent, any heterogeneous system can be mapped into a homogeneous one, and oscillations cannot emerge. We illustrate these consequences using models from statistical physics, opinion dynamics, and disease spreading. Finally, we discuss the framework limitations and its potential further developments.

physics.soc-ph↗

arXiv2026

Targeting Behavior or Intention? Intervention Strategies in Expressed-Private Opinion Dynamics

Exogenous interventions, including economic incentives, can be used to promote behavioral change and the adoption of new products or practices. They may act on different levels, either directly affecting customers' behavior (expressed level) or changing intentions (private level). The key question is which intervention strategy is more effective: targeting the expressed or the private level. Although expressed-private opinion (EPO) models are especially suitable for addressing this problem, they have not yet been used in this context. To fill this gap, we extend previous agent-based EPO models by incorporating exogenous interventions and compare different intervention strategies. We analyze the resulting model using a mean-field approximation, complemented by Monte Carlo simulations on a complete graph. Our results show that there is no universal answer to whether an intervention should target the expressed or the private opinion. The effectiveness of an intervention depends on the adoption level at the moment of its introduction. Interventions acting on the expressed level are more effective when adoption is still low, whereas interventions acting on the private level are more effective when adoption is already high and the goal is to support internal acceptance and reduce dissonance. Moreover, the model shows that high adoption is accompanied by low dissonance between expressed and private opinions, which is consistent with self-congruity theory. This agreement provides theoretical support for the model and strengthens its policy implications.

physics.soc-ph↗

arXiv2025

When Does Population Diversity Matter? A Unified Framework for Binary-Choice Dynamics

We propose a modeling framework for binary-choice dynamics in which agents update their states using two mechanisms selected based on individual preference drawn from an arbitrary distribution. We compare annealed dynamics, where preferences change over time, and quenched dynamics, where they remain fixed. Our framework bridges gaps between existing models and provides a systematic approach to assess when individual-level diversity affects collective dynamics and when it can be effectively ignored. We identify a constraint on transition probabilities that makes annealed and quenched dynamics equivalent. We show that when this condition is satisfied, the quenched dynamics reduces to a one-dimensional system, ruling out oscillatory behavior that may otherwise emerge.

physics.soc-ph↗

arXiv2024

Symmetric conformity functions make decision-making processes independent of the distribution of learning strategies

Two main procedures characterize the way in which social actors evaluate the qualities of the options in decision-making processes: they either seek to evaluate their intrinsic qualities (individual learners), or they rely on the opinion of the others (social learners). For the latter, social experiments have suggested that the mathematical form of the probability of adopting an option, called the conformity function, is symmetric in the adoption rate. However, the literature on decision-making includes models where social learners employ either symmetric or nonsymmetric conformity functions. We generalize a particular case studied in a previous work, and we show analytically that if the conformity function is symmetric, the details of the probability distribution of the propensity of the agents to behave as a social or an individual learner do not matter, only its expected value influences the determination of the steady state. We also show that in this case, the same steady state is reached for two extreme dynamical processes: one that considers propensities as idiosyncratic properties of the agents (each agent being an individual learner always with the same probability), and the opposite one, which allows them to change their propensity during the dynamics. This is not the case if the conformity function is nonsymmetric. This fact can inspire experiments that could shed light on the debate about mathematical properties of conformity functions.

physics.soc-ph↗

arXiv2022

Pair approximation for the q-voter models with quenched disorder on networks

Using two models of opinion dynamics, the $q$-voter model with independence and the $q$-voter model with anticonformity, we discuss how the change of disorder from annealed to quenched affects phase transitions on networks. To derive phase diagrams on networks, we develop the pair approximation for the quenched versions of the models. This formalism can be also applied to other quenched dynamics of similar kind. The results indicate that such a change of disorder eliminates all discontinuous phase transitions and broadens ordered phases. We show that although the annealed and quenched types of disorder lead to the same result in the $q$-voter model with anticonformity at the mean-field level, they do lead to distinct phase diagrams on networks. These phase diagrams shift towards each other as the average node degree of a network increases, and eventually, they coincide in the mean-field limit. In contrast, for the $q$-voter model with independence, the phase diagrams move towards the same direction regardless of the disorder type, and they do not coincide even in the mean-field limit. To validate our results, we carry out Monte Carlo simulations on random regular graphs and Barabási-Albert networks. Although the pair approximation may incorrectly predict the type of phase transitions for the annealed models, we have not observed such errors for their quenched counterparts.

physics.soc-ph↗

arXiv2022

Electricity Price Forecasting: The Dawn of Machine Learning

Electricity price forecasting (EPF) is a branch of forecasting on the interface of electrical engineering, statistics, computer science, and finance, which focuses on predicting prices in wholesale electricity markets for a whole spectrum of horizons. These range from a few minutes (real-time/intraday auctions and continuous trading), through days (day-ahead auctions), to weeks, months or even years (exchange and over-the-counter traded futures and forward contracts). Over the last 25 years, various methods and computational tools have been applied to intraday and day-ahead EPF. Until the early 2010s, the field was dominated by relatively small linear regression models and (artificial) neural networks, typically with no more than two dozen inputs. As time passed, more data and more computational power became available. The models grew larger to the extent where expert knowledge was no longer enough to manage the complex structures. This, in turn, led to the introduction of machine learning (ML) techniques in this rapidly developing and fascinating area. Here, we provide an overview of the main trends and EPF models as of 2022.

q-fin.ST↗

arXiv2020

Spontaneous symmetry breaking of active phase in coevolving nonlinear voter model

We study an adaptive network model driven by a nonlinear voter dynamics. Each node in the network represents a voter and can be in one of two states that correspond to different opinions shared by the voters. A voter disagreeing with its neighbor's opinion may either adopt it or rewire its link to another randomly chosen voter with any opinion. The system is studied by means of the pair approximation in which a distinction between the average degrees of nodes in different states is made. This approach allows us to identify two dynamically active phases, a symmetric and an asymmetric one. The asymmetric active phase, in contrast to the symmetric, is characterized by different numbers of nodes in the opposite states that coexist in the network. The pair approximation predicts the possibility of spontaneous symmetry breaking, which leads to a continuous phase transition between the symmetric and the asymmetric active phases. In this case, the absorbing transition occurs between the asymmetric active and the absorbing phases after the spontaneous symmetry breaking. Discontinuous phase transitions and hysteresis loops between both active phases are also possible. Interestingly, the asymmetric active phase is not displayed by the model where the rewiring occurs only to voters sharing the same opinion, studied by other authors. Our results are backed up by Monte Carlo simulations.

physics.soc-ph↗

arXiv2020

Competing local and global interactions in social dynamics: how important is the friendship network?

Motivated by the empirical study that identifies a correlation between particular social responses and different interaction ranges, we study the $q$-voter model with various combinations of local and global sources of conformity and anticonformity. The models are investigated by means of the pair approximation and Monte Carlo simulations on Watts-Strogatz and Barabási-Albert networks. We show that within the model with local conformity and global anticonformity, the agreement in the system is the most difficult to achieve, and the role of the network structure is the most significant. Interestingly, the model with swapped interaction ranges, namely with global conformity and local anticonformity, becomes almost insensitive to the changes in the network structure. The obtained results may have far reaching consequences for marketing strategies conducted via social media channels.

physics.soc-ph↗

arXiv2020

Nonlinear $q$-voter model from the quenched perspective

We compare two versions of the nonlinear $q$-voter model: the original one, with annealed randomness, and the modified one, with quenched randomness. In the original model, each voter changes its opinion with a certain probability $ε$ if the group of influence is not unanimous. In contrast, the modified version introduces two types of voters that act in a deterministic way in case of disagreement in the influence group: the fraction $ε$ of voters always change their current opinion, whereas the rest of them always maintain it. Although both concepts of randomness lead to the same average number of opinion changes in the system on the microscopic level, they cause qualitatively distinct results on the macroscopic level. We focus on the mean-field description of these models. Our approach relies on the stability analysis by the linearization technique developed within dynamical system theory. This approach allows us to derive complete, exact phase diagrams for both models. The results obtained in this paper indicate that quenched randomness promotes continuous phase transitions to a greater extent, whereas annealed randomness favors discontinuous ones. The quenched model also creates combinations of continuous and discontinuous phase transitions unobserved in the annealed model, in which the up-down symmetry may be spontaneously broken inside or outside the hysteresis loop. The analytical results are confirmed by Monte Carlo simulations carried out on a complete graph.

physics.soc-ph↗

arXiv2019

Statistical Physics Of Opinion Formation: is it a SPOOF?

We present a short review based on the nonlinear $q$-voter model about problems and methods raised within statistical physics of opinion formation (SPOOF). We describe relations between models of opinion formation, developed by physicists, and theoretical models of social response, known in social psychology. We draw attention to issues that are interesting for social psychologists and physicists. We show examples of studies directly inspired by social psychology like: "independence vs. anticonformity" or "personality vs. situation". We summarize the results that have been already obtained and point out what else can be done, also with respect to other models in SPOOF. Finally, we demonstrate several analytical methods useful in SPOOF, such as the concept of effective force and potential, Landau's approach to phase transitions, or mean-field and pair approximations.

physics.soc-ph↗

arXiv2018

Think then act or act then think?

We introduce a new agent-based model of opinion dynamics in which binary opinions (yes/no) of each agent can be measured and described regarding both pre- and post-influence at both of two levels, public and private, vis-à-vis the influence source. The model combines ideas introduced within the $q$-voter model with noise, proposed by physicists, with the descriptive, four-dimensional model of social response, formulated by social psychologists. We investigate two versions of the same model that differ only by the updating order: an opinion on the public level is updated before an opinion on the private level or vice versa. We show how the results on the macroscopic scale depend on this order. The main finding of this paper is that both models produce the same outcome if one looks only at such a macroscopic variable as the total number of the individuals with positive opinions. However, if also the level of internal harmony (viz., dissonance) is measured, then significant, qualitative differences are seen between these two versions of the model. All results were obtained simultaneously within Monte Carlo simulations and analytical calculations. We discuss the importance of our studies and findings from three points of view: the theory of phase transitions, agent-based modeling of social systems, and social psychology.

physics.soc-ph↗

arXiv2018

Impact of memory on opinion dynamics

We investigate an agent-based model of opinion dynamics with two types of social response: conformity and independence. Conformity is introduced to the model analogously as in the Sznajd model or $q$-voter model, which means that only unanimous group exerts peer pressure on individuals. The novelty, in relation to previous versions of the $q$-voter model, is memory possessed by each agent and external noise $T$, which plays the role of social temperature. Each agent has its own memories of past experiences related to the social costs and benefits of being independent or conformist. If an agent was awarded in past more for being independent, it will have a greater tendency to be independent than conformist and vice versa. We will show that depending on the social temperature $T$ the system spontaneously organizes into one of two regimes. Below a certain critical social temperature $T_c$, all agents in the society acquire personal traits (so called person state). Some of them become permanent conformists and others start to behave forever independently. This means that initially homogeneous population becomes heterogeneous, and agents respond differently to social influence. For $T>T_c$, all agents with equal probabilities behave independently or conform to peer pressure (so called situation state). This regime change between person and situation state, which reminds the idea of an annealed vs. quenched disorder, affects also public opinion. Particularly interesting results are obtained for individualistic societies, in which public opinion is non-monotonic function of $T$, which means that there is an optimal social temperature for which an agreement in the society is the highest.

physics.soc-ph↗

arXiv2018

Pair approximation for the q-voter model with independence on complex networks

We investigate the q-voter model with stochastic noise arising from independence on complex networks. Using the pair approximation, we provide a comprehensive, mathematical description of its behavior and derive a formula for the critical point. The analytical results are validated by carrying out Monte Carlo experiments. The pair approximation prediction exhibits substantial agreement with simulations, especially for networks with weak clustering and large average degree. Nonetheless, for the average degree close to q, some discrepancies originate. It is the first time we are aware of that the presented approach has been applied to the nonlinear voter dynamics with noise. Up till now, the analytical results have been obtained only for a complete graph. We show that in the limiting case the prediction of pair approximation coincides with the known solution on a fully connected network.

physics.soc-ph↗

arXiv2017

Kinetic Ising models with various single-spin flip dynamics on quenched and annealed random regular graphs

We investigate a kinetic Ising model with several single-spin flip dynamics (including Metropolis and heat-bath) on quenched and annealed random regular graphs. As expected, on the quenched structures all proposed algorithms reproduce the same results since the conditions for the detailed balance and the Boltzmann distribution in an equilibrium are satisfied. However, on the annealed graphs situation is far less clear -- the network annealing disturbs the equilibrium moving the system away from it. Consequently, distinct dynamics lead to different steady states. We show that some algorithms are more resistant to the annealed disorder, which causes only small quantitative changes in the model behavior. On the other hand, there are dynamics for which the influence of annealing on the system is significant, and qualitative changes arise like switching the type of phase transition from continuous to discontinuous one. We try to identify features of the proposed dynamics which are responsible for the above phenomenon.

cond-mat.stat-mech↗

arXiv2015

Mapping the $q$-voter model: From a single chain to complex networks

We propose and compare six different ways of mapping the modified $q$-voter model to complex networks. Considering square lattices, Barabási-Albert, Watts-Strogatz and real Twitter networks, we ask the question if always a particular choice of the group of influence of a fixed size $q$ leads to different behavior at the macroscopic level. Using Monte Carlo simulations we show that the answer depends on the relative average path length of the network and for real-life topologies the differences between the considered mappings may be negligible.

physics.soc-ph↗