Session G31: Physics Approaches for Modeling Human Social Systems

Nonlinear dynamics of belief formation over social networks

In the presented work, we investigate how social effects shape belief formation and social decisions using a new agent-based nonlinear model of belief formation dynamics. We motivate, analyze, and apply this model to gain new insights about the dynamics of social systems. 

Following the seminal work of DeGroot, mathematical models of belief dynamics have been a popular tool central to interdisciplinary investigations of collective behavior. These models assign real-valued opinions or beliefs to agents in a social network and describe how they are updated in time in response to interactions with neighboring agents. An individual's belief state may reflect, for example, the value assigned to an option under evaluation, strength of preference towards a candidate in an election, or alignment with a political topic.

Existing models often have strong limitations, mainly focusing on scalar beliefs and linear dynamics. Our model, however, integrates recent insights from social psychology to account for multiple interdependent belief states that evolve simultaneously, seeking to overcome various internal and external sources of cognitive dissonance. The model captures complex interactions of beliefs between individuals in a social network, as well as within individuals’ cognition.

We illustrate rigorously that our model captures key features of complex social systems, such as multistability of belief states and critical state transitions. Furthermore, we analyze how groups overcome deadlock to form strong beliefs, how the structure of social relationships and of the underlying belief system shape social decisions, and how the group’s decision can be strongly swayed by the biases of a small number of influential individuals.   

Dynamic Risk and Decision Making in Markov Models of Wildfire

Birth and death Markov processes can model stochastic physical systems including disease spread, human population growth and immigration, queueing, thermodynamic diffusion, mathematical biology, and wildfires. We introduce and analyze a birth-death-suppression Markov process as a model of controlled culling of an abstract dynamic population. Using analytic techniques, we characterize the probabilities and timescales of outcomes like absorption at zero (extinguishment) and the probability of the cumulative population (burned area) reaching a given size. The latter requires control over the embedded Markov chain: this discrete process is solved using the Pollazcek orthogonal polynomials, a deformation of the Gegenbauer/ultraspherical polynomials. This allows analysis of processes with bounded cumulative population, corresponding to finite burnable substrate in the wildfire interpretation, with probabilities represented as spectral integrals. This technology is developed in order to lay the foundations for a dynamic decision support framework. We devise real-time risk metrics and suggest future directions for determining optimal suppression strategies, including multi-event resource allocation problems and potential applications for reinforcement learning.   

Cognitive biases can move opinion dynamics from consensus to chaos

Research in the area of how networks of people form consensus opinions has exploded recently, with statistical physics approaches and contributions from economists both suggesting that there is convergence to a fixed point in belief networks. We straightforwardly generalize the model used by economists to describe Bayesian updating so that the likelihood of a piece of data depends on ground truth and, potentially, the alignment of the receiver's beliefs with the sender's beliefs and the data point itself. Confirmation bias occurs when the data point is considered more likely when it aligns with the receiver's beliefs; a version of in-group bias occurs when the receiver further considers the data point to be more likely when the receiver's beliefs and the sender's beliefs are aligned. When the likelihood of the data point only depends on ground truth, so that receivers exhibit no confirmation bias or in-group bias, the network of people always converges to complete consensus. With confirmation bias, there can be polarization in the final state. When in-group bias is added, consensus and polarization are still possible; but when agents do their best to counteract confirmation bias, so is chaos. This is the first work to suggest that chaos might be a feature of opinion dynamics when cognitive biases, or attempts to counteract cognitive biases, are taken into account.   

Dynamics of Innovation: From Particles to Ideas

Innovation dynamics is a widespread phenomenon found across various seemingly unrelated domains, including viral evolution, corporate market share, social networks, and the propagation of ideas. In this study, we propose that innovation processes share analogous characteristics, all regulated by a common mechanism related to the creation and annihilation of particles through collisions.

Our model portrays individuals engaging with and disengaging from innovation trends through a diffusive process encapsulated by a time-dependent Markov chain. 

By calculating the expected number of participants in an innovation trend, we formulate a function that captures the temporal evolution of these trends, transcending specific contextual nuances.

We validate our results using a Recurrent Neural Network (RNN). To achieve this, we introduce a novel training approach that fits ordinary differential equations (ODE) with a loss function that considers both data and its derivative. The RNN fitting process yields confidence values around 90% that substantiate the suitability of our proposed model for describing innovation trends.

Our model also exhibits predictive capabilities, enabling the anticipation of future tendencies with limited observations, particularly beneficial in contexts necessitating trend management. Additionally, our observations reveal that deviations from the model's analytical solution can be attributed to unforeseeable external 

factors influencing innovation dynamics.   

Is groundbreaking research controversial during peer review?

Groundbreaking research is disruptive. Novel, trailblazing papers can have a hard time during traditional peer review by being misjudged by editors and/or referees who may be too conservative or entrenched to appreciate their transformative potential. In these situations, negative opinions from experts can impede innovative research, delay scientific progress, and derail promising careers in science. We explore this effect by combining data analytics from anonymized referee databases with case studies of classic papers. We discuss whether referee discord during peer review can be used as a flag for potentially transformative papers.   

Understanding the scaling of social organizations using Reddit

When individuals form social organizations around shared interests or common goals, they can generate new ideas and accomplish complex tasks. To understand why some organizations are more successful than others at attracting supporters and reaching their goals, we need a model of organizations that can be experimentally validated. We identify Reddit's r/place experiment as a model system in which we can study organizations and their ability to achieve a collective goal. In this unique experiment, different groups on Reddit compete to craft pixel art on a size-limited canvas of pixels, which allows us to observe the behavior of communities and their individuals as they compete for space on the canvas. Using the pixel and user data, we examine scaling laws that relate the community size to variables that describe their art and user dynamics. We find categories of variables that scale sub-linearly, linearly, and super-linearly with the size of the group. These results suggest the presence of underlying interaction networks that drive the formation and behavior of organizations, similar to the role of networks in biological systems and cities, where various scaling laws are also observed. We aim to understand how the structural properties of these networks relate to the behavior of the organizations, which could enable us to develop a mechanistic model for the formation and efficiency of social organizations.   

Learning about early warning signals and the structure of collaborations with a large-scale experiment on Reddit

For three days in April 2022, 10 million Reddit users placed colored pixels on a giant canvas, at a maximum per-user rate of one pixel every five minutes. This game-experiment "r/place" is a great window into human collective behavior, as users needed to collaborate to build significant "compositions" (i.e. discernible drawings). We studied the transitions in these compositions (i.e. their replacement by another drawing), which could provide general insights on transitions in socio-ecological systems. To build a warning system for these transitions, we use gradient-boosted decision trees to combine multiple time-dependent variables in each composition. The resulting early warning signals predict half of the transitions coming within 20 minutes (6 hours) with only 0.5% (14%) false positives, which improves highly on considering a single time series and on more standard signals such as variance and autocorrelation of a state variable. The 2023 edition of r/place serves as an ultimate test that the warning system is efficient even considering inter-year variability. This massive experiment teaches us new ways to foresee transitions is socio-ecological systems, while shedding light on the optimal structures of collaborations, as we can correlate the type of network of users of a composition to its resilience.   

Humans efficiently predict in a sequence learning task

Much of human behavior is driven by prediction of sequences, as this allows one to navigate complex environments. Large language models such as ChatGPT are in fact built on prediction of symbols in sequences. But how well and how human participants efficiently predict non-naturalistic sequences. We use three highly artificial stimuli to answer these questions. We find that participants are near-optimal efficient predictors of sequences in an information-theoretic sense and that their strategy appears to be a Bayesian approach to order-R Markov modeling. Some participants appear to predict like Long Short-Term Memory Units (LSTMs), state-of-the-art recurrent neural networks, and indeed, LSTMs have been previously used to model human behavior. This study confirms the previously theoretical notion that humans are efficient predictors of artificial input and proposes a typical mechanism by which humans model and predict the world.   

Physicalization of Social Experiments: Harnessing Large Language Models for Automated Exploration of Emergent Behaviors in Simulated Social Systems

Two significant impediments to success of the social sciences in comparison to physics are the inherent difficulty in both rapidly executing multiple controlled experiments to explore a parameter space and determining what parameter space to explore. In this work, we present a computational framework and platform that simulates the entire social scientific process, leveraging Large Language Models (LLMs) to study human actors within social systems. We create controlled environments, akin to toy models in physics, that systematically explore the space parameter of variables relevant to any social system (such as attributes of human actors), allowing for the exponentially faster discovery of emergent social behaviors as compared to traditional social science experimentation. Central to our approach is the automatic generation of Structural Causal Models (SCMs) that generate statistical correlations of potential interactions within a social system and outline the requisite metrics and tools to observe and measure these nonlinear dynamics. With the flexibility to vary controlled variables across a nearly infinite parameter space, our system offers a sandbox to simulate and analyze various social scenarios – from wage bargaining and auction mechanics to nuclear weapon negotiations. Our framework and platform offers a new playground for physicists to study the nonlinear dynamics and emergent phenomena in human social systems.   

The impact of bias on the accuracy of early and late deciders in groups

How does a decision made quickly differ from a more deliberate one? In this talk, we answer this question for a large heterogeneous population of independent agents and show how initial bias influences the accuracy of early and late deciders. In particular, we consider a population of agents who stochastically accumulative evidence until crossing a threshold, triggering a decision. Remarkably, we are able to determine the exact order statistics of this passage process in the asymptotic limit of not merely the first and last decider but of all early and late deciders. In the extreme decider case, we find that the first agent to decide almost always holds the strongest initial bias and decides accordingly. Slow agents, conversely, decide as if they held no initial bias. Hence, we conclude that in large groups an early decision reflects the initial bias of an agent, while a late decision is made as if the agent had no initial bias at all.   

Musical rhythm and meter as an ordered phase of sound

Rhythm and meter appear in the music of virtually all human societies. The temporal patterns of events associated with rhythm and meter can be viewed as a reduced symmetry state as compared to non-musical sound. Motivated by this, we apply methods from statistical mechanics to explore how musical rhythm and meter can emerge from fundamental assumptions about human psychology. Following a similar approach to our previous work on musical harmony [1], we posit that the temporal ordering of events in music is governed by two conflicting factors: (1) a desire to perceive repeating patterns, and (2) a desire for novelty and variation. We map these factors to the (negative of) internal energy and entropy of a system, respectively, where the balance between them is set by the temperature, via a free energy. As a function of temperature, as well as a chemical potential that governs the average concentration of events in time, we observe phase transitions occurring between disordered, Poissonian events, and ordered patterns of events that closely reproduce familiar musical meter. As an initial demonstration, we use our model to predict the distribution of note lengths as a function of temperature and chemical potential, and find good agreement with the range of distributions found in the 36 movements of J. S. Bach’s Suites for Solo Cello.

[1] Berezovsky, J., 2019. The structure of musical harmony as an ordered phase of sound: A statistical mechanics approach to music theory. Science advances, 5(5), p.eaav8490.   

Extreme outbreak statistics in stochastic populations: large and small fluctuations

Population dynamics share certain general nonlinear dynamical properties and topology which can be found in human driven disease epidemics, population inversions in lasers, as well as chemical kinetics. In all cases, due to the interactions between individuals, the presence of noise and the underlying nonlinear dynamical topology, there exists the potential for large fluctuations. Here we consider the general problem of calculating the dynamics and likelihood of extensive large transient fluctuations in general stochastic populations for a large class of population models, including outbreaks in the susceptible-infected-recovered (SIR) model and intensity fluctuations in class B lasers. In the limit of large populations, we compute the probability distribution for all extensive outbreaks including those that entail unusually large or small proportions compared to the mean of a population, given both internal and parameter noise. Our approach reveals that, unlike other well-known examples of large fluctuations occurring in stochastic systems, the statistics of extreme outbreaks emanate from a full continuum of optimal paths satisfying unique boundary conditions. Moreover, we find that both the variance and the probabilities for extreme outbreaks depend sensitively on the source of noise.