By Peter Steiglechner1, Marijn Keijzer2
1 Complexity Science Hub, Austria; steiglechner@csh.ac.at
2 Institute for Advanced Study in Toulouse, France
Abstract
‘Noisy’ behavior, belief updating, or decision-making is universally observed, yet typically treated superficially or not even accounted for at all by social simulation modelers. Here, we show how noise can affect model dynamics and outcomes, argue why injecting noise should become a central part of model analyses, and how it can help our understanding of (our mathematical models for) social behavior. We formulate some general lessons from the literature around noise, and illustrate how considering a more complete taxonomy of different types of noise may lead to novel insights.
‘Flooding the zone’ with noise
In his inaugural address in January 2025, US president Trump announced that he would “tariff and tax foreign countries to enrich [US] citizens”. Since then, Trump has flooded the world news with a back-and-forth of threatening, announcing, and introducing tariffs, only to pause, halt, or even revoke them within a matter of days. Trump’s statements on tariffs are just one (albeit rather extreme) example of how noisy and ambiguous political signaling can be. Ambiguity in politics can be strategic (Page, 1976), but it can also simply result from a failure to accurately describe one’s position. Most of us are probably familiar with examples of noise in our own personal lives as well—we may wholeheartedly support one thing, and take a skeptical stance in the next discussion. People have always been inherently noisy (Vul & Pashler, 2008; Kahneman, Sibony, & Sunstein, 2021). But the pervasiveness of noise has become particularly evident in recent years, as social media have made it easier to frequently signal our political opinions (e.g. through like-buttons) and to track the noisy or inconsistent behaviors of others.
Noise can flip model dynamics
As quantitative scientists, most of us are not aware of how important noise can be. Conventional statistical models used in the social sciences typically assume noise away. This is because unexplained variance in simple regression models—if not too abnormally distributed—should not affect the validity of the results; so why should we care? Social simulation models play by different rules. With strictly operating behavioral rules on the micro-level and strong interdependence, noise on the individual level plays a pivotal role in shaping collective outcomes. The importance of noise contrasts with the fact that many models still assume that individual-level properties and actions are fully deterministic, consistent, accurate, and certain.
For example, opinion dynamics models like the Bounded Confidence model (Deffuant et al., 2000; Hegselmann & Krause, 2002) and the Dissemination of Culture model (Axelrod, 1997), both illustrate how global diversity (or ‘polarization’) emerges because of local homogeneity (or ‘consensus’). But this core principle is highly dependent on the absence of noise! The persistence of different cultural areas completely collapses under even the smallest probability of differentiation (Klemm et al., 2003; Flache & Macy, 2011), and fragmentation and polarization become unlikely when agents sometimes independently change their opinions (Pineda, Toral, & Hernández-García, 2011). Similarly, adding noise to the topology of connections can drastically change the dynamics of diffusion and contagion (Centola & Macy, 2007). In computational, agent-based models of social systems, noise does not necessarily cancel out. Many social processes are complex, path-dependent, computationally irreducible and highly non-linear. As such, noise can trigger cascades of ‘errors’ that lead to statistically and qualitatively different behaviors (Macy & Tsvetkova, 2015).
What is noise? What is it not?
There is no one way to introduce noise, or to dedicate and define a source of noise. Noise comes in different shapes and forms. When introducing noise into a model of social phenomena, there are some important lessons to consider:
- Noise is not just unpredictable randomness. Instead, noise often represents uncertainty (Macy & Tsvetkova, 2015), which can mean a lack of precision in measurements, ambiguity, or inconsistency. Heteroskedasticity—or the fact that the variance of noise depends on the context—is more than a nuisance in statistical estimation. In ABM research in particular, the variance of uncertainty can be a source of nonlinearity. As such, introducing noise into a model should not be equated merely with ‘running the simulations with different random seeds’ or ‘drawing agent attributes from a normal distribution’.
- Noise enters social systems in many ways and in every aspect of the system. This includes noisy observations of others or the environment (Gigerenzer & Brighton, 2009), noisy transmission of signals (McMahan & Evans, 2018), noisy application of heuristics (Mäs & Nax, 2016), noisy interaction patterns (Lloyd-Smith et al., 2005), heterogeneity across societies and across individuals (Kahneman, Sunstein, & Sibony, 2021), and inconsistencies over time (Vul & Pashler, 2008). This is crucial because noise representing different forms and different sources of uncertainty or randomness can affect social phenomena such as social influence, consensus, and polarization in quite distinct ways (as we will outline in the next section).
- Noise can be adaptive and heterogeneous across individuals. Noise is not a passive property of a system, but can be a context-dependent, dynamically adapted strategy (Frankenhuis, Panchanathan, & Smaldino, 2022). For example, some individuals tend to be more covert and less precise than others for instance when they perceive themselves to be in a minority (Smaldino & Turner, 2022). Some situations require individuals to be more noisy or unpredictable, like when taking a penalty in soccer, other situations less so, such as writing an online dating ad. People need to decide and adapt the degree of noise in their social signals. Smaldino et al. (2023) highlighted that all strategies that lead collectives to perform well in solving complex tasks depend in some way on maintaining (but also adapting to) a certain level of transient noise.
- Noise is itself a signal. There are famous examples of institutions or individuals using noise signaling to spread doubt and uncertainty in debates about climate change or the health effects of smoking (see ‘Merchants of Doubt’ by Oreskes & Conway, 2010). Such actors signal noise to diffuse and discredit valuable information. One could certainly argue that Trump’s noisy stance on tariffs also falls into this category.
In short, noise represents meaningful, multi-faceted, adaptive, and strategic aspects of a system. In social systems—which are, by definition, systems of interdependence—noise is essential to understanding that system. As Macy & Tsvetkova put it: ‘strip away the noise and you may strip away the explanation’ (2015).
A taxonomy of noise in opinion dynamics
In our paper ‘Noise and opinion dynamics’ published last year in Royal Society of Open Science, we reviewed and examined if and how different sources of noise affect the results in a model of opinion dynamics (Steiglechner et al., 2024). The model builds on the bounded confidence model by Deffuant et al. (2000), calibrated on a survey measuring environmental attitudes. We identified at least four different types of noise in a system of opinion formation through dyadic social influence: exogenous noise, selectivity noise, adaptation noise and ambiguity noise.
Figure 1. Sources of noise in social influence models for opinion dynamics (adapted from Steiglechner et al., 2024)
Each type of noise in our taxonomy enters at a different stage of the interaction process (as shown in Figure 1). Ambiguity and adaptation noise both depend on the current attitudes of the sender and the receiver, respectively, whereas selectivity noise acts on the connections between individuals. Exogenous noise is a ‘catch-all’ category of noise added to the agent’s attributes regardless of the (success of) interaction. Some of these types of noise may have similar effects on population-level opinion dynamics in the thermodynamic limit (Nugent , Gomes, & Wolfram; 2024). But they can lead to quite different trajectories and conclusions about the noise effect when we look at real cases of finite-size and finite-time simulations.
Previous work had established that even small amounts of noise can affect the tendency of the bounded confidence model to produce complete consensus or multiple fragmented, internally coherent groups, but our results highlight that different types of noise can have quite distinct signatures. For example, while selectivity noise always increases the coherence of groups, only intermediate levels of exogenous noise unite individuals. Moreover, exogenous noise leads to convergence because it destroys the internal coherence within the fragmented groups, whereas selectivity noise leads to convergence because it connects polarized individuals across these groups. Ambiguity noise has yet another signature. For example, while low levels of ambiguity have no effect on fragmentation (similar to exogenous and adaptation noise), intermediate and even high levels of ambiguity can produce a somewhat coherent majority-group (similar to selectivity noise). More importantly, ambiguity noise also produces drift: a gradual shift in the average opinion toward a more extreme position (Steiglechner et al., 2024). This is a remarkable result, because not only does ambiguous messaging alter the robustness of the clean, noiseless model, it actually produces a novel type of extremization using only positive influence!
Make some noise!
The above taxonomy is, of course, only a starting point for further discussion: It is not comprehensive and does not take into account adaptiveness or strategy. However, already this variety of effects of the different types of noise on consensus, polarization, and social influence should make us more aware of noise in general—not just as an ‘afterthought’ or a robustness check, but as a modeling choice that represents a critical component of the model. Many modeling studies do consider how noise can affect the model outputs, but it matters—a lot—where and how they introduce noise (see also De Sanctis & Galla, 2009).
Noise is an essential aspect of human behavior, social systems, and politics, as Trump’s back-and-forth on tariffs illustrates quite effectively these days. When studying social phenomena such as opinion formation and polarization, we should take the effects of noise as seriously as the effects of behavioral biases or heuristics (Kahneman, Sunstein, & Sibony, 2021). That is, while we social systems modelers tend to spend a lot of time to formulate, justify, and analyze behavioral rules of individuals—generally considered the core of the model—, we should devote more time to formalize what kind of noise enters the modeled system where and how and analyze how this affects the dynamics (as also argued in the exchange of letters between Kahneman et al. and Krakauer & Wolpert, 2022). Noise is a meaningful, multi-faceted, adaptive, and strategic component of social systems. Rather than ‘just a robustness check’, it is a fundamental ingredient of the modeled system—a type of behavior in itself—and, thus, an object of study on its own. This is a call to all modelers (in the house) to make some noise!
Acknowledgments
We thank Victor Møller Poulsen and Paul E. Smaldino for their feedback.
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Review of Artificial Societies and Social Simulation 