Hidden Forces: How Unseen Attention Shapes Social Influence

When a social media user scrolls through their feed, they’re not equally swayed by every post they see. In fact, they’re likely influenced by almost none of them. Yet most models of social influence—used to predict everything from political polarization to market trends—assume that people absorb and react to all the opinions around them. This assumption, while mathematically convenient, is fundamentally wrong. A new study reveals that when we account for two hidden psychological mechanisms—who people pay attention to, and whether they let that exposure change their mind—the strength and shape of social influence shift dramatically. On 14 out of 15 real-world datasets, models that include these latent attention mechanisms predict future opinions far more accurately. And in more than half the cases, they flip the scientific verdict: what once looked like simple, linear conformity now appears as complex, nonlinear social dynamics. The implication? We’ve been underestimating the subtlety of human influence because we’ve been blind to the filters in our minds.

The Science

The paper, Learning Social Influence with Unobserved Attention (Thompson et al., 2026), introduces a probabilistic agent-based model (PGABM) that explicitly accounts for two unobserved attention mechanisms: selection and retention. Selection refers to the fact that individuals typically engage with only one source of influence at a time—even if they’re surrounded by many. On a social network, this means a user might see dozens of posts but only truly “hear” one. Retention captures the common psychological phenomenon where people are exposed to an opinion but simply don’t change their mind. Studies show that the most frequent response to social influence is no response at all (Chacoma et al., 2021; Muthukrishna et al., 2020). Yet traditional models often interpret such stability as evidence of weak influence, rather than a deliberate cognitive choice.

The model builds on classical opinion dynamics frameworks, where an agent’s opinion update is proportional to the discrepancy between their view and a neighbor’s, scaled by an interaction kernel $k_\phi(|d_e|)$. This kernel defines how influence changes with opinion distance: linear models like DeGroot assume constant responsiveness; bounded confidence models assume people only listen to those close in opinion; and smoothed attraction-repulsion (SAR) models allow for both attraction and repulsion depending on distance.

But Thompson and colleagues go further. They treat both which neighbor is attended to (selection) and whether the agent responds (retention) as latent variables—unobserved but inferable through statistical modeling. The retention mechanism is modeled as a Bernoulli trial with probability $\pi$, the influence rate, representing the chance that an exposure leads to a social response. When no response occurs, the agent’s update follows a baseline drift $\mu_0$, capturing exogenous changes like personal reflection or external news.

Crucially, the model supports efficient maximum-likelihood inference via expectation-maximization (EM), allowing researchers to fit it to real-world opinion traces—even when attention is never directly observed. The authors test their framework on both synthetic data, where the ground truth is known, and 15 empirical datasets ranging from lab experiments to online social behavior.

What They Found

On synthetic data, omitting either selection or retention leads to severe bias. When the true data-generating process includes retention (say, $\pi = 0.5$), models that ignore it infer a much weaker interaction kernel—roughly half the strength (Figure 3a). Worse, they fail to detect nonlinearity: a clearly nonlinear SAR kernel appears nearly linear when retention is unmodeled (Figure 3b). This happens because the model interprets non-responses as noise or weak influence, diluting the signal of those who do change.

Figure 2: The four parametric interaction kernels tested in the study. Only the smoothed attraction-repulsion (SAR) model allows for repulsion at large opinion distances. Insets show synthetic opinion trajectories on the Les Misérables network.

In real-world data, the story is even more striking. The authors evaluate models with and without latent attention mechanisms using held-out predictive likelihood—a gold standard for model comparison. Across 15 diverse datasets, adding attention mechanisms improves predictive performance in 14 cases. The gain is often larger than switching from a linear to a nonlinear kernel—meaning that how we model attention matters more than what functional form we assume for influence.

One of the most compelling examples comes from the “Village Knowledge” (VK) games, controlled experiments where participants estimate quantities like the number of dots on a screen, then see others’ guesses. Traditional models suggest weak, linear influence. But when retention and selection are added, the inferred influence kernel becomes stronger and more nuanced. The model reveals that participants often ignore others entirely (retention), but when they do respond, they follow a nonlinear pattern—stronger influence at moderate disagreement, less at extremes.

Improvement in Predictive Likelihood from Adding Attention Mechanisms

Label	Value
Baseline	0
+ Selection	0.12
+ Retention	0.18
+ Both	0.23

Source: Thompson et al. (2026). Gains are relative to baseline model with no latent attention mechanisms.

Model	Avg. Held-Out MLL Gain (nats/transition)
Baseline (no attention)	0.00
+ Selection	0.12
+ Retention	0.18
+ Both	0.23
Table: Average improvement in held-out predictive likelihood when adding attention mechanisms across 15 datasets. Gains are measured in nats per transition.

The study also tracks two key properties of the inferred kernels: strength $S$ and curvature $C$. Strength is the root-mean-square gain of influence over observed opinion distances:

$$S={\left(\frac{1}{|d_e{|}_{\max }}{\int }_0^{|d_e{|}_{\max }}(\hat{\lambda }{k}_{\mathbf{\varphi }}(|d_e|){)}^{2}d|d_e|\right)}^{1/2}$$

Curvature measures how much the influence function changes with opinion distance:

$$C={\int }_0^{|d_e{|}_{\max }}\left|\hat{\lambda }{k}_{\mathbf{\varphi }}^{\prime }(|d_e|)\right|d|d_e|$$

A linear kernel has $C=0$. The authors find that adding retention consistently increases $S$—sometimes doubling it—because it stops the model from misattributing non-responses to weak influence. The effect on $C$, however, depends on the dataset. In some cases, curvature increases, revealing hidden nonlinearity; in others, it decreases, suggesting simpler dynamics once noise is properly accounted for.

Figure 5: Empirical updates (gray points) vs. fitted models in VK games. The orange line shows the influence mode; blue shows the retention mode (baseline drift). The dashed gray line is the model without latent mechanisms. Triangles represent updates weighted by posterior probability of influence from each candidate source.

Perhaps most dramatically, the inclusion of attention mechanisms changes the verdict on nonlinearity in 9 out of 15 datasets. In other words, in more than half the cases, models that ignore attention falsely conclude that influence is linear—when, in fact, it’s not.

Why This Changes Things

For decades, social scientists have debated whether influence is linear or nonlinear. Does persuasion work steadily across all opinion distances, or do we only listen to those close to us? Do we avoid or attack those who disagree strongly? These questions shape how we design interventions—from public health campaigns to political messaging.

But this study suggests that the debate may have been misframed. The apparent linearity of influence in many past studies may not reflect human psychology at all. Instead, it may be an artifact of models that fail to account for the fact that people select what they pay attention to and retain their opinions more often than they change them.

Consider a public health campaign on social media. If analysts use a traditional model, they might conclude that exposure to pro-vaccine messages has only a weak, linear effect. They might recommend broader reach—more ads, more influencers. But if the real issue is retention—that most people see the message and simply ignore it—then broader reach won’t help. The solution isn’t more exposure; it’s better engagement. The model by Thompson et al. doesn’t just improve prediction—it reframes the problem.

This has implications far beyond public health. In financial markets, traders are bombarded with signals. A model that assumes they react to all of them will misjudge the true drivers of price movements. In politics, voters are exposed to countless opinions, but only a few cut through. Models that ignore attention will underestimate the power of resonant messages and overestimate the impact of sheer volume.

Even more subtly, the study challenges a deep assumption in network science: that the structure of connections determines influence. But if influence depends on attention, then two people with identical networks may behave very differently—one curates their feed carefully, the other scrolls passively. The real network isn’t the follower graph; it’s the attention graph, which we rarely observe.

The finding that retention alone can double the inferred strength of influence is particularly consequential. It means that past studies may have systematically underestimated how persuasive people can be—because they mistook indifference for resistance. A friend’s opinion might not change your mind today, but that doesn’t mean it’s weak. It might mean you’re not ready to listen.

What’s Next

The model opens several new directions. First, the assumption of uniform selection—choosing a source at random from the neighborhood—is clearly a simplification. In reality, attention is shaped by algorithms, emotions, identity, and cognitive biases. Future work could incorporate more realistic attention rules, such as preferential attachment to strong ties or algorithmic amplification.

Second, the current model treats the influence kernel as shared across all individuals. But people vary: some are persuadable, others stubborn. A next step is to allow for heterogeneity in $\pi$ (influence rate) or $k_\phi$ (kernel shape), perhaps linked to personality or social role.

Third, while the model infers latent attention, it doesn’t predict it. Can we build models that forecast not just opinions, but what people will pay attention to? This would require integrating content, context, and cognitive load—ambitious, but essential for real-world applications.

Finally, the study relies on opinion traces—sequences of numerical estimates or survey responses. But in many settings, opinions are inferred from behavior: clicks, shares, purchases. Extending the framework to such data would broaden its reach.

The biggest challenge may be cultural. For years, researchers have favored simple, interpretable models. The idea that we need to model unobserved cognitive mechanisms may feel like adding epicycles. But as this study shows, those mechanisms aren’t just noise—they’re signal. Ignoring them doesn’t make models more parsimonious; it makes them wrong.

As social life moves further into digital spaces, where attention is the scarcest resource, models that ignore it will become increasingly obsolete. The work of Thompson et al. is a step toward a more realistic, more human science of influence—one that doesn’t assume we’re constantly swayed by everyone around us, but recognizes that when we do listen, the effect can be profound.