Bystander effect emerges from individual psychological prospects

TL;DR

The paper analyzes the bystander effect through two complementary models grounded in prospect theory and social learning. A static, risk-perception-based model shows that the propensity to intervene declines with group size due to social risk, modulated by loss aversion whose distribution across individuals shapes the curve; a dynamic extension demonstrates that social learning can amplify the effect over time, depending on network structure and learning rates. Validation comes from a compiled database of $42$ studies across diverse bystander contexts, indicating the effect is prominent in non-dangerous, ambiguous situations and that heterogeneity in loss aversion and slower social learning are key contributors. The work suggests practical interventions that adjust perceived risks and learning dynamics to mitigate or tailor the bystander effect across different situational contexts.

Abstract

The bystander effect is a social psychological phenomenon in which individuals are less likely to help a person potentially in need if there are others present. Sociologists and psychologists have proposed multiple plausible reasons for the bystander effect, from situational ambiguity and social contagion to diffusion of responsibility and mutual denial. We build a new model of an individual's decision to intervene in a bystander situation based on these social psychological hypotheses, along with ideas borrowed from prospect theory. This model shows, for the first time, that the bystander effect emerges from social risk perception among non-coordinating individuals in ambiguous bystander situations. Expanding upon this static model, we explore the effect of social learning, where individuals update their perceived risk of intervening after experiencing or witnessing the social repercussions of previous interventions. A novel result of this model is that social learning exacerbates the bystander effect. We validate these models using a new database of 42 experimental and observational studies across a wide range of bystander situations, demonstrating a straightforward and generalizable explanation for the observed phenomenon, which may suggest effective interventions tailored to specific bystander situations.

Figures (15)

• Figure 1: Assuming a gamma distribution of loss aversion ratios with $\mu=2$ and $\sigma=0.5$ (top inset) following experimentally determined values arora2015riskblake2021quantifyingkahneman2011thinking, the corresponding distributions of expected values of acting shift left as crowd size $N$ increases (top). For this example, $r=0.12$ is the perceived chance that a particular person will condemn intervention in a bystander situation. The fraction of $f_V$ that falls in the range $v\in(0,\infty)$ represents the proportion of individuals who would intervene ($I$), which decreases as the crowd size grows (bottom).
• Figure 2: Relationship between the fraction of witnesses who will intervene in a bystander situation versus the fraction of victims in a bystander situation that will be helped, shown here with a gamma distribution of loss aversion ratios with $\mu=2$ and $\sigma=0.5$ and with action appropriateness $r=0.15$. The bystander curves retain the same qualitative shape, but are shifted right (for any given number of witnesses, the probability the witness is helped is larger than the probability that any given witness helps).
• Figure 3: Fraction of bystanders who intervene as a function of the number of bystanders $N$. Unless otherwise stated, we assume a gamma distribution of loss aversion ratios with $\mu=2$ and $\sigma=0.5$arora2015riskblake2021quantifyingkahneman2011thinking and action appropriateness $r=0.15$. Holding all else constant, increasing action appropriateness $r$ causes the bystander curve to shift left (top center). Increasing the average loss aversion ratio causes the bystander curve to compress left (bottom left). Increasing the loss aversion standard deviation causes the large-$N$ intervention fraction to increase, while the small-$N$ intervention fraction decreases (bottom right).
• Figure 4: Representative simulation sampling initial risks from $r_i(0) \sim \mathcal{U}(0,0.1)$ with $N=5$ and only learning from one's own actions: $a=1, b=0.01, c=d=0$ (left). Contributions to social learning from one's own poorly-received actions (top right) and one's own well-received actions (bottom right), as measured by the probability of those outcomes occurring. We see that learning is piecewise in time, with learning only occurring while the individual is taking action. For instance, 'yellow' begins with a high risk and never learns because they never act, while 'green' begins with a low risk and learns from a gradually increasing probability of condemnation until they finally stop acting.
• Figure 5: Representative simulation sampling initial risks from $r_i(0) \sim \mathcal{U}(0,0.1)$ with $N=5$ and learning from reactions to self and others' actions: $a=1, b=0.01, c=0.1, d=0.001$ (left), based on evidence that learning from experience is faster than learning from observation moraes2025unravellingriley2017activeblanie2018impactperuch2004active and learning from negative outcomes is faster than learning from positive outcomes yin2023differentialwachter2009differentialsidowski1956influencegregory2007effectsjones2021increased. Contributions to social learning from one's own poorly-received actions (top middle), one's own well-received actions (bottom middle), others' poorly-received actions (top right), others' well-received actions (bottom right), as measured by the probability of those outcomes occurring. When individuals also learn from others' actions, we see that witnesses switch from learning exclusively from their own actions to learning from others' actions. For instance, 'blue' begins by learning from their own actions until their learned risk reaches a threshold when they stop acting; after that time, 'blue' continues to learn increased risk by watching others get condemned for acting.